an integrated optimization-simulation framework …...an integrated optimization-simulation...

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An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations Burak Boyacı a,* , Konstantinos G. Zografos a , Nikolas Geroliminis b a Centre for Transport and Logistics (CENTRAL), Lancaster University Management School, Lancaster, LA1 4YX, UK b Urban Transport Systems Laboratory (LUTS), Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), Switzerland Abstract One-way electric vehicle carsharing systems are receiving increasing attention due to their mobility, environmental, and societal benefits. One of the major issues faced by the operators of these systems is the optimization of the relocation operations of person- nel and vehicles. These relocation operations are essential in order to ensure that vehicles are available for use at the right place at the right time. Vehicle availability is a key indicator expressing the level of service oered to customers. However, the relocation operations, that ensure this availability, constitute a major cost component for the provision of these services. Therefore, clearly there is a trade-obetween the cost of vehicle and personnel relocation and the level of service oered. In this paper we are de- veloping, solving, and applying, in a real world context, an integrated multi-objective mixed integer linear programming (MMILP) optimization and discrete event simulation framework to optimize operational decisions for vehicle and personnel relocation in a carsharing system with reservations. We are using a clustering procedure to cope with the dimensionality of the operational problem without compromising on the quality of the obtained results. The optimization framework involves three mathematical models: (i) station clustering, (ii) operations optimization and (iii) personnel flow. The output of the optimization is used by the simulation in order to test the feasibility of the optimization outcome in terms of vehicle recharging requirements. The optimization model is solved iteratively considering the new constraints restricting the vehicles that require further charging to stay in the station until the results of the simulation are feasible in terms of electric vehicles’ battery charging levels. The application of the proposed framework using data from a real world system operating in Nice, France sheds light to trade-os existing between the level of service oered, resource utilization, and certainty of fulfilling a trip reservation. Keywords: one-way carsharing, vehicle relocation optimization, integer programming, network flow 1. Introduction The emergence of carsharing as a new transportation mean between public and private transport is quite recent. People benefiting from this service have to register and then can use vehicles located within a designated service area. Carsharing is an approach to increase vehicle utilization while decreasing the cost encountered to each user. Expenses associated to car ownership are nowadays quite high linked to purchase, gaso- line, insurance, parking and maintenance. Avoiding these ex- penses may be a motivation for a driver to adopt carsharing as a regular transportation mean if the system is able to provide high quality of service (accessibility and availability of vehi- cles both at origin and destination of his/her trip at reasonable cost). In addition to users’ benefits, carsharing systems are pro- ducing broader societal and environmental benefits such as re- duction of congestion, air pollution, and the urban space needed for parking. Carsharing systems can be classified in dierent categories according to the rental conditions. Free-floating systems al- * Corresponding author Email addresses: [email protected] (Burak Boyacı), [email protected] (Konstantinos G. Zografos), [email protected] (Nikolas Geroliminis) low people to park the vehicles anywhere in the covered area, whereas non-floating impose restrictions to users to park the ve- hicles at stations with limited number of parking spots. Another dierentiating feature is the “one-way/round-trip” characteris- tic: Round-trip systems force the user to return the car to the location where it was picked-up whereas one-way systems al- low drop-oat any station. The type of vehicle (combustion, electric, etc.) aects also the system’s use. Rental operations naturally induce imbalances in the spa- tial and temporal distribution of vehicles of one-way carsharing systems. To maximize the demand served, vehicle distribution needs to be rebalanced by performing relocations to maximize vehicle availability. There may be a wide variety of demand types depending on their reservation pattern: some reservations are made at the last minute while others are made long time in advance when a vehicle is needed for a scheduled activity. Both types of demand introduce constraints for the operator. Thus, the operational management of carsharing systems is complex due to the stochastic and dynamic nature of demand in time and space, and the limited availability of information. The opera- tor of such a system has to manage it in a way that maximizes the use of the system while at the same time all operational and business constraints are satisfied. We focus in this paper on non-floating one-way electric car- Postprint submitted to Transportation Research Part B: Methodological October 15, 2016

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Page 1: An integrated optimization-simulation framework …...An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations

An integrated optimization-simulation framework for vehicle and personnel relocations ofelectric carsharing systems with reservations

Burak Boyacıa,∗, Konstantinos G. Zografosa, Nikolas Geroliminisb

aCentre for Transport and Logistics (CENTRAL), Lancaster University Management School, Lancaster, LA1 4YX, UKbUrban Transport Systems Laboratory (LUTS), Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland

Abstract

One-way electric vehicle carsharing systems are receiving increasing attention due to their mobility, environmental, and societalbenefits. One of the major issues faced by the operators of these systems is the optimization of the relocation operations of person-nel and vehicles. These relocation operations are essential in order to ensure that vehicles are available for use at the right place atthe right time. Vehicle availability is a key indicator expressing the level of service offered to customers. However, the relocationoperations, that ensure this availability, constitute a major cost component for the provision of these services. Therefore, clearlythere is a trade-off between the cost of vehicle and personnel relocation and the level of service offered. In this paper we are de-veloping, solving, and applying, in a real world context, an integrated multi-objective mixed integer linear programming (MMILP)optimization and discrete event simulation framework to optimize operational decisions for vehicle and personnel relocation in acarsharing system with reservations. We are using a clustering procedure to cope with the dimensionality of the operational problemwithout compromising on the quality of the obtained results. The optimization framework involves three mathematical models: (i)station clustering, (ii) operations optimization and (iii) personnel flow. The output of the optimization is used by the simulationin order to test the feasibility of the optimization outcome in terms of vehicle recharging requirements. The optimization modelis solved iteratively considering the new constraints restricting the vehicles that require further charging to stay in the station untilthe results of the simulation are feasible in terms of electric vehicles’ battery charging levels. The application of the proposedframework using data from a real world system operating in Nice, France sheds light to trade-offs existing between the level ofservice offered, resource utilization, and certainty of fulfilling a trip reservation.

Keywords: one-way carsharing, vehicle relocation optimization, integer programming, network flow

1. Introduction

The emergence of carsharing as a new transportation meanbetween public and private transport is quite recent. Peoplebenefiting from this service have to register and then can usevehicles located within a designated service area. Carsharingis an approach to increase vehicle utilization while decreasingthe cost encountered to each user. Expenses associated to carownership are nowadays quite high linked to purchase, gaso-line, insurance, parking and maintenance. Avoiding these ex-penses may be a motivation for a driver to adopt carsharing asa regular transportation mean if the system is able to providehigh quality of service (accessibility and availability of vehi-cles both at origin and destination of his/her trip at reasonablecost). In addition to users’ benefits, carsharing systems are pro-ducing broader societal and environmental benefits such as re-duction of congestion, air pollution, and the urban space neededfor parking.

Carsharing systems can be classified in different categoriesaccording to the rental conditions. Free-floating systems al-

∗Corresponding authorEmail addresses: [email protected] (Burak Boyacı),

[email protected] (Konstantinos G. Zografos),[email protected] (Nikolas Geroliminis)

low people to park the vehicles anywhere in the covered area,whereas non-floating impose restrictions to users to park the ve-hicles at stations with limited number of parking spots. Anotherdifferentiating feature is the “one-way/round-trip” characteris-tic: Round-trip systems force the user to return the car to thelocation where it was picked-up whereas one-way systems al-low drop-off at any station. The type of vehicle (combustion,electric, etc.) affects also the system’s use.

Rental operations naturally induce imbalances in the spa-tial and temporal distribution of vehicles of one-way carsharingsystems. To maximize the demand served, vehicle distributionneeds to be rebalanced by performing relocations to maximizevehicle availability. There may be a wide variety of demandtypes depending on their reservation pattern: some reservationsare made at the last minute while others are made long time inadvance when a vehicle is needed for a scheduled activity. Bothtypes of demand introduce constraints for the operator. Thus,the operational management of carsharing systems is complexdue to the stochastic and dynamic nature of demand in time andspace, and the limited availability of information. The opera-tor of such a system has to manage it in a way that maximizesthe use of the system while at the same time all operational andbusiness constraints are satisfied.

We focus in this paper on non-floating one-way electric car-

Postprint submitted to Transportation Research Part B: Methodological October 15, 2016

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sharing systems because of their increased flexibility towardsthe user compared to round-trip systems and their eco-friendlycharacteristics. In particular, the objective of this paper is todevelop and apply an integrated framework for optimizing op-erational decisions related to vehicle and relocation personnelrelocation decisions. The developed framework could be ex-tended to free-floating one-way systems.

2. Previous related research

Carsharing systems have been studied intensively in recentyears. The existing body of literature addresses issues relatedto carsharing systems characteristics and types, assessment ofcarsharing system impacts, and modelling of strategic, tacticaland operational decisions. For a more comprehensive literaturereview the reader refers to Jorge and Correia (2013), Shaheenand Cohen (2013) and Boyacı et al. (2015). Given the focusof this paper on operational decisions we limit our literaturereview to papers that are mostly relevant to the modelling ofoperational decisions for one-way carsharing systems. Thesedecisions relate to the allocation and re-allocation of carshar-ing vehicles and relocation personnel to stations. Optimizationand/or simulation are the methodological approaches that havebeen used to support one-way carsharing operational decisions.

Barth et al. (1999) developed a queuing based discrete eventsimulation model to evaluate operational decisions for a sharedvehicle system of a resort community in Southern California.The types of decisions addressed include vehicle availability,vehicle distribution, and energy management. This model usesa variety of performance measure, such as total average waittime, number of customers waiting, number of relocations, andaverage battery state of charge, to assess the performance of thesystem.

Kek et al. (2006) introduced a time-stepping simulationmodel for assessing relocation operations using shortest timeand inventory balancing criteria. Zero-vehicle time, full-porttime, and number of relocations were the three indicators usedto assess the performance of the relocation operations. Keket al. (2009) used a three-phase optimization-trend-simulation(OTS) approach to develop a decision support system (DSS),for relocation operations. The optimization phase is based ona mixed integer programming (MIP) formulation which is usedto determine the resources needed to operate the carsharing sys-tem at minimum cost. In the second phase the output of the op-timization phase is “filtered” to produce the parameters neededto simulate the operation of the carsharing system. The simula-tor developed in Kek et al. (2006) is used in the third step of theproposed DSS.

Nair and Miller-Hooks (2011) proposed a stochastic mixedinteger programming (MIP) model to generate minimum costvehicle redistribution plans to satisfy a proportion of the near-term stochastic demand of the carsharing system. The proposedmodel was demonstrated on a real-world carsharing system inSingapore.

Correia and Antunes (2012) developed an optimization ap-proach for station location and trip selection schemes to max-imize profit for one-way systems with stations. This work

showed that offering a high level of service to one-way systemswithout involving relocation requires a very large fleet to copewith the demand and high involved cost. Thus, integrating a re-location module is necessary to deal with spatial and temporalasymmetry of demand. Correia et al. (2014) considered howinformation about vehicle availability in stations and flexibilityof users in renting from a station nearby, but not the closest sta-tion, can improve the demand served. No relocation strategieshave been integrated in this formulation.

Relocation strategies and inventory management for bike-sharing systems already exist in the literature (Nair et al., 2013;Raviv et al., 2013; Raviv and Kolka, 2013; Benchimol et al.,2011; Sayarshad et al., 2012). While bike- and carsharing sys-tems share plenty of similarities both at the tactical and opera-tional level, a significant difference is that relocation is usuallyperformed with trucks that are able to reposition simultaneouslya large amount of bicycles, while for carsharing systems, theseactions are more time- and personnel-consuming.

Weikl and Bogenberger (2015a,b) provided relocation strate-gies for free-floating systems for pick up and drop-off. Theycombine a macroscopic relocation optimization policy of mov-ing vehicles between zones, with a rule based heuristic for sta-tion to station relocations. Specific movements of relocationpersonnel, frequency of relocation policies and detailed cost es-timates are not provided in the paper. This approach was testedin a free-floating system in Munich and is one of the few re-ported tests in the literature.

Kaspi et al. (2014) considered a system with reservations andmodel it as a dynamic system with Markovian characteristics.The authors showed that under specific demand profiles, reser-vations can improve the performance of the system comparedto free-access sharing systems. Nevertheless, the destinationspot is reserved at the beginning of the trip, which might cre-ate under utilization of the system. Instead, if the return timeof the vehicle is known to some extend, more advanced reloca-tion policies can guarantee a free spot at the destination and ata desired time. We utilize this approach in our current work.

Pfrommer et al. (2014) developed a dynamic redistributionmodel for a public bicycle sharing (PBS) system. The proposedsystem is based on predictive control principles which are usedto dynamically calculate rewards for system users. The goal ofthis model is to provide incentives to users to return the rentedbicycles to under-utilized stations in order to reduce bicyclerepositioning costs.

Bruglieri et al. (2014) addressed the vehicle relocation prob-lem for an one way electric carsharing system in Milan. Amixed integer programming (MIP) model was developed to de-termine the optimum sequence of pick-up and delivery opera-tions that should be performed by vehicle-relocation personnel.

Jorge et al. (2015) presented a mathematical programmingmodel for maximizing profitability of a carsharing system op-timizing relocation operations for one-way carsharing system.In addition a discrete-event time-driven simulation model wasproposed to evaluate alternative relocation policies.

Nourinejad and Roorda (2014) introduced an optimization-simulation framework for supporting decisions for one way car-sharing systems. The proposed framework includes a static

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benchmark module and a dynamic module. The static com-ponent determines the optimum number of vehicles needed toserve the entire demand for the system. The dynamic relocationcomponent involves a vehicle relocation (VRO) and a parkinginventory model (PIO). The vehicle relocation model seeks tooptimize system revenues by relocating vehicles from the des-tination of user i to the origin of user j. The parking inventorymodel aims to minimize the total cost of parking by determiningthe optimal relocation times for the vehicles determined by thevehicle relocation optimization model. The VRO and PIO mod-els are run in conjunction to a discrete-event simulation modelwhere an event is defined by a new user arrival. The solution ofthe VRO and PIO determine the customer requests that will besatisfied, the vehicles that will be relocated, and the time thatthese relocations will take place.

Jorge et al. (2015) influenced vehicle imbalances by integrat-ing a pricing scheme with a demand choice model that chargeshigh prices for the trips that contribute to imbalances and lowerprices for the ones that bring the system to more equilibriumstates. This analysis showed that pricing without any reloca-tion strategies can improve the balance of the system, but withless demand served, which might create less attractiveness inthe service. Investigating trip pricing combined with relocationpolicies should be investigated.

The model proposed in this paper differs in many respectsfrom the papers mentioned above and complements the exist-ing literature. In particular, in this paper we are introducing anintegrated optimization-simulation framework for vehicle andpersonnel relocations for one-way electric carsharing systemswith reservations.

The proposed optimization framework is a multi-objectivemixed integer linear programming problem (MMILP) with hi-erarchical objective functions. While in many multi-objectiveproblems, the objective functions are combined in a single ob-jective function after applying variable weights, we prefer tochoose a hierarchical approach to ensure the satisfaction ofthe objectives according to the importance assigned to themby the decision makers. Our results highlight that there is alarge multi-optimal solution set for each objective function thatallows a meaningful application of the hierarchical approach.More discussion is provided later. In order of importance, weintend to maximize the demand of trips served and to minimizethe relocation cost after rental.

Demand served is prioritized over relocation cost and profitbecause we would like to provide high quality of service andmaximize the vehicle availability for the users especially whenwe are dealing with a system with reservations. The treatmentof a multi-objective problem allows for interesting policy impli-cations and different types of relocation strategies to be studied.

The problem formulation allows to determine the optimaltemporal and spatial distribution of vehicles in stations and alsothe personnel responsible for the relocation. To deal with thecomputational complexity of the problem, physical character-istics are considered when designing the mathematical formu-lation. A simulation module is integrated in the optimizationin order to ensure the feasibility of the optimization outcomein terms of vehicle recharging requirements. A direct integra-

tion of charging levels into the optimization model will not al-low for solving large problem instances. As we formulate theproblem as a network with nodes and arcs, we are not usingindividual stations to assign vehicles and personnel. Insteadwe consider clusters of stations based on travel times in arcs,that will aggregate stations with similar characteristics duringthe optimization. More details about clustering are provided insection 3.5. Station clustering is used to reduce the computa-tional complexity of the problem. The remainder of the paperis organized as follows: Section 3 presents the methodologicalframework involving an optimization and a simulation module.Section 4 provides the results of implementing and solving theproblem with data from a real case-study for different systemrealizations and relocation policies. The last section provides adiscussion and further future directions.

3. Methodological framework

The proposed framework consists of the following two mod-ules: (i) optimization, and (ii) simulation. Within the optimiza-tion module, a clustering algorithm is developed which createsclusters of stations in order to reduce the dimensionality of theoptimization module.

The optimization module involves three mathematical mod-els: (i) station clustering, (ii) operations optimization and (iii)personnel flow. The operations optimization formulation doesnot explicitly account for battery levels and this is addressedindirectly through the simulation module. The output of the op-timization module is used by the simulation module in orderto test the feasibility of the optimization outcome in terms ofvehicle recharging requirements. After the first iteration of theoptimization process, if the results of the simulation are feasiblethen the optimization process is stopped. If the simulation re-sults are not feasible, the vehicles that require further chargingare restricted to stay in the station and the optimization model issolved again considering the new constraints. The structure ofthe proposed model and the interrelationship between its mod-ules are illustrated in Fig. 1.

3.1. Modelling assumptions and conceptsThe assumptions underlying the operations of the system are:

• The carsharing system is modelled as a network of sta-tions. The state of each station at each time interval (de-scribed in the next bullet) is the number of vehicles parked.

• The operating time of the carsharing system is divided intoequal time intervals (15 minutes). Using the network ofstations, a time-augmented network is generated by in-cluding all station-time interval pairs and repeating thenetwork of stations for each time interval.

• Every trip and relocation with/without vehicle takes atleast one time interval.

• Each vehicle can have only one state at each time interval:parked, serving trip (called trip from now on) or under re-location (called relocation from now on). These 3 states

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INPUT DATA Operations

OptimizationModel

Simulation

Is the solution feasible?

Access of the solution

Yes

Constraint variables to adhere to charging level threshold value.

No

Personnel Flow Model

Optimization Module

Simulation Module

Station Clustering

Figure 1: Flow chart for the solution framework

appear as arcs in Fig. 2. These 3 states are defined as fol-lows:

Parked: Vehicle is available waiting at one of the stations.

Trip: Vehicle is picked-up by one of the users and will beunavailable until it is dropped-off.

Relocation: Vehicle is relocated by one of the personneland will be unavailable until its relocation is ended.

• Each (relocation) personnel can have only one state at eachtime interval: idle, driving or moving.

Idle: Personnel is available waiting at one of the stations.

Driving: Personnel is relocating one of the vehicles andwill be unavailable until the relocation is completed.

Moving: Personnel is moving from his/her previous sta-tion to another station and will be unavailable untilthe moving is finalized

These assumptions allow the realistic representation of theproblem and facilitate its mathematical formulation. In additionto the stated assumptions the following concepts underpin themathematical formulation of the problem.

• The operations of vehicles and personnel are described intime-augmented networks, a single network for cars andseparate networks, one for each personnel shift, are cre-ated. Interactions between the networks are described inthe next bullet points.

• In the time-augmented networks, each node is defined withtwo attributes, i.e. station and time interval, and representsthe number of vehicles or personnel depending on the net-work, for given time interval (Figs. 2 and 3). The arcs ofthe networks represent the states of vehicles and person-nel. In Fig. 2, only the arcs starting and ending from nodesat time interval 4 are shown. For example, vehicle is rentedfrom station 1 at time interval 1 and is returned to station3 at time interval 4, where it is parked afterwards. Notethat relocation arcs in the vehicle network of Fig. 3 are al-ways associated with a driving arc in personnel networksof Fig. 3. Time augmented networks of personnel containonly nodes related to the time intervals that the personnelworks (Fig. 3).

1,1 2,1 3,1 4,1 5,1 6,1 |T|,1...

2,1 2,2 3,2 4,2 5,2 6,2 |T|,2...

3,1 3,2 3,3 4,3 5,3 6,3 |T|,3...

1,|J| 2,|J| 3,|J| 4,|J| 5,|J| 6,|J| 7,|J|

7,1

7,2

7,3

... ... ... ... ... ... ...... ...

...

t,j

LEGENDtime-space

nodeparked arcrelocation arctrip arc

Figure 2: Time augmented vehicle network for a set of stations (J) and timeintervals (T ). Different types of arcs (i.e. park, trip and relocation) are shownstarting and ending from the nodes at time interval 4.

• Since every operation (e.g. trip, driving, moving) starts atthe beginning and ends at the end of a time interval, a ve-hicle (or a personnel) starting the operation at time intervalt from node j has to be at node j at the end of the previoustime interval t − 1. Under the same reasoning, a vehicle(or a personnel) ending the operation at time interval u atnode l is available for a new operation the earliest at timeinterval u + 1.

• When a trip is accepted to be served from station j to l,starting at time interval t and ending at time interval u, aunit flow is sent from nodes ( j, t) to (l, u) in the vehicles’network. In Fig. 3, 5 trips are shown with arcs T1-T5.

• When a driving is executed for a vehicle at station j to l,starting at time interval t and ending at time interval u, aunit flow is sent from nodes ( j, t) to (l, u) in both the vehicleand personnel networks. In Fig. 3, 5 drivings are shownwith arcs R1-R5 in the vehicle network. Those drivingsare executed by personnel from shift 1 (R1-R2) and shift2 (R3-R5). Note that, there are driving arcs (D1-D2 andD3-D5 respectively) starting exactly from the same nodesin the personnel network by whom the driving is executed.

• In addition to driving, relocation personnel can change sta-tion by moving (i.e. they can ride to a vehicle driven bysomeone else). This type of operation is labelled with M1and M2 in Fig. 3. When a member of staff from personnelshift s is moving from station j to l starting at time inter-val t and ending at time interval u, a unit flow is sent from

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D1 M1

D2

R4

D3

D4

D5

R5R2 R31

2

3

|J|

...

1

2

3

|J|

...

1

2

3

|J|

...

R1

vehi

cles

pers

onne

l shi

ft 1

pers

onne

l shi

ft 2

time-space nodes

parked arc (vehicle)

relocation arc (vehicle)

idle arc (personnel shift)

moving arc (personnel shift)

driving arc (personnel shift)

LEGEND

1 2 3 t+1 t+2 t+3 t+4 |T|-1 |T|

M2

... ...

Figure 3: Time augmented vehicle and personnel shift networks for a set ofstations (J) and time intervals (T ). Different types of arcs are used for differentoperations in different networks. Parked (P) and relocation (R) arcs are used invehicle’s network. Idle (I), moving (M) and driving (D) arcs are used personnelshifts network. Trip arcs for the vehicles are excluded from the figure to keep itsimpler.

( j, t) to (l, u) in the personnel network of the shift s. If apersonnel from shift s does not change its location at timet and stays in station j, a unit flow is sent from stay arcfrom ( j, t) to ( j, t + 1).

• In the exact operations optimization model, all possiblerelocation, i.e. driving and moving, arcs are created. Notethat, the duration of all these operations are parametersof the model. In other words, for any given relocation,driving and moving arc from station j to station l startingat time interval t, there is only one end time interval u.

• In order to decrease the number of variables in the oper-ations optimization model (see Fig. 1), stations are clus-tered for driving and moving operations. A second layer isadded for both driving and moving operations and eachof these operations is handled at the cluster level. Inother words, in the operations optimization model, driving(moving) from station j to station l from time interval t tou is done in three “artificial” states: (i) from origin stationj to origin station’s cluster b at time interval t, (ii) fromorigin station’s cluster b to destination station’s cluster dstarting at time interval t and ending at time interval u and(iii) from destination stations cluster d to destination sta-tion l at time interval u. Any relocation between a cluster

and a station is named intra-relocation and any relocationbetween two clusters is named inter-relocation.

• Clusters of stations are created using an approach similarto k-Medoid algorithm (Kaufman and Rousseeuw, 1987).Further information about the algorithm is given in Section3.5. Since clustering depends only on the network topol-ogy, the clustering algorithm is the very first algorithm tobe executed and is not updated with time. The clusteringalgorithm is applied for driving and moving arcs separatelysince different speeds and routes are used in these two op-erations (see Fig. 1).

• After solving the operations optimization model, the per-sonnel flow model is used to create personnel assignmentsfrom flows between clusters and between clusters and sta-tions for any given time interval.

• Instead of forcing every vehicle to be fully charged be-fore rental, charging levels of vehicles are controlled witha simulator. The operations optimization model, the per-sonnel flow model, and the simulation model are run itera-tively until a charging level feasible solution is obtained. Ifthere is an infeasibility in the charging level of any vehicle,this vehicle is forced to be charged before it is assigned toits next task (i.e. relocation or trip). The flow chart of theentire solution framework can be seen in Fig. 1.

3.2. Operations Optimization Model3.2.1. Sets and Indicesi ∈ I : trips

j and l ∈ J : stations

t, u and w ∈ T : time intervals

s ∈ S : working shifts

b and d ∈ B : station clusters

3.2.2. Parametersstart/end(s) : start/end time intervals of working shift s

start/end(i) : start/end time intervals of trip i

origin/dest(i) : origin/destination stations of trip i

c.end(i) : the last interval that vehicle of trip i can be charged

d.end/m.end(t, b, d) : the time interval that driving/movingfrom cluster b to d ends if it starts at time interval t

PCs : cost of a relocation personnel for working shift s

RC j : intra-relocation cost from/to station j

RCbd : inter-relocation cost from a station in cluster b to a sta-tion in cluster d

SG : (safety gap) number of time intervals the drop-off spotis kept reserved at the destination station of a trip startingfrom its stated end time

Ic : set of trips after which the vehicle serving these tripsshould be charged

5

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3.2.3. Variables

zi : binary variable indicating if trip i is served or not

vs : number of personnel used from shift s

ntj : number of vehicles in station j at the beginning of time

interval t

ntj : number of vehicles in station j forced to be charged during

time interval t

mts j : number of personnel from shift s in station j at the begin-

ning of time interval t

rts j : number of vehicles relocated by personnel of shift s from

station j starting at time interval t

rts j : number of vehicles relocated by personnel of shift s to

station j finishing at time interval t

pts j : number of personnel of shift s moved from station j start-

ing at time interval t

pts j : number of personnel of shift s moved to station j finishing

at time interval t

rt(u)sbd : number of vehicles relocated by personnel of shift s from

a station in cluster b to a station from cluster d started attime interval t and ending at time interval u

pt(u)sbd : number of personnel of shift s moved from a station in

cluster b to a station from cluster d started at time intervalt and ending at time interval u

3.2.4. Formulation

max∑

i

zi (1)

min

inter-relocation cost︷ ︸︸ ︷∑b,d

RCbd rt(u)sbd +

intra-relocation cost︷ ︸︸ ︷∑j,t

RC j

(rt

s j + rts j

)+

personnel cost︷ ︸︸ ︷∑s

PCsvs (2)

s.t. nt+1j = nt

j −∑

i:start(i)=torigin(i)= j

zi −∑

s

rts j

+∑

i:end(i)=tdest(i)= j

zi +∑

s

rts j ∀ j, t\tlast (3)

ntj ≥

∑i:start(i)=torigin(i)= j

zi +∑

s

rts j ∀ j, t (4)

∑j

mstart(s)s j = vs

∑j

mend(s)s j = vs ∀s (5)

mt+1s j = mt

s j − pts j − rt

s j + pts j + rt

s j ∀ j, s, t\tlast (6)

mts j ≥ pt

s j + rts j ∀ j, s, t (7)∑

d

rt(u)sbd =

∑j∈Jb

rts j

∑d

ru(t)sdb =

∑j∈Jb

rts j ∀s, b, t (8)

∑d

pt(u)sbd =

∑j∈Js

b

pts j

∑d

pu(t)sdb =

∑j∈Js

b

pts j ∀s, b, t (9)

ntj ≤ CAPt

j ∀ j, t (10)

ntj −

∑i:start(i)=torigin(i)= j

zi −∑

s

rts j ≥

∑i: dest(i)= j, i∈Ic

end(i)<t≤c.end(i)

zi ∀ j, t (11)

ntj −

∑i:start(i)=torigin(i)= j

zi −∑

s

rts j ≥

∑i: dest(i)= j

end(i)<t≤end(i)+SG

zi ∀ j, t (12)

zi ∈ {0, 1} ; ntj, vs ∈ N ∀i, j, t, s (13)

mts j, r

ts j, r

ts j, p

ts j, p

ts j, r

t(u)sbd , p

t(u)sbd ∈ N ∀s, j, t, b (14)

The proposed optimization model is a MMILP with lexico-graphically ordered objective functions. The model, involves inorder of importance, the following two objectives: (i) maximizenumber of trips served and (ii) minimize relocation cost.

The first-priority objective of the model (Eq. 1) is to maxi-mize the number of trip requests served.

The second-priority objective of the model (Eq. 2) is to min-imize total relocation cost. This objective function has threecomponents:

• Inter-relocation cost includes the fuel cost associated withrelocation operations between clusters. Note that, whenthere is a relocation between two stations, it is assumedthat each relocation is performed in three artificial states:(i) from origin station to origin station’s cluster, (ii) fromorigin station’s cluster to destination station’s cluster and(iii) from destination station’s cluster to destination sta-tion. This function is related to state (ii), i.e. relocationbetween clusters.

• Intra-relocation cost includes the fuel cost associated withrelocation operations between stations and clusters. Inother words, these are the costs related to artificial states(i) and (iii) of the relocation operations described before.

• Personnel cost is the total cost of personnel used. It is as-sumed that there is a number of working shifts and themodel determines the number of employees needed pershift.

Demand served is prioritized over relocation cost because wewould like to maximize the availability of the system to theusers especially when we assume that the trip has been alreadyaccepted and service is offered to the customer.

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Constraints 3 are the flow conservation equations for vehiclesfor each station and time interval. For all stations and time inter-vals, the total number of vehicles at station j at the beginning oftime interval t+1

(nt+1

j

)is equal to the number of vehicles at the

beginning of time interval t(nt

j

)minus the number of vehicles

that have left station j at time interval t by trip(∑ i:start(i)=t

origin(i)= jzi

)and

relocation(∑

s rts j

)plus the number of vehicles that have arrived

to station j at time interval t by trip(∑ i:end(i)=t

dest(i)= jzi

)and relocation(∑

s rts j

). Flow on the top of the rectangle at time interval t of

Fig. 4 represents this relationship.

mts j mt+1

s j

pts j︸︷︷︸

movingfrom

rts j︸︷︷︸

drivingfrom

rts j︸︷︷︸

drivingto

pts j︸︷︷︸

movingto

ntj nt+1

j

tripsfrom︷ ︸︸ ︷∑

i:start(i)=torigin(i)= j

zi

drivingfrom︷ ︸︸ ︷∑s

rts j

drivingto︷︸︸︷∑

s

rts j

tripsto︷ ︸︸ ︷∑

i:end(i)=tdest(i)= j

zi

timeinterval

t − 1 time interval t

timeinterval

t + 1Figure 4: Flow diagram of vehicles (top) and personnel shift s (bottom) instation j at time interval t.

Constraints 4 ensure that there are enough number of vehiclesto start trips and relocations at each station at each time interval.These constraints prevent vehicles to start trips and relocationsat the time interval at which they end their trips and relocations.With these constraints, it is guaranteed that every vehicle canhave one and only one state (i.e. parked, under rental, underrelocation) at each time interval. For all stations and time in-tervals, the number of vehicles in station j at the beginning oftime interval t

(nt

j

)should be more than or equal to the num-

ber of vehicles that have left station j at time interval t by trip(∑ i:start(i)=torigin(i)= jzi

)and relocation

(∑s rt

s j

).

Constraints 5 keep track of the number personnel allocated ineach shift. In the first set of constraints, for all shifts, the totalnumber of personnel started working at different stations at thebeginning of the start time interval of shift s should be equal tothe number of personnel allocated in the same shift. Similarlyfor the second set of constraints, for all shifts, the total numberof personnel ended working at different stations at the end ofthe end time interval of shift s should be equal to the number ofpersonnel allocated in the same shift.

Constraints 6 are the flow conservation equations for eachshift, each station and time interval. For all shifts, stations andtime intervals, the total number of personnel from shift s at sta-tion j at the beginning of time interval t + 1

(mt+1

s j

)is equal to

the number of vehicles at the beginning of time interval t(mt

s j

)

minus the number of personnel that have left station j at timeinterval t by moving

(pt

s j

)or driving

(rt

s j

)plus the number of

personnel that arrived the station j at time interval t by mov-ing

(pt

s j

)or driving

(rt

s j

). Flow on the bottom rectangle at time

interval t of Fig. 4 illustrates this relationship.Constraints 7 ensure that there are enough number of per-

sonnel from each shift to execute moving and driving at eachstation at each time interval. These constraints prevent person-nel to start drivings and movings at the time interval at whichthey end their drivings and movings. With these constraints, it isguaranteed that every personnel can have one and only one state(i.e. idle, moving, driving) at each time interval. For all shifts,stations and time intervals, the number of personnel from shifts in station j at the beginning of time interval t

(mt

s j

)should

be more than or equal to the number of personnel that have leftstation j at time interval t by driving

(pt

s j

)and moving

(rt

s j

).

Constraints 8 are used to preserve flow conservation betweenclusters and stations of clusters for driving operations. In thefirst set of constraints, for all shifts, clusters and time intervals,the total number of personnel of shift s started driving from thestations of cluster b at time interval t should be equal to thenumber of personnel driving from all stations of cluster b

(J s

b

)at the same time interval. Similarly, in the second constraint,for all shifts, clusters and time intervals, the total number ofpersonnel of shift s ended driving at the stations of cluster bending at time interval t should be equal to the number of per-sonnel driving to all stations of cluster b

(J s

b

)at the same time

interval.Constraints 9 are used to preserve flow conservation between

clusters and the stations of clusters for moving operations. Inthe first set of constraints, for all shifts, clusters and time in-tervals, the total number of personnel of shift s started movingfrom the stations of cluster b starting at time interval t shouldbe equal to the number of personnel moving from all stations ofcluster b

(J s

b

)at the same time interval. Similarly, in the second

set of constraints, for all shifts, clusters and time intervals, totalnumber of personnel of shift s ended moving at the stations ofcluster b ending at time interval t should be equal to the numberof personnel moving to all stations of cluster b

(J s

b

)at the same

time interval.Constraints 10 set the capacity restrictions for each station j

at each time interval t.Constraints 11 are used to keep track of charging vehicles

after rentals. As it is stated in Section 3, we use simulation tocheck the charging level feasibility of the solution. The outputof the simulation is used to update the set Ic. Feedback from thesimulation adds the trips with infeasible starting charging levelsto this set. The right hand sides of these constraints are onlyapplicable to the trips in this set. In the mathematical model,we force vehicles to be charged after these trips (i ∈ Ic) if theyare served (i.e. zi = 1). The constraints are not binding forunserved trips (i.e. zi = 0). We satisfy these constraints byforcing the number of parked vehicles after these trips at thedestination stations during the charging period (end(i) < t ≤c.end(i)). Note that, for a given station and time interval, thetrips and relocations departing from the station are subtracted

7

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from the number of vehicles at the beginning of the time intervalat the left hand side of the constraint. Without this update, themodel can assign any charging vehicles for a trip or a relocationand cover its place with another vehicle arriving to the samestation without violating these constraints.

Constraints 12 are used to apply the safety gap of vehicle re-turning time provided for the users. These constraints are usedto reserve destination stations for the duration of the safety gap(SG) which is defined in the units of time intervals. For in-stance, if SG is 2 and the time interval length is 15 minutesthen the destination spots of every accepted trips (i.e. zi = 1) isreserved starting from the end time of the trip for 30 minutes.The constraints are not binding for unserved trips (i.e. zi = 0).With these constraints we guarantee two things: (i) There willalways be a spot available for the vehicle starting from its statedtrip end time for a period of the safety gap. (ii) The returned ve-hicle will not be relocated or rented until the end of the safetyperiod, i.e. trip end time plus safety gap. We satisfy these twoconditions by forcing the vehicle to stay at the station from theend of the trip for a duration of the safety gap. These constraintswork very similar to constraints 11. Constraints 12 are appliedto all trips for a period of safety gap whereas 11 are applied toonly trips in set Ic until the charging end time.

Constraints 13-14 are used to define the domains of eachvariable: zi’s are restricted to be binary variables, the rest ofthem are positive integers.

3.3. Personnel Flow Model

For each working shift s, the following model is solved withthe values acquired from the operations optimization model(Eqs. 15-20).

3.3.1. Sets and Indicesk ∈ K : personnel

j ∈ J : stations

b and d ∈ B : clusters

t ∈ T : time intervals

f ∈ F : flows

3.3.2. Parametersmt

s j : number of personnel of shift s in station j at the beginningof time interval t

rts j : number of personnel of shift s starting driving (state D)

from station j at time interval t

rts j : number of personnel of shift s finishing driving (state D)

to station j at time interval t

pts j : number of personnel of shift s starting moving (state M)

from station j at time interval t

pts j : number of personnel of shift s finishing moving (state M)

to station j at time interval t

rt(u)sbd : number of personnel of shift s driving from a station in

cluster b to a station from cluster d starting at time intervalt and ending at time interval u

pt(u)sbd : number of personnel of shift s moving from a station in

cluster b to a station from cluster d starting at time intervalt and ending at time interval u

vs : number of personnel used from shift s

start/end( f ) : start/end time interval of flow f

origin/dest.( f ) : origin/destination stations of flow f

3.3.3. Variablesxt

jk : binary variable indicating if personnel k is in node j at thebeginning of time interval t or not

y f k : binary variable indicating if personnel k follows flow f ornot

3.4. Formulation

A prerequisite for setting-up the personnel flow model is torun the operations optimization model in order to obtain theoptimal values of the flows rt

s j, rts j, r

t(u)sbd , p

ts j, p

ts j and pt(u)

sbd. A flowcontains two intra-flows and one inter-flow of the same type,i.e. driving or moving. In other words, in order to generate aflow from two intra- and one inter-flows, (i) the first inter-flow’stime interval should be the starting time interval of the intra-flow, (ii) the station of the first intra-flow should be element ofthe origin cluster of the intra-flow, (iii) the second inter-flow’stime interval should be ending time interval of the intra-flow,and (iv) the station of the second intra-flow should be elementof the destination cluster of the intra-flow. All these generatedflows constitute set F. In order to simplify representation, allflows, drivings (r) and movings (p), are represented with q.

min∑f ,k

dist( f )y f k (15)

s.t.∑

k

xtjk = mt

s j

∑j

xtjk ≤ 1 ∀ j, k, t (16)

xt+1jk = xt

jk −∑

f :start( f )=torigin( f )= j

y f k +∑

f :end( f )=tdest( f )= j

y f k ∀ j, k, t (17)

∑f :start( f )=torigin( f )= j

y f k = qts j

∑f :end( f )=tdest( f )= j

y f k = qts j ∀ j, t (18)

∑f :start( f )=t,origin( f )∈Jb

end( f )=u,dest( f )∈Jd

y f k = qt(u)sbd ∀b, d, t (19)

xtjk, y f k ∈ {0, 1} ∀ f , j, k, t (20)

The objective of the personnel flow model (Eq. 15) aims tominimize total distance travelled. We can minimize the totaldifference between real relocation time and assumed relocationtime with clustering, which is discussed later.

8

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First set of constraints 16 count the number of personnel fromshift s at each station j at each time interval t and sets this num-ber equal to the number calculated by the operations optimiza-tion model, i.e. xt

jk. Second set of constraints 16 require that,every personnel can be at most in one station at each time in-terval t. Note that, the LHS of these constraints not necessarilyequal to 1 since there may be driving and moving operationswhich take more than one time interval.

Constraints 17 are the flow conservation equations for indi-vidual personnel. If personnel k is at node j at the beginningof time interval t and he/she does not start driving or moving toanother station during that period, then he/she should be in sta-tion j at the beginning of time interval t + 1. On the other hand,if personnel k is not at node j at the beginning of time intervalt and he/she performs driving or moving to station j from anystation finalizing at time interval t, he/she should be in station jat the beginning of time interval t + 1.

Constraints 18 and 19 are used to cover the same flow oper-ations found by operations optimization model in the previousstep. Constraints 18 ensure that, the total number of flows as-signed to all personnel from shift s should exactly cover all firstand second intra-flows with/without vehicle. Similarly, con-straints 19 ensure that the total number of flows assigned toall personnel from shift s should exactly cover all inter-flowswith/without vehicle.

qts j qu

sl

qt(u)sbd

y f kstart( f )=t

origin( f )= j

y f kend( f )=udest( f )=l

y f kstart( f )=t, origin( f )= j

end( f )=u, dest( f )=l

j ∈ Jbat timeinterval t l ∈ Jd

at timeinterval u

Ope

ratio

nsO

ptim

izat

ion

Mod

elPe

rson

nel

Flow

Mod

el

Figure 5: The representation of flows (driving/moving) in two mathematicalmodels. In the operations optimization model, there is at least one flows fromstation j to l from time interval t to u executed by personnel shift s. The countof these flows are kept with three variables: qt

s j, qt(u)sbd and qu

sl. In personnel flowmodel, this flow is performed by personnel k from personnel shift s. Only onebinary variable is needed to describe this flow, y f k .

3.5. Clustering Algorithm

Although it is possible to develop a mathematical modelwithout using clusters, this would be computationally very de-manding. Since we allow dynamic relocations throughout theday, we need to create in the order of O(|T ||J|2) number of vari-ables for driving and moving operations only in which T is theset of time intervals and J is the set of stations. In order to de-crease the number of variables and solution time as a result, we

develop clusters and assume relocations are happening betweenclusters. This approach decreases the number of driving andmoving variables to the order of O(|T ||C|2 + 2|T ||C|) in which Cis the set of clusters. Note that, if every cluster is set with oneand only one stations, the proposed model is equivalent to themathematical model without clusters.

A clustering model is developed to find clusters that mini-mize the error created by aggregating stations to a given numberof clusters. Since our model works with time intervals, the ob-jective of the clustering model is to minimize the sum of squaresof the deviation of relocation time of every pair of different sta-tions. If T( j, l) is defined as the travel time from station j tostation l and

(TB

min( j, l),TBmax( j, l)

]is the interval of the dura-

tion of relocation from cluster of station j to cluster of stationl; positive (dev+

B) and negative (dev−B) deviations’ can be calcu-lated using Eqs. 21-22. Note that if travel time from origin todestination station is in the interval of the duration of relocationfrom the cluster of origin to the cluster of destination station,both positive and negative deviations are zero.

dev+B( j, l) = max

{T( j, l) − TB

max( j, l), 0}

(21)

dev−B( j, l) = max{TB

min( j, l) − T( j, l), 0}

(22)

The algorithm developed for clustering is similar to k-Medoid algorithm (Kaufman and Rousseeuw, 1987). The algo-rithm starts with an initial solution and iterates until the stop-ping criterion, i.e. iteration count, is met. This problem isquite complex to solve with an exact algorithm. We preferk-Medoid instead of k-means since former aims to minimizedissimilarities within clusters whereas latter minimizes sum ofsquared Euclidean distances. Since the time is discretized inthe mathematical model, our “similarity” function is discreteand k-Medoid algorithm allows us to reflect this on our objec-tive function.

Initial solution is created step by step by assigning each sta-tion consecutively to the limited number of clusters. In everyiteration, the station is added to the cluster that minimizes theobjective function, the sum of positive and negative deviations.

After the initial solution is created, the configuration thatimproves the objective function is found with consecutive ex-change of stations to different clusters. Each exchange is ex-ecuted in two steps. First, we remove each station from theirclusters iteratively to see which removal of the station improvesthe objective function most. Then this station is added to eachof the clusters iteratively except its previous cluster. We cal-culate the objective function improvement at each addition tosee to which cluster we should add the station to improve ob-jective function most. After each exchange operations, best so-lution is updated with the current solution if current solutionhas smaller objective function than the best solution so far. Thebest solution is reported when one of the stopping criterion ismet. The pseudocode of the clustering algorithm can be seenin Algorithm 1 for the set of stations (J), the maximum numberof clusters (nB), the number of iterations (nc) and the objectivefunction value for clusters B (F(B)). The set of clusters (B?)

9

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with the best objective function is returned at the end of the al-gorithm. Results of the clustering algorithm are presented inSection 4 of the paper.

3.6. Simulation ModuleFor carsharing systems with combustion engine vehicles, the

solutions generated by the optimization module are always fea-sible. However, this is not the case for systems with electric ve-hicles. The charging level of each vehicle at each time intervalshould be controlled in order to satisfy charging level feasibil-ity of the solution. The charging level feasibility means that agiven vehicle has enough battery to allow it to fulfill the nexttrip. For this purpose, a simulation module is used by the solu-tion framework.

The purpose of the simulation module is to check the feasibil-ity of the solution generated by the optimization module. If thesolution is feasible, it is accepted. If it is not feasible, the sim-ulation module returns the infeasible vehicle with its assignedrentals. The optimization module puts a charging restriction forthis vehicle and forces it to be charged. In other words, if thereis a vehicle to be rented with a charging level below thresh-old, we force the vehicle which serves the same demand to staylonger at the station that was previously rented in order to becharged properly. It is worth noting that this strategy terminateswithin a limited number of iterations. The maximum numberof iterations is not more than the total number of requested trip,but during the implementation we notice that occurs in realitywith a much smaller number of iterations in most cases.

In order to find the optimal charging strategy, the modelneeds to test all possible charging restrictions which requiresexponential number of runs. That is the reason, we select thevehicle with infeasible charging and apply forced charging toit. Furthermore, the strategy always returns a feasible solution.The duration of the charging is just enough to replenish the elec-tric energy consumed in the last trip. Note that, forced chargingconstraint is active only if a demand for a trip is served. Inthe worst case, there might be a request for charging after ev-ery trip. In such a case, any solution would be charging levelfeasible since this will be a model with all forced charging re-strictions. A system with a restriction of fully charging afterevery trip would be a carsharing system which only allows fullycharged vehicles to be rented. This strategy is not preferred atthe very first step because it sharply decreases the capacity ofthe system (the availability of vehicles).

We have developed a discrete event simulator, which is de-scribed in more details in Repoux et al. (2015). The generalstructure is included in Fig. 6. Rentals and relocations arefed to the simulator (see Read Rentals and Read Relocationsevents) as parameters. Every rental and relocation of vehicles,and movements of personnel are simulated with the help of thissimulator.

4. Model Application

The solution framework represented with the flow chart inSection 3 (see Fig. 1) was applied to support operational deci-sions for the one-way electric carsharing system in Nice, France

Input: J, nB, nc and F(B)Output: B?

// Initialization

for b← 1 to nB doBb ← ∅ // initialize clusters

endfor j← 1 to |J| // for all stations do

Z ← ∞ // initialize objective

for b← 1 to nB // for all clusters doBb ← Bb ∪ { j} // add

if F(B) < Z thenb? ← b and Z ← F(B) // update selected

endBb ← Bb \ { j} // remove

endBb? ← Bb? ∪ { j} // assign to selected cluster

endB? ← B and Z? ← F(B) // initialize best

// Iteration

for c← 1 to nc do// Find station to be removed

Z ← ∞ // initialize c.best objective

for b← 1 to nB // for all clusters doforeach j ∈ Bb // for all stations do

Bb ← Bb \ { j} // remove

if F(B) < Z thenj? ← j, b? ← b and Z ← F(B) // update

endBb ← Bb ∪ { j} // add

endendBb∗ ← Bb∗ \ { j∗} // remove from selected

// Find cluster to be added

Z ← ∞ // initialize objective

for b← 1 to nB doif b = b? then

continue // skip if the same

endBb ← Bb ∪

{j?

}// add

if F(B) < Z thenb? ← b and Z ← F(B) // update cluster

endBb ← Bb \

{j?

}// remove

endBb? ← Bb? ∪

{j?

}// assign to selected

// Update best solution

if Z? < F(B) thenB? ← B and Z? ← F(B)

endend

Algorithm 1: Pseudocode for the clustering algoritm de-scribed in Section 3.5.

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Rental Start

Rental End

Read Relocations

Relocation Start

Personnel Move Start

Relocation End

Personnel Move End

Long Term Rental Assign

Personnel Availability

Start Personnel Availability

End

REN

TALS

R

ELO

CA

TIO

NS

Read Rentals

Figure 6: Simplified structure of events and their links to each other in thesimulator.

operated by VENAP Auto Bleue (see Fig. 7). VENAP AutoBleue has been operating a round-trip system with 66 stationssince 2011. In 2014, the system provided service to one-waytrips. In our model application, anonymised rental and stationlocation data1 provided by VENAP Auto Bleue are used. Thedemand data from individual days are aggregated. For differ-ent demand levels, subsets with different number of trips aregenerated randomly (for also confidentiality purposes).

Figure 7: Stations of the carsharing system of the city of Nice, France.

The whole model including the simulator, clustering algo-rithm and mathematical models were implemented in C# .NETenvironment. IBM ILOG Cplex Version 12.6 with ConcertTechnology was used for solving MILPs.

The duration of each time interval is set to 15 minutes. It isassumed that relocation personnel move between stations eitherwith a car (if a vehicle is relocated) or with a bike (if a vehicleis not relocated). The driving and cycling distances were es-timated using Google Maps API (Google, 2015). Driving andcycling speeds are set to 30 and 15 kilometres per hour respec-tively. Different speeds could be integrated in the optimizationmodule if historical (or real time) traffic data can be provided totest the effect of traffic congestion in the system operations.

1The full dataset cannot be shared publicly as it contains sensitive commer-cial and private data. Readers could contact the authors to obtain a subset ofdata for research purpose.

4.1. Clustering Stations

First, separate clusters for driving (D) and moving (M) arecreated. The aim of the clustering algorithm is to increase theefficiency of the optimization algorithms by reducing the di-mensionality of the problem. Note that, the difference betweenthe durations of relocations with (driving) and without (mov-ing) vehicles results in two separate clusters. The clusteringalgorithm described in Subsection 3.5 (see Algorithm 1) is ap-plied for different number of clusters.

The results for the different number of clusters are shownin Fig. 8 for both driving (Figs. 8a-8e) and moving (Fig. 8f)operations. In these figures, the numbers on the first row andcolumn show the station numbers. Values in the upper triangleshow the travel duration between the two stations (see the firstrow and column) in seconds. This value is the largest of the twotravel durations between every pair of stations. Values in thelower triangle are the number of time intervals needed to travelbetween the two stations, simply the smallest integer larger thanthe value symmetric to the diagonal divided by 900, i.e. the timeinterval length in seconds. To facilitate the visualization of thefigure, colour of each cell shows the number of time intervalsneeded to travel between each pair of nodes.

Each partition is separated with horizontal and vertical lines.For instance, in Fig. 8a there are four clusters. The first clusterhas 50 stations starting with station 0 and ending with station59; the second cluster has seven stations: 14, 15, 54, 55, 62, 63and 65; and so on and so forth.

In the runs, we assume that the travel time between two sta-tions is equal to the biggest difference of the travel time betweenthe pairs of stations of the two clusters. With this assumption,the clustering algorithm always produces feasible relocation op-erations. We have opted to overestimate relocation durationsinstead of ending up with infeasible solutions due to the under-estimation of relocation durations. As a result we never havea positive difference (21) for any station pairs. Our objectiveonly minimizes the sum of negative differences (22) betweenall pairs. For instance, any travel between the stations of cluster1 and the stations of cluster 2 takes three time intervals sincefor some pairs of stations from cluster 1 and 2, travelling takesthree time intervals (see orange cells). Travels from the stationsof cluster 2 to the stations of cluster 2 takes four time intervalsbecause of some red cells, for station pairs {15, 62} and {55,62}.

The score of the cluster in Fig. 8a, which is calculated withthe help of algorithm described in Section 3.5, is 3302.7. Thisalgorithm calculates the sum of square errors expressed in termsof time intervals squared between all pairs of different stationsbecause of the clustering which is represented by the verticalaxes in Fig. 9.

There is a trade-off between the efficiency and the accuracyin selecting the number of clusters to be used for relocationswith/without vehicles. Higher number of clusters results in lessoverestimation in relocation durations but increases the num-ber of variables and as a result the model complexity. Lowernumber of clusters results in higher overestimation in reloca-tion times but decreases the number of variables and results in

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2 1 1 218 620 530 447 222 115 224 402 355 308 256 350 532 283 298 433 446 613 277 512 389 229 201 392 322 310 512 335 466 250 277 467 393 292 219 164 277 439 366 211 304 251 334 187 645 199 247 1193 1682 1333 1658 1065 1562 1054 650 612 647 888 804 1027 700 2525 2720

3 1 1 1 443 325 206 86 170 153 437 433 206 97 200 629 278 212 305 281 372 189 271 274 175 264 261 195 285 287 312 601 164 112 503 344 127 43 82 154 271 314 138 142 232 313 224 438 204 211 1269 1735 1368 1711 949 1697 961 787 447 683 1018 847 1164 692 2593 2773

4 1 1 1 1 118 256 474 568 429 578 503 350 375 320 687 620 365 634 460 237 365 208 710 587 720 239 368 442 167 347 604 398 362 643 686 350 396 539 374 216 313 591 424 632 398 644 129 626 397 1838 2321 1809 2297 916 1366 1419 790 316 822 1307 962 1166 1147 2243 3359

5 1 1 1 1 1 134 374 478 339 518 436 288 244 195 611 439 303 453 343 136 302 89 434 406 539 167 305 380 49 285 529 336 244 623 506 223 278 374 283 125 250 376 333 451 335 463 127 445 334 1552 2019 1430 1994 950 1625 1238 715 248 739 946 818 1091 967 2276 3056

6 1 1 1 1 1 1 260 386 245 459 376 158 122 98 552 320 248 334 211 185 225 85 316 286 419 111 141 331 95 242 469 255 125 564 387 100 159 220 196 65 195 257 175 332 279 344 245 326 271 1188 1664 1370 1639 990 1566 1119 656 242 680 886 759 1032 848 2406 2701

7 1 1 1 1 1 1 1 148 124 357 296 172 101 203 488 305 181 333 335 426 159 325 301 203 292 228 163 221 341 198 421 131 160 423 373 175 96 85 116 280 220 131 120 260 212 220 484 231 153 1147 1637 1288 1612 977 1517 988 709 500 603 969 725 982 706 2480 2674

8 1 1 1 1 1 1 1 1 173 350 302 256 199 332 480 348 246 374 419 565 225 459 342 244 266 340 270 257 455 284 413 197 250 416 437 265 171 116 187 386 314 163 205 290 282 206 596 253 195 1141 1630 1281 1606 1017 1511 1069 598 647 596 1009 865 975 765 2473 2668

9 1 1 1 1 1 1 1 1 1 285 224 121 169 163 415 410 107 419 451 461 87 355 387 289 394 200 134 149 321 145 348 59 217 350 458 208 154 156 77 247 175 231 123 346 140 326 454 318 80 1075 1565 1216 1540 1063 1445 1133 533 617 530 770 653 910 893 2407 2602

10 1 1 1 1 1 1 1 1 1 1 116 329 414 399 182 676 234 690 605 655 271 544 671 642 572 395 347 167 495 293 177 265 502 96 743 499 477 383 358 448 294 430 423 688 238 505 637 618 205 859 1349 1000 1325 1345 1273 1433 325 840 314 568 584 694 1072 2192 2386

11 1 1 1 1 1 1 1 1 1 1 1 270 359 315 264 592 188 607 522 573 220 460 588 559 524 299 305 106 401 202 170 209 419 154 659 406 410 318 309 366 205 382 365 604 151 457 574 565 148 930 1406 1070 1381 1262 1267 1381 399 639 385 632 560 775 1024 2262 2443

12 1 1 1 1 1 1 1 1 1 1 1 1 101 87 442 430 117 444 353 344 88 242 425 397 374 135 17 194 258 99 353 93 131 395 497 103 166 251 64 196 96 280 103 442 152 362 422 314 136 1103 1561 1258 1536 1100 1450 1070 545 421 574 775 647 922 802 2398 2597

13 1 1 1 1 1 1 1 1 1 1 1 1 1 95 558 323 201 326 251 308 179 206 294 190 279 163 91 280 207 190 476 173 48 544 365 62 54 118 120 187 187 146 74 286 239 236 358 218 220 1195 1670 1377 1645 970 1572 975 662 417 686 893 765 1038 706 2468 2707

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 492 377 193 391 296 276 161 175 371 343 476 89 69 271 172 179 409 162 119 504 443 88 153 234 113 125 158 347 122 388 215 400 326 382 212 1128 1604 1310 1579 1046 1505 1176 595 353 620 826 699 971 904 2402 2641

17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 769 374 783 698 748 398 637 764 735 779 480 485 308 589 386 310 396 595 140 835 593 607 513 542 541 388 560 585 780 355 634 730 748 345 703 1192 842 1167 1439 1406 1568 148 934 157 387 708 536 1201 2035 2230

18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 528 118 398 487 523 385 164 108 155 425 347 610 401 502 686 449 282 781 130 296 308 269 455 442 484 231 375 67 478 206 552 118 491 1405 1881 1587 1856 838 1783 828 872 535 897 1103 976 1249 583 2679 2918

19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 542 435 425 56 323 523 401 467 170 134 100 272 73 290 82 307 310 595 220 226 239 112 211 102 294 168 540 70 400 437 502 65 1041 1498 1175 1474 1198 1388 1318 492 548 490 725 583 868 967 2335 2536

20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 412 500 521 399 122 140 253 439 361 624 415 515 700 458 296 795 100 310 310 296 469 455 498 258 458 165 492 287 711 216 485 1419 1895 1601 1870 763 1796 878 887 419 908 1117 990 1263 567 2759 2932

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 355 438 284 340 328 442 345 266 502 319 386 616 447 212 711 418 250 251 331 371 276 377 314 323 385 428 403 421 384 460 1335 1811 1517 1786 832 1712 1141 802 166 827 1033 905 1179 869 2609 2848

22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 415 102 698 453 586 295 326 501 169 407 665 457 292 760 553 280 325 421 404 248 372 423 359 498 465 511 155 493 456 1889 2372 2215 2348 968 1546 1286 851 218 876 1361 954 1530 1013 2294 3410

23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 313 489 404 448 170 103 135 265 93 326 56 216 337 590 188 203 218 80 203 111 272 139 535 92 379 436 427 72 1061 1534 1202 1509 1165 1423 1194 521 542 517 752 619 898 946 2370 2571

24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 380 351 484 193 225 394 65 305 554 346 190 649 452 179 224 320 298 148 270 321 259 397 363 409 181 391 355 1576 2399 1455 2374 994 1650 1184 740 163 765 971 844 1117 913 2320 3436

25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 167 299 421 342 605 397 497 681 427 278 776 176 291 278 265 450 437 480 226 371 211 474 269 662 240 452 1400 1876 1583 1852 697 1778 924 868 354 893 1099 971 1244 613 2782 2913

26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 132 392 313 436 368 468 653 329 203 747 194 200 180 167 361 408 451 128 251 76 445 124 518 72 355 1372 1847 1553 1823 844 1749 829 839 494 863 1070 943 1216 560 2645 2885

27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 525 356 536 502 602 698 419 317 638 265 289 237 234 390 541 584 175 384 124 528 125 652 71 416 1362 1905 1503 1881 978 1794 881 972 607 818 1203 988 1349 571 2742 2942

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 134 244 136 153 397 196 188 436 492 157 232 388 143 75 118 447 194 437 203 449 304 431 202 1117 1592 1300 1567 1095 1494 1225 584 350 615 815 687 960 953 2390 2629

30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 211 275 116 403 107 113 412 413 85 145 214 69 214 114 245 98 358 170 314 439 296 154 1122 1578 1276 1553 1017 1499 1053 589 404 590 820 697 966 784 2396 2615

31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 351 134 218 125 374 203 677 355 364 290 182 288 163 302 249 622 97 412 514 504 99 968 1468 1108 1444 1280 1315 1320 462 594 424 695 542 838 1036 2300 2506

32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 256 505 305 207 600 468 185 240 337 256 86 220 338 300 413 293 426 195 407 296 1224 1700 1406 1675 989 1602 1201 691 224 716 922 795 1068 929 2316 2737

33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 303 114 261 398 568 261 278 377 118 193 64 402 160 514 82 454 419 435 125 1022 1498 1204 1472 1172 1399 1301 490 505 514 719 595 866 1029 2296 2534

34 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 329 512 217 753 509 561 446 459 458 304 493 503 698 272 637 646 728 268 962 1420 1116 1394 1356 1096 1486 388 850 431 634 615 788 1126 2256 2456

38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 228 331 498 193 164 196 77 244 144 232 136 386 118 352 470 398 67 1056 1546 1196 1522 1102 1426 1172 513 613 511 778 638 890 919 2389 2583

39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 607 349 46 65 161 170 190 273 163 122 260 301 232 357 214 267 1231 1707 1414 1682 952 1609 970 699 350 724 930 802 1076 744 2505 2744

40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 848 604 607 448 487 553 399 495 553 793 304 570 741 748 241 800 1290 940 1265 1450 1313 1563 257 945 256 496 713 635 1136 2133 2327

41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 362 349 336 521 508 551 298 442 178 545 316 796 228 524 1472 1948 1654 1922 729 1849 825 939 518 964 1169 1042 1315 514 2878 2984

42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 79 175 159 164 199 177 113 308 298 246 335 228 239 1228 1704 1411 1680 965 1606 985 696 367 721 927 799 1073 716 2502 2741

45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 82 161 224 238 89 115 237 290 182 391 208 212 1246 1756 1414 1731 953 1657 964 747 418 724 978 824 1124 736 2554 2793

46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 182 311 380 73 200 224 378 166 487 185 194 1173 1663 1313 1638 940 1543 952 630 496 628 888 746 1007 720 2506 2700

47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 183 135 224 76 418 148 324 397 416 119 1178 1654 1294 1628 1109 1555 1173 645 538 604 876 715 1022 818 2452 2691

48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 158 322 226 453 244 465 243 447 234 1177 1652 1359 1628 1111 1555 1241 644 306 669 875 748 1021 969 2401 2690

49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 439 185 496 118 551 383 527 143 1023 1499 1205 1475 1154 1400 1283 491 496 515 722 591 868 1012 2297 2536

50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 179 185 414 119 488 147 274 1220 1710 1360 1685 901 1590 913 896 479 675 1127 882 1054 673 2552 2747

51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 334 203 317 439 280 184 1222 1697 1403 1673 1083 1599 1036 689 445 713 920 755 1066 811 2495 2735

52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 490 163 563 73 433 1417 1892 1599 1868 890 1794 812 884 547 908 1115 988 1261 502 2690 2930

53 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 487 469 496 98 991 1491 1169 1466 1148 1369 1278 458 541 484 689 565 835 1027 2265 2528

56 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 576 109 349 1295 1844 1435 1820 944 1733 978 838 568 750 1071 927 1214 623 2681 2882

57 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 557 468 1784 2267 2110 2243 863 1435 1351 833 265 858 1324 1001 1747 1079 2189 3305

58 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 395 1387 1924 1555 1898 921 1825 785 915 550 865 1145 1019 1292 499 2722 2960

59 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1005 1495 1145 1470 1128 1364 1270 462 573 460 733 580 839 915 2338 2532

14 2 2 2 2 3 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 782 367 622 2384 2012 2204 773 1736 607 424 1339 459 1862 1814 1820

15 3 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 3 2 3 3 3 2 3 3 3 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 3 3 3 2 1 205 101 2867 2496 2680 1235 2452 1048 907 1815 847 2333 2297 1185

54 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 1 153 2450 2299 2386 933 1751 748 743 1520 637 2002 2106 1256

55 3 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3 2 3 3 3 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 3 3 3 2 1 1 1 2843 2471 2655 1210 2427 1022 882 1790 821 2308 2273 1252

62 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 3 4 3 4 2452 1054 1542 759 1552 1949 1646 2347 1014 2789 3905

63 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 3 3 3 3 2582 1441 1768 1528 1702 1238 1906 2222 978 2969

65 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 1 2 3 3 3 3 2 3 1672 1307 1687 1903 1775 2048 373 3478 3718

29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 2 2 1037 244 458 807 603 1400 1834 2272

35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 2 3 1 2 2 2 1061 1267 1022 1414 1035 2374 3489

36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 2 2 2 2 1 2 254 830 417 1317 1874 2084

37 2 2 1 2 2 2 1 2 2 1 1 1 1 1 1 1 2 1 2 2 2 1 2 2 2 2 1 1 1 2 1 1 1 2 1 2 2 2 1 1 1 1 2 2 2 1 2 2 2 1 1 2 1 1 3 2 3 1 2 1 1037 412 1630 1636 1944

43 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 2 1 2 3 2 2 2 2 2 1 2 1 2 1184 1415 2201 2852

44 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 1 2 2 2 1 2 2 2 2 2 2 1 2 1 1 1 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1 1 1 1 1 3 3 3 1 2 1 1 2 1702 1776 1984

64 1 1 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 2 1 1 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 1 1 2 2 1 1 1 2 1 2 1 2 3 3 3 3 2 3 1 2 2 2 2 2 2 3170 3370

60 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 4 3 4 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 4 2 4 3 3 3 2 3 2 4 1658

61 4 4 4 4 4 4 4 3 3 3 3 3 3 4 3 3 4 3 4 4 4 3 4 4 4 4 3 3 3 4 3 3 3 4 3 4 4 4 3 3 3 3 4 4 4 3 4 4 4 3 3 2 2 2 5 4 5 3 4 3 3 4 3 4 2

(a) 4 clusters for relocation with vehicle

60 61 0 1 4 5 10 18 20 21 22 24 25 26 27 32 35 41 52 56 57 58 17 29 36 40 43 2 3 6 7 8 9 11 12 13 16 19 23 28 30 31 33 34 38 39 42 45 46 47 48 49 50 51 53 59 37 44 62 64 65 14 15 54 55 6360 1658 2666 2642 2243 2276 2192 2679 2759 2609 2294 2320 2782 2645 2742 2316 2374 2878 2690 2681 2189 2722 2035 1834 1874 2133 2201 2525 2593 2406 2480 2473 2407 2262 2398 2468 2402 2335 2370 2390 2396 2300 2296 2256 2389 2505 2502 2554 2506 2452 2401 2297 2552 2495 2265 2338 1636 1776 2789 3170 3478 1814 2297 2106 2273 978

61 2 2866 2881 3359 3056 2386 2918 2932 2848 3410 3436 2913 2885 2942 2737 3489 2984 2930 2882 3305 2960 2230 2272 2084 2327 2852 2720 2773 2701 2674 2668 2602 2443 2597 2707 2641 2536 2571 2629 2615 2506 2534 2456 2583 2744 2741 2793 2700 2691 2690 2536 2747 2735 2528 2532 1944 1984 3905 3370 3718 1820 1185 1256 1252 2969

0 3 4 133 643 462 498 160 224 401 509 407 260 92.4 106 424 567 269 109 66.6 574 70.8 715 822 842 563 911 171 224 343 209 232 287 451 352 238 399 371 349 448 316 406 452 621 327 276 248 185 163 314 464 544 116 307 467 342 1162 1198 938 605 887 1372 1829 1527 1804 1718

1 3 4 1 583 403 639 68.4 109 361 449 348 152 78.6 166 365 499 160 77.4 186 515 104 733 835 860 744 940 268 242 284 269 328 373 556 394 287 340 491 487 389 310 574 465 649 413 245 259 271 233 418 404 448 194 338 442 439 1066 1213 830 593 862 1368 1844 1550 1819 1746

4 3 4 1 1 118 578 620 634 460 237 208 710 587 720 167 316 686 632 644 129 626 687 790 822 643 962 620 443 256 474 568 429 503 350 375 320 365 365 239 368 442 347 604 398 362 350 396 539 374 216 313 591 424 398 397 1307 1166 916 1147 1419 1838 2321 1809 2297 1366

5 3 4 1 1 1 518 439 453 343 136 89.4 434 406 539 48.6 248 506 451 463 127 445 611 715 739 623 818 530 325 134 374 478 339 436 288 244 195 303 302 167 305 380 285 529 336 244 223 278 374 283 125 250 376 333 335 334 946 1091 950 967 1238 1552 2019 1430 1994 1625

10 3 3 1 1 1 1 676 690 605 655 544 671 642 572 495 840 743 688 505 637 618 182 325 314 96 584 402 437 459 357 350 285 116 329 414 399 234 271 395 347 167 293 177 265 502 499 477 383 358 448 294 430 423 238 205 568 694 1345 1072 1433 859 1349 1000 1325 1273

18 3 4 1 1 1 1 1 118 398 487 385 164 108 155 401 535 130 67.2 206 552 118 769 872 897 781 976 283 278 320 305 348 410 592 430 323 377 528 523 425 347 610 502 686 449 282 296 308 269 455 442 484 231 375 478 491 1103 1249 838 583 828 1405 1881 1587 1856 1783

20 4 4 1 1 1 1 1 1 412 500 399 122 140 253 415 419 99.6 165 287 711 216 783 887 908 795 990 433 305 334 333 374 419 607 444 326 391 542 521 439 361 624 515 700 458 296 310 310 296 469 455 498 258 458 492 485 1117 1263 763 567 878 1419 1895 1601 1870 1796

21 3 4 1 1 1 1 1 1 1 355 284 340 328 442 319 166 418 385 403 421 384 698 802 827 711 905 446 281 211 335 419 451 522 353 251 296 435 438 345 266 502 386 616 447 212 250 251 331 371 276 377 314 323 428 460 1033 1179 832 869 1141 1335 1811 1517 1786 1712

22 3 4 1 1 1 1 1 1 1 1 102 698 453 586 169 218 553 498 511 155 493 748 851 876 760 954 613 372 185 426 565 461 573 344 308 276 425 415 295 326 501 407 665 457 292 280 325 421 404 248 372 423 359 465 456 1361 1530 968 1013 1286 1889 2372 2215 2348 1546

24 3 4 1 1 1 1 1 1 1 1 1 380 351 484 65.4 163 452 397 409 181 391 637 740 765 649 844 512 271 84.6 325 459 355 460 242 206 175 323 313 193 225 394 305 554 346 190 179 224 320 298 148 270 321 259 363 355 971 1117 994 913 1184 1576 2399 1455 2374 1650

25 4 4 1 1 1 1 1 1 1 1 1 1 167 299 397 354 176 211 269 662 240 764 868 893 776 971 389 274 316 301 342 387 588 425 294 371 523 489 421 342 605 497 681 427 278 291 278 265 450 437 480 226 371 474 452 1099 1244 697 613 924 1400 1876 1583 1852 1778

26 3 4 1 1 1 1 1 1 1 1 1 1 1 132 368 494 194 75.6 124 518 72 735 839 863 747 943 229 175 286 203 244 289 559 397 190 343 401 404 392 313 436 468 653 329 203 200 180 167 361 408 451 128 251 445 355 1070 1216 844 560 829 1372 1847 1553 1823 1749

27 4 4 1 1 1 1 1 1 1 1 1 1 1 1 502 607 265 124 125 652 71.4 779 972 818 638 988 201 264 419 292 266 394 524 374 279 476 467 448 525 356 536 602 698 419 317 289 237 234 390 541 584 175 384 528 416 1203 1349 978 571 881 1362 1905 1503 1881 1794

32 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 224 468 413 426 195 407 589 691 716 600 795 512 287 94.8 341 455 321 401 258 207 172 272 265 136 275 351 256 505 305 207 185 240 337 256 85.8 220 338 300 293 296 922 1068 989 929 1201 1224 1700 1406 1675 1602

35 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 518 547 568 265 550 934 1037 1061 945 1022 612 447 242 500 647 617 639 421 417 353 548 542 350 404 594 505 850 613 350 367 418 496 538 306 496 479 445 541 573 1267 1414 759 1035 1307 1736 2452 1751 2427 1768

41 4 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 178 316 796 228 835 939 964 848 1042 393 344 387 373 437 458 659 497 365 443 595 590 492 413 677 568 753 498 349 362 349 336 521 508 551 298 442 545 524 1169 1315 729 514 825 1472 1948 1654 1922 1849

52 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 163 563 72.6 780 884 908 793 988 251 232 332 260 290 346 604 442 286 388 540 535 437 358 622 514 698 386 260 308 237 224 418 453 496 185 334 490 433 1115 1261 890 502 812 1417 1892 1599 1868 1794

56 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 576 109 634 838 750 570 927 187 224 344 220 206 326 457 362 236 400 400 379 449 314 412 454 637 352 232 246 182 166 324 465 551 119 317 487 349 1071 1214 944 623 978 1295 1844 1435 1820 1733

57 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 557 730 833 858 741 1001 645 438 245 484 596 454 574 422 358 326 437 436 304 439 514 419 646 470 357 335 391 487 397 243 383 488 439 469 468 1324 1747 863 1079 1351 1784 2267 2110 2243 1435

58 4 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 748 915 865 748 1019 199 204 326 231 253 318 565 314 218 382 502 427 431 296 504 435 728 398 214 228 208 185 416 447 527 147 280 496 395 1145 1292 921 499 785 1387 1924 1555 1898 1825

17 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 148 157 140 708 532 629 552 488 480 415 264 442 558 492 374 398 480 485 308 386 310 396 595 593 607 513 542 541 388 560 585 355 345 387 536 1439 1201 1568 703 1192 842 1167 1406

29 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 2 1 244 257 807 650 787 656 709 598 533 399 545 662 595 492 521 584 589 462 490 388 513 699 696 747 630 645 644 491 896 689 458 462 458 603 1542 1400 1672 773 1235 933 1210 1441

36 3 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 256 830 647 683 680 603 596 530 385 574 686 620 490 517 615 590 424 514 431 511 724 721 724 628 604 669 515 675 713 484 460 254 417 1552 1317 1687 607 1048 748 1022 1528

40 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 713 467 503 564 423 416 350 154 395 544 504 310 337 436 412 203 398 217 331 607 604 607 448 487 553 399 495 553 304 241 496 635 1450 1136 1563 800 1290 940 1265 1313

43 3 4 2 2 2 1 1 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 1 1 1 1 804 847 759 725 865 653 560 647 765 699 583 619 687 697 542 595 615 638 802 799 824 746 715 748 591 882 755 565 580 1037 1184 1646 1415 1775 1339 1815 1520 1790 1238

2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 218 447 222 115 224 355 308 256 350 298 277 392 322 310 335 466 250 277 292 219 164 277 439 366 211 304 334 247 888 1027 1065 700 1054 1193 1682 1333 1658 1562

3 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 206 85.8 170 153 433 206 96.6 200 212 189 261 195 285 312 601 164 112 127 43.2 81.6 154 271 314 138 142 313 211 1018 1164 949 692 961 1269 1735 1368 1711 1697

6 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 260 386 245 376 158 122 98.4 248 225 111 141 331 242 469 255 125 100 159 220 196 65.4 195 257 175 279 271 886 1032 990 848 1119 1188 1664 1370 1639 1566

7 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 148 124 296 172 101 203 181 159 228 163 221 198 421 131 160 175 96 84.6 116 280 220 131 120 212 153 969 982 977 706 988 1147 1637 1288 1612 1517

8 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 173 302 256 199 332 246 225 340 270 257 284 413 197 250 265 171 116 187 386 314 163 205 282 195 1009 975 1017 765 1069 1141 1630 1281 1606 1511

9 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 224 121 169 163 107 87 200 134 149 145 348 59.4 217 208 154 156 76.8 247 175 231 123 140 80.4 770 910 1063 893 1133 1075 1565 1216 1540 1445

11 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 270 359 315 188 220 299 305 106 202 170 209 419 406 410 318 309 366 205 382 365 151 148 632 775 1262 1024 1381 930 1406 1070 1381 1267

12 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 101 87 117 88.2 135 16.8 194 99 353 93 131 103 166 251 64.2 196 96 280 103 152 136 775 922 1100 802 1070 1103 1561 1258 1536 1450

13 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 94.8 201 179 163 90.6 280 190 476 173 48 61.8 54 118 120 187 187 146 74.4 239 220 893 1038 970 706 975 1195 1670 1377 1645 1572

16 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 193 161 89.4 69 271 179 409 162 119 88.2 153 234 113 125 158 347 122 215 212 826 971 1046 904 1176 1128 1604 1310 1579 1505

19 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 55.8 170 134 99.6 72.6 290 82.2 307 220 226 239 112 211 102 294 168 70.2 65.4 725 868 1198 967 1318 1041 1498 1175 1474 1388

23 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 170 103 135 93 326 55.8 216 188 203 218 80.4 203 111 272 139 91.8 72 752 898 1165 946 1194 1061 1534 1202 1509 1423

28 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 134 244 153 397 196 188 157 232 388 143 75 118 447 194 203 202 815 960 1095 953 1225 1117 1592 1300 1567 1494

30 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 211 116 403 107 113 85.2 145 214 69 214 114 245 97.8 170 154 820 966 1017 784 1053 1122 1578 1276 1553 1499

31 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 134 218 125 374 355 364 290 182 288 163 302 249 96.6 99 695 838 1280 1036 1320 968 1468 1108 1444 1315

33 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 303 114 261 261 278 377 118 193 63.6 402 160 81.6 125 719 866 1172 1029 1301 1022 1498 1204 1472 1399

34 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 329 512 509 561 446 459 458 304 493 503 272 268 634 788 1356 1126 1486 962 1420 1116 1394 1096

38 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 228 193 164 196 77.4 244 144 232 136 118 66.6 778 890 1102 919 1172 1056 1546 1196 1522 1426

39 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45.6 64.8 161 170 190 273 163 122 301 267 930 1076 952 744 970 1231 1707 1414 1682 1609

42 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 79.2 175 159 164 199 177 113 298 239 927 1073 965 716 985 1228 1704 1411 1680 1606

45 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 81.6 161 224 238 89.4 115 290 212 978 1124 953 736 964 1246 1756 1414 1731 1657

46 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 182 311 380 73.2 200 378 194 888 1007 940 720 952 1173 1663 1313 1638 1543

47 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 183 135 224 76.2 148 119 876 1022 1109 818 1173 1178 1654 1294 1628 1555

48 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 158 322 226 244 234 875 1021 1111 969 1241 1177 1652 1359 1628 1555

49 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 439 185 118 143 722 868 1154 1012 1283 1023 1499 1205 1475 1400

50 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 179 414 274 1127 1054 901 673 913 1220 1710 1360 1685 1590

51 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 203 184 920 1066 1083 811 1036 1222 1697 1403 1673 1599

53 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98.4 689 835 1148 1027 1278 991 1491 1169 1466 1369

59 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 733 839 1128 915 1270 1005 1495 1145 1470 1364

37 2 3 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 1 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 2 2 1 1 412 1949 1630 1903 424 907 743 882 1702

44 2 3 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 1 2 2 2 1 1 2 2 1 1 1 1 2 2 2 2 2 2 1 2 2 1 1 1 2347 1702 2048 459 847 637 821 1906

62 4 5 2 1 2 2 2 1 1 1 2 2 1 1 2 2 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 1014 1054 2384 2867 2450 2843 2452

64 4 4 1 1 2 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 1 2 2 2 2 2 1 1 1 1 1 1 2 1 1 2 2 2 2 1 2 2 2 2 1 1 1 1 1 2 2 1 1 2 2 2 2 2 373 1862 2333 2002 2308 2222

65 4 5 1 1 2 2 2 1 1 2 2 2 2 1 1 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 1 2204 2680 2386 2655 2582

14 3 3 2 2 3 2 1 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 3 3 3 782 367 622 2012

15 3 2 3 3 3 3 2 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 4 3 3 1 205 101 2496

54 3 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 3 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 3 3 3 1 1 153 2299

55 3 2 3 3 3 3 2 3 3 2 3 3 3 3 3 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 4 3 3 1 1 1 2471

63 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3

(b) 6 clusters for relocation with vehicle0 1 5 18 20 21 24 25 26 27 35 41 52 56 58 15 55 63 14 37 44 54 17 29 36 40 43 62 64 65 60 61 4 22 57 2 3 6 7 8 9 10 11 12 13 16 19 23 28 30 31 32 33 34 38 39 42 45 46 47 48 49 50 51 53 59

0 133 462 160 224 401 407 260 92.4 106 567 269 109 66.6 70.8 1829 1804 1718 1372 1162 1198 1527 715 822 842 563 911 938 605 887 2666 2866 643 509 574 171 224 343 209 232 287 498 451 352 238 399 371 349 448 316 406 424 452 621 327 276 248 185 163 314 464 544 116 307 467 342

1 1 403 68.4 109 361 348 152 78.6 166 499 160 77.4 186 104 1844 1819 1746 1368 1066 1213 1550 733 835 860 744 940 830 593 862 2642 2881 583 449 515 268 242 284 269 328 373 639 556 394 287 340 491 487 389 310 574 365 465 649 413 245 259 271 233 418 404 448 194 338 442 439

5 1 1 439 453 343 89.4 434 406 539 248 506 451 463 445 2019 1994 1625 1552 946 1091 1430 611 715 739 623 818 950 967 1238 2276 3056 118 136 127 530 325 134 374 478 339 518 436 288 244 195 303 302 167 305 380 48.6 285 529 336 244 223 278 374 283 125 250 376 333 335 334

18 1 1 1 118 398 385 164 108 155 535 130 67.2 206 118 1881 1856 1783 1405 1103 1249 1587 769 872 897 781 976 838 583 828 2679 2918 620 487 552 283 278 320 305 348 410 676 592 430 323 377 528 523 425 347 610 401 502 686 449 282 296 308 269 455 442 484 231 375 478 491

20 1 1 1 1 412 399 122 140 253 419 99.6 165 287 216 1895 1870 1796 1419 1117 1263 1601 783 887 908 795 990 763 567 878 2759 2932 634 500 711 433 305 334 333 374 419 690 607 444 326 391 542 521 439 361 624 415 515 700 458 296 310 310 296 469 455 498 258 458 492 485

21 1 1 1 1 1 284 340 328 442 166 418 385 403 384 1811 1786 1712 1335 1033 1179 1517 698 802 827 711 905 832 869 1141 2609 2848 460 355 421 446 281 211 335 419 451 605 522 353 251 296 435 438 345 266 502 319 386 616 447 212 250 251 331 371 276 377 314 323 428 460

24 1 1 1 1 1 1 380 351 484 163 452 397 409 391 2399 2374 1650 1576 971 1117 1455 637 740 765 649 844 994 913 1184 2320 3436 208 102 181 512 271 84.6 325 459 355 544 460 242 206 175 323 313 193 225 394 65.4 305 554 346 190 179 224 320 298 148 270 321 259 363 355

25 1 1 1 1 1 1 1 167 299 354 176 211 269 240 1876 1852 1778 1400 1099 1244 1583 764 868 893 776 971 697 613 924 2782 2913 710 698 662 389 274 316 301 342 387 671 588 425 294 371 523 489 421 342 605 397 497 681 427 278 291 278 265 450 437 480 226 371 474 452

26 1 1 1 1 1 1 1 1 132 494 194 75.6 124 72 1847 1823 1749 1372 1070 1216 1553 735 839 863 747 943 844 560 829 2645 2885 587 453 518 229 175 286 203 244 289 642 559 397 190 343 401 404 392 313 436 368 468 653 329 203 200 180 167 361 408 451 128 251 445 355

27 1 1 1 1 1 1 1 1 1 607 265 124 125 71.4 1905 1881 1794 1362 1203 1349 1503 779 972 818 638 988 978 571 881 2742 2942 720 586 652 201 264 419 292 266 394 572 524 374 279 476 467 448 525 356 536 502 602 698 419 317 289 237 234 390 541 584 175 384 528 416

35 1 1 1 1 1 1 1 1 1 1 518 547 568 550 2452 2427 1768 1736 1267 1414 1751 934 1037 1061 945 1022 759 1035 1307 2374 3489 316 218 265 612 447 242 500 647 617 840 639 421 417 353 548 542 350 404 594 224 505 850 613 350 367 418 496 538 306 496 479 445 541 573

41 1 1 1 1 1 1 1 1 1 1 1 178 316 228 1948 1922 1849 1472 1169 1315 1654 835 939 964 848 1042 729 514 825 2878 2984 686 553 796 393 344 387 373 437 458 743 659 497 365 443 595 590 492 413 677 468 568 753 498 349 362 349 336 521 508 551 298 442 545 524

52 1 1 1 1 1 1 1 1 1 1 1 1 163 72.6 1892 1868 1794 1417 1115 1261 1599 780 884 908 793 988 890 502 812 2690 2930 632 498 563 251 232 332 260 290 346 688 604 442 286 388 540 535 437 358 622 413 514 698 386 260 308 237 224 418 453 496 185 334 490 433

56 1 1 1 1 1 1 1 1 1 1 1 1 1 109 1844 1820 1733 1295 1071 1214 1435 634 838 750 570 927 944 623 978 2681 2882 644 511 576 187 224 344 220 206 326 505 457 362 236 400 400 379 449 314 412 426 454 637 352 232 246 182 166 324 465 551 119 317 487 349

58 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1924 1898 1825 1387 1145 1292 1555 748 915 865 748 1019 921 499 785 2722 2960 626 493 557 199 204 326 231 253 318 618 565 314 218 382 502 427 431 296 504 407 435 728 398 214 228 208 185 416 447 527 147 280 496 395

15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 101 2496 782 907 847 205 1192 1235 1048 1290 1815 2867 2333 2680 2297 1185 2321 2372 2267 1682 1735 1664 1637 1630 1565 1349 1406 1561 1670 1604 1498 1534 1592 1578 1468 1700 1498 1420 1546 1707 1704 1756 1663 1654 1652 1499 1710 1697 1491 1495

55 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 1 2471 622 882 821 153 1167 1210 1022 1265 1790 2843 2308 2655 2273 1252 2297 2348 2243 1658 1711 1639 1612 1606 1540 1325 1381 1536 1645 1579 1474 1509 1567 1553 1444 1675 1472 1394 1522 1682 1680 1731 1638 1628 1628 1475 1685 1673 1466 1470

63 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 3 2012 1702 1906 2299 1406 1441 1528 1313 1238 2452 2222 2582 978 2969 1366 1546 1435 1562 1697 1566 1517 1511 1445 1273 1267 1450 1572 1505 1388 1423 1494 1499 1315 1602 1399 1096 1426 1609 1606 1657 1543 1555 1555 1400 1590 1599 1369 1364

14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 3 424 459 367 703 773 607 800 1339 2384 1862 2204 1814 1820 1838 1889 1784 1193 1269 1188 1147 1141 1075 859 930 1103 1195 1128 1041 1061 1117 1122 968 1224 1022 962 1056 1231 1228 1246 1173 1178 1177 1023 1220 1222 991 1005

37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 412 743 387 458 254 496 1037 1949 1630 1903 1636 1944 1307 1361 1324 888 1018 886 969 1009 770 568 632 775 893 826 725 752 815 820 695 922 719 634 778 930 927 978 888 876 875 722 1127 920 689 733

44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 3 1 1 637 536 603 417 635 1184 2347 1702 2048 1776 1984 1166 1530 1747 1027 1164 1032 982 975 910 694 775 922 1038 971 868 898 960 966 838 1068 866 788 890 1076 1073 1124 1007 1022 1021 868 1054 1066 835 839

54 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 3 1 1 1 842 933 748 940 1520 2450 2002 2386 2106 1256 1809 2215 2110 1333 1368 1370 1288 1281 1216 1000 1070 1258 1377 1310 1175 1202 1300 1276 1108 1406 1204 1116 1196 1414 1411 1414 1313 1294 1359 1205 1360 1403 1169 1145

17 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 1 1 148 157 140 708 1439 1201 1568 2035 2230 687 748 730 532 629 552 488 480 415 182 264 442 558 492 374 398 480 485 308 589 386 310 396 595 593 607 513 542 541 388 560 585 355 345

29 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 2 2 1 1 1 2 1 244 257 807 1542 1400 1672 1834 2272 790 851 833 650 787 656 709 598 533 325 399 545 662 595 492 521 584 589 462 691 490 388 513 699 696 747 630 645 644 491 896 689 458 462

36 1 1 1 1 2 1 1 1 1 1 2 2 2 1 1 2 2 2 1 1 1 1 1 1 256 830 1552 1317 1687 1874 2084 822 876 858 647 683 680 603 596 530 314 385 574 686 620 490 517 615 590 424 716 514 431 511 724 721 724 628 604 669 515 675 713 484 460

40 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 1 2 1 1 1 713 1450 1136 1563 2133 2327 643 760 741 467 503 564 423 416 350 96 154 395 544 504 310 337 436 412 203 600 398 217 331 607 604 607 448 487 553 399 495 553 304 241

43 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 1 1 1 1 1646 1415 1775 2201 2852 962 954 1001 804 847 759 725 865 653 584 560 647 765 699 583 619 687 697 542 795 595 615 638 802 799 824 746 715 748 591 882 755 565 580

62 2 1 2 1 1 1 2 1 1 2 1 1 1 2 2 4 4 3 3 3 3 3 2 2 2 2 2 1014 1054 2789 3905 916 968 863 1065 949 990 977 1017 1063 1345 1262 1100 970 1046 1198 1165 1095 1017 1280 989 1172 1356 1102 952 965 953 940 1109 1111 1154 901 1083 1148 1128

64 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 3 3 3 3 2 2 3 2 2 2 2 2 2 373 3170 3370 1147 1013 1079 700 692 848 706 765 893 1072 1024 802 706 904 967 946 953 784 1036 929 1029 1126 919 744 716 736 720 818 969 1012 673 811 1027 915

65 1 1 2 1 1 2 2 2 1 1 2 1 1 2 1 3 3 3 3 3 3 3 2 2 2 2 2 2 1 3478 3718 1419 1286 1351 1054 961 1119 988 1069 1133 1433 1381 1070 975 1176 1318 1194 1225 1053 1320 1201 1301 1486 1172 970 985 964 952 1173 1241 1283 913 1036 1278 1270

60 3 3 3 3 4 3 3 4 3 4 3 4 3 3 4 3 3 2 3 2 2 3 3 3 3 3 3 4 4 4 1658 2243 2294 2189 2525 2593 2406 2480 2473 2407 2192 2262 2398 2468 2402 2335 2370 2390 2396 2300 2316 2296 2256 2389 2505 2502 2554 2506 2452 2401 2297 2552 2495 2265 2338

61 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 4 3 3 3 2 3 3 3 3 4 5 4 5 2 3359 3410 3305 2720 2773 2701 2674 2668 2602 2386 2443 2597 2707 2641 2536 2571 2629 2615 2506 2737 2534 2456 2583 2744 2741 2793 2700 2691 2690 2536 2747 2735 2528 2532

4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 3 2 2 3 1 1 1 1 2 2 2 2 3 4 237 129 620 443 256 474 568 429 578 503 350 375 320 365 365 239 368 442 167 347 604 398 362 350 396 539 374 216 313 591 424 398 397

22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 3 2 2 3 1 1 1 1 2 2 2 2 3 4 1 155 613 372 185 426 565 461 655 573 344 308 276 425 415 295 326 501 169 407 665 457 292 280 325 421 404 248 372 423 359 465 456

57 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 2 2 2 3 1 1 1 1 2 1 2 2 3 4 1 1 645 438 245 484 596 454 637 574 422 358 326 437 436 304 439 514 195 419 646 470 357 335 391 487 397 243 383 488 439 469 468

2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 218 447 222 115 224 402 355 308 256 350 298 277 392 322 310 512 335 466 250 277 292 219 164 277 439 366 211 304 334 247

3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 206 85.8 170 153 437 433 206 96.6 200 212 189 261 195 285 287 312 601 164 112 127 43.2 81.6 154 271 314 138 142 313 211

6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 260 386 245 459 376 158 122 98.4 248 225 111 141 331 94.8 242 469 255 125 100 159 220 196 65.4 195 257 175 279 271

7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 148 124 357 296 172 101 203 181 159 228 163 221 341 198 421 131 160 175 96 84.6 116 280 220 131 120 212 153

8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 173 350 302 256 199 332 246 225 340 270 257 455 284 413 197 250 265 171 116 187 386 314 163 205 282 195

9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 1 285 224 121 169 163 107 87 200 134 149 321 145 348 59.4 217 208 154 156 76.8 247 175 231 123 140 80.4

10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 116 329 414 399 234 271 395 347 167 495 293 177 265 502 499 477 383 358 448 294 430 423 238 205

11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 270 359 315 188 220 299 305 106 401 202 170 209 419 406 410 318 309 366 205 382 365 151 148

12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 1 1 1 1 101 87 117 88.2 135 16.8 194 258 99 353 93 131 103 166 251 64.2 196 96 280 103 152 136

13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 94.8 201 179 163 90.6 280 207 190 476 173 48 61.8 54 118 120 187 187 146 74.4 239 220

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 193 161 89.4 69 271 172 179 409 162 119 88.2 153 234 113 125 158 347 122 215 212

19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 55.8 170 134 99.6 272 72.6 290 82.2 307 220 226 239 112 211 102 294 168 70.2 65.4

23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 170 103 135 265 93 326 55.8 216 188 203 218 80.4 203 111 272 139 91.8 72

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 134 244 136 153 397 196 188 157 232 388 143 75 118 447 194 203 202

30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 211 275 116 403 107 113 85.2 145 214 69 214 114 245 97.8 170 154

31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 351 134 218 125 374 355 364 290 182 288 163 302 249 96.6 99

32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 256 505 305 207 185 240 337 256 85.8 220 338 300 293 296

33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 303 114 261 261 278 377 118 193 63.6 402 160 81.6 125

34 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 329 512 509 561 446 459 458 304 493 503 272 268

38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 228 193 164 196 77.4 244 144 232 136 118 66.6

39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45.6 64.8 161 170 190 273 163 122 301 267

42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 79.2 175 159 164 199 177 113 298 239

45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 81.6 161 224 238 89.4 115 290 212

46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 182 311 380 73.2 200 378 194

47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 1 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 183 135 224 76.2 148 119

48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 158 322 226 244 234

49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 439 185 118 143

50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 179 414 274

51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 203 184

53 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98.4

59 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

(c) 8 clusters for relocation with vehicle

54 35 0 21 56 10 11 19 23 31 33 34 38 49 53 59 17 40 29 36 2 3 6 7 8 13 39 42 45 50 51 61 60 9 12 16 28 30 46 47 48 44 37 64 27 41 58 65 4 22 57 43 1 18 26 62 5 24 32 15 55 14 63 20 25 5254 0 21 56 10 11 19 23 31 33 34 38 49 53 59 17 40 29 36 2 3 6 7 8 13 39 42 45 50 51 61 60 9 12 16 28 30 46 47 48 44 37 64 27 41 58 65 4 22 57 43 1 18 26 62 5 24 32 15 55 14 63 20 25 52 1599

35 2 567 166 568 840 639 548 542 594 505 850 613 496 541 573 934 945 1037 1061 612 447 242 500 647 417 350 367 418 479 445 3489 2374 617 421 353 350 404 496 538 306 1414 1267 1035 607 518 550 1307 316 218 265 1022 499 535 494 759 248 163 224 2452 2427 1736 1768 419 354 547

0 2 1 401 66.6 498 451 371 349 406 452 621 327 544 467 342 715 563 822 842 171 224 343 209 232 238 276 248 185 116 307 2866 2666 287 352 399 448 316 163 314 464 1198 1162 605 106 269 70.8 887 643 509 574 911 133 160 92.4 938 462 407 424 1829 1804 1372 1718 224 260 109

21 2 1 1 403 605 522 435 438 502 386 616 447 377 428 460 698 711 802 827 446 281 211 335 419 251 212 250 251 314 323 2848 2609 451 353 296 345 266 331 371 276 1179 1033 869 442 418 384 1141 460 355 421 905 361 398 328 832 343 284 319 1811 1786 1335 1712 412 340 385

56 2 1 1 1 505 457 400 379 412 454 637 352 551 487 349 634 570 838 750 187 224 344 220 206 236 232 246 182 119 317 2882 2681 326 362 400 449 314 166 324 465 1214 1071 623 125 316 109 978 644 511 576 927 186 206 124 944 463 409 426 1844 1820 1295 1733 287 269 163

10 2 1 1 1 1 116 234 271 167 293 177 265 294 238 205 182 96 325 314 402 437 459 357 350 414 502 499 477 430 423 2386 2192 285 329 399 395 347 383 358 448 694 568 1072 572 743 618 1433 578 655 637 584 639 676 642 1345 518 544 495 1349 1325 859 1273 690 671 688

11 2 1 1 1 1 1 188 220 106 202 170 209 205 151 148 264 154 399 385 355 433 376 296 302 359 419 406 410 382 365 2443 2262 224 270 315 299 305 318 309 366 775 632 1024 524 659 565 1381 503 573 574 560 556 592 559 1262 436 460 401 1406 1381 930 1267 607 588 604

19 2 1 1 1 1 1 1 55.8 99.6 72.6 290 82.2 102 70.2 65.4 374 310 492 490 298 212 248 181 246 201 307 220 226 294 168 2536 2335 107 117 193 170 134 239 112 211 868 725 967 467 595 502 1318 365 425 437 583 491 528 401 1198 303 323 272 1498 1474 1041 1388 542 523 540

23 2 1 1 1 1 1 1 1 135 93 326 55.8 111 91.8 72 398 337 521 517 277 189 225 159 225 179 216 188 203 272 139 2571 2370 87 88.2 161 170 103 218 80.4 203 898 752 946 448 590 427 1194 365 415 436 619 487 523 404 1165 302 313 265 1534 1509 1061 1423 521 489 535

31 2 1 1 1 1 1 1 1 1 134 218 125 163 96.6 99 308 203 462 424 310 285 331 221 257 280 374 355 364 302 249 2506 2300 149 194 271 244 211 290 182 288 838 695 1036 536 677 504 1320 442 501 514 542 574 610 436 1280 380 394 351 1468 1444 968 1315 624 605 622

33 2 1 1 1 1 1 1 1 1 1 303 114 63.6 81.6 125 386 398 490 514 335 312 242 198 284 190 261 261 278 402 160 2534 2296 145 99 179 153 116 377 118 193 866 719 1029 602 568 435 1301 347 407 419 595 465 502 468 1172 285 305 256 1498 1472 1022 1399 515 497 514

34 2 1 1 1 1 1 1 1 1 1 1 329 304 272 268 310 217 388 431 466 601 469 421 413 476 512 509 561 493 503 2456 2256 348 353 409 397 403 446 459 458 788 634 1126 698 753 728 1486 604 665 646 615 649 686 653 1356 529 554 505 1420 1394 962 1096 700 681 698

38 2 1 1 1 1 1 1 1 1 1 1 1 144 118 66.6 396 331 513 511 250 164 255 131 197 173 228 193 164 232 136 2583 2389 59.4 93 162 196 107 196 77.4 244 890 778 919 419 498 398 1172 398 457 470 638 413 449 329 1102 336 346 305 1546 1522 1056 1426 458 427 386

49 2 1 1 1 1 1 1 1 1 1 1 1 1 118 143 388 399 491 515 366 314 195 220 314 187 273 199 238 439 185 2536 2297 175 96 158 118 114 380 135 158 868 722 1012 584 551 527 1283 313 372 383 591 448 484 451 1154 250 270 220 1499 1475 1023 1400 498 480 496

53 2 1 1 1 1 1 1 1 1 1 1 1 1 1 98.4 355 304 458 484 334 313 279 212 282 239 301 298 290 414 203 2528 2265 140 152 215 203 170 378 148 244 835 689 1027 528 545 496 1278 398 465 469 565 442 478 445 1148 335 363 293 1491 1466 991 1369 492 474 490

59 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 345 241 462 460 247 211 271 153 195 220 267 239 212 274 184 2532 2338 80.4 136 212 202 154 194 119 234 839 733 915 416 524 395 1270 397 456 468 580 439 491 355 1128 334 355 296 1495 1470 1005 1364 485 452 433

17 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 140 148 157 532 629 552 488 480 558 595 593 607 560 585 2230 2035 415 442 492 480 485 513 542 541 536 387 1201 779 835 748 1568 687 748 730 708 733 769 735 1439 611 637 589 1192 1167 703 1406 783 764 780

40 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 257 256 467 503 564 423 416 544 607 604 607 495 553 2327 2133 350 395 504 436 412 448 487 553 635 496 1136 638 848 748 1563 643 760 741 713 744 781 747 1450 623 649 600 1290 1265 800 1313 795 776 793

29 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 244 650 787 656 709 598 662 699 696 747 896 689 2272 1834 533 545 595 584 589 630 645 644 603 458 1400 972 939 915 1672 790 851 833 807 835 872 839 1542 715 740 691 1235 1210 773 1441 887 868 884

36 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 647 683 680 603 596 686 724 721 724 675 713 2084 1874 530 574 620 615 590 628 604 669 417 254 1317 818 964 865 1687 822 876 858 830 860 897 863 1552 739 765 716 1048 1022 607 1528 908 893 908

2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 218 447 222 115 256 277 292 219 211 304 2720 2525 224 308 350 392 322 164 277 439 1027 888 700 201 393 199 1054 620 613 645 804 268 283 229 1065 530 512 512 1682 1658 1193 1562 433 389 251

3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 206 85.8 170 96.6 112 127 43.2 138 142 2773 2593 153 206 200 261 195 81.6 154 271 1164 1018 692 264 344 204 961 443 372 438 847 242 278 175 949 325 271 287 1735 1711 1269 1697 305 274 232

6 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 260 386 122 125 100 159 257 175 2701 2406 245 158 98.4 111 141 220 196 65.4 1032 886 848 419 387 326 1119 256 185 245 759 284 320 286 990 134 84.6 94.8 1664 1639 1188 1566 334 316 332

7 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 148 101 160 175 96 131 120 2674 2480 124 172 203 228 163 84.6 116 280 982 969 706 292 373 231 988 474 426 484 725 269 305 203 977 374 325 341 1637 1612 1147 1517 333 301 260

8 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 199 250 265 171 163 205 2668 2473 173 256 332 340 270 116 187 386 975 1009 765 266 437 253 1069 568 565 596 865 328 348 244 1017 478 459 455 1630 1606 1141 1511 374 342 290

13 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 48 61.8 54 146 74.4 2707 2468 169 101 94.8 163 90.6 118 120 187 1038 893 706 279 365 218 975 375 308 358 765 287 323 190 970 244 206 207 1670 1645 1195 1572 326 294 286

39 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45.6 64.8 163 122 2744 2505 217 131 119 188 113 161 170 190 1076 930 744 317 349 214 970 362 292 357 802 245 282 203 952 244 190 207 1707 1682 1231 1609 296 278 260

42 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 79.2 177 113 2741 2502 208 103 88.2 157 85.2 175 159 164 1073 927 716 289 362 228 985 350 280 335 799 259 296 200 965 223 179 185 1704 1680 1228 1606 310 291 308

45 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 89.4 115 2793 2554 154 166 153 232 145 81.6 161 224 1124 978 736 237 349 208 964 396 325 391 824 271 308 180 953 278 224 240 1756 1731 1246 1657 310 278 237

50 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 179 2747 2552 231 280 347 447 245 73.2 224 322 1054 1127 673 175 298 147 913 591 423 488 882 194 231 128 901 376 321 338 1710 1685 1220 1590 258 226 185

51 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2735 2495 123 103 122 194 97.8 200 76.2 226 1066 920 811 384 442 280 1036 424 359 439 755 338 375 251 1083 333 259 300 1697 1673 1222 1599 458 371 334

61 2 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 3 3 4 4 4 4 4 4 1658 2602 2597 2641 2629 2615 2700 2691 2690 1984 1944 3370 2942 2984 2960 3718 3359 3410 3305 2852 2881 2918 2885 3905 3056 3436 2737 1185 1252 1820 2969 2932 2913 2930

60 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2407 2398 2402 2390 2396 2506 2452 2401 1776 1636 3170 2742 2878 2722 3478 2243 2294 2189 2201 2642 2679 2645 2789 2276 2320 2316 2297 2273 1814 978 2759 2782 2690

9 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 121 163 200 134 156 76.8 247 910 770 893 394 458 318 1133 429 461 454 653 373 410 289 1063 339 355 321 1565 1540 1075 1445 419 387 346

12 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 87 135 16.8 251 64.2 196 922 775 802 374 497 314 1070 350 344 422 647 394 430 397 1100 288 242 258 1561 1536 1103 1450 444 425 442

16 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 89.4 69 234 113 125 971 826 904 476 443 382 1176 320 276 326 699 340 377 343 1046 195 175 172 1604 1579 1128 1505 391 371 388

28 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 134 388 143 75 960 815 953 525 492 431 1225 239 295 304 687 389 425 392 1095 167 193 136 1592 1567 1117 1494 439 421 437

30 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 214 69 214 966 820 784 356 413 296 1053 368 326 439 697 310 347 313 1017 305 225 275 1578 1553 1122 1499 361 342 358

46 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 182 311 1007 888 720 234 336 185 952 539 421 487 746 233 269 167 940 374 320 337 1663 1638 1173 1543 296 265 224

47 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 183 1022 876 818 390 521 416 1173 374 404 397 715 418 455 361 1109 283 298 256 1654 1628 1178 1555 469 450 418

48 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1021 875 969 541 508 447 1241 216 248 243 748 404 442 408 1111 125 148 85.8 1652 1628 1177 1555 455 437 453

44 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 412 1702 1349 1315 1292 2048 1166 1530 1747 1184 1213 1249 1216 2347 1091 1117 1068 847 821 459 1906 1263 1244 1261

37 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 2 2 2 2 3 2 1 1 1 1 1 1 1 1 1 1630 1203 1169 1145 1903 1307 1361 1324 1037 1066 1103 1070 1949 946 971 922 907 882 424 1702 1117 1099 1115

64 3 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 2 2 1 1 1 2 2 2 571 514 499 373 1147 1013 1079 1415 593 583 560 1014 967 913 929 2333 2308 1862 2222 567 613 502

27 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 2 2 1 265 71.4 881 720 586 652 988 166 155 132 978 539 484 502 1905 1881 1362 1794 253 299 124

41 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 2 2 1 1 228 825 686 553 796 1042 160 130 194 729 506 452 468 1948 1922 1472 1849 99.6 176 178

58 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 2 2 1 1 1 785 626 493 557 1019 104 118 72 921 445 391 407 1924 1898 1387 1825 216 240 72.6

65 3 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 4 2 2 2 2 2 2 2 2 3 3 1 1 1 1 1419 1286 1351 1775 862 828 829 1054 1238 1184 1201 2680 2655 2204 2582 878 924 812

4 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 237 129 962 583 620 587 916 118 208 167 2321 2297 1838 1366 634 710 632

22 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 155 954 449 487 453 968 136 102 169 2372 2348 1889 1546 500 698 498

57 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1001 515 552 518 863 127 181 195 2267 2243 1784 1435 711 662 563

43 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 940 976 943 1646 818 844 795 1815 1790 1339 1238 990 971 988

1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 68.4 78.6 830 403 348 365 1844 1819 1368 1746 109 152 77.4

18 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 108 838 439 385 401 1881 1856 1405 1783 118 164 67.2

26 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 844 406 351 368 1847 1823 1372 1749 140 167 75.6

62 3 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 4 2 2 2 2 2 2 2 2 3 3 2 2 1 2 2 2 2 1 2 1 1 1 950 994 989 2867 2843 2384 2452 763 697 890

5 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 2 89.4 48.6 2019 1994 1552 1625 453 434 451

24 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 2 1 65.4 2399 2374 1576 1650 399 380 397

32 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1700 1675 1224 1602 415 397 413

15 1 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 1 2 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 2 101 782 2496 1895 1876 1892

55 1 3 3 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 1 1 3 3 3 3 3 3 3 3 2 3 3 3 4 3 3 2 1 622 2471 1870 1852 1868

14 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 1 1 3 2 2 2 3 3 3 2 2 2 2 2 3 2 2 2 1 1 2012 1419 1400 1417

63 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 3 2 3 2 3 3 3 2 2 2 2 2 2 2 3 2 2 2 3 3 3 1796 1778 1794

20 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 3 2 2 122 165

25 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 3 3 2 2 1 211

52 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 3 2 2 1 1

(d) 24 clusters for relocation with vehicle11 19 23 31 33 34 38 49 53 59 4 22 32 56 44 25 17 64 3 39 42 45 50 51 43 0 14 20 65 54 41 15 40 55 57 63 2 6 13 7 8 27 58 9 12 30 46 47 60 16 28 48 61 52 35 36 29 1 18 26 62 37 21 5 24 10

11 188 220 106 202 170 209 205 151 148 503 573 401 457 775 588 264 1024 433 419 406 410 382 365 560 451 930 607 1381 1070 659 1406 154 1381 574 1267 355 376 359 296 302 524 565 224 270 305 318 309 2262 315 299 366 2443 604 639 385 399 556 592 559 1262 632 522 436 460 116

19 1 55.8 99.6 72.6 290 82.2 102 70.2 65.4 365 425 272 400 868 523 374 967 212 307 220 226 294 168 583 371 1041 542 1318 1175 595 1498 310 1474 437 1388 298 248 201 181 246 467 502 107 117 134 239 112 2335 193 170 211 2536 540 548 490 492 491 528 401 1198 725 435 303 323 234

23 1 1 135 93 326 55.8 111 91.8 72 365 415 265 379 898 489 398 946 189 216 188 203 272 139 619 349 1061 521 1194 1202 590 1534 337 1509 436 1423 277 225 179 159 225 448 427 87 88.2 103 218 80.4 2370 161 170 203 2571 535 542 517 521 487 523 404 1165 752 438 302 313 271

31 1 1 1 134 218 125 163 96.6 99 442 501 351 412 838 605 308 1036 285 374 355 364 302 249 542 406 968 624 1320 1108 677 1468 203 1444 514 1315 310 331 280 221 257 536 504 149 194 211 290 182 2300 271 244 288 2506 622 594 424 462 574 610 436 1280 695 502 380 394 167

33 1 1 1 1 303 114 63.6 81.6 125 347 407 256 454 866 497 386 1029 312 261 261 278 402 160 595 452 1022 515 1301 1204 568 1498 398 1472 419 1399 335 242 190 198 284 602 435 145 99 116 377 118 2296 179 153 193 2534 514 505 514 490 465 502 468 1172 719 386 285 305 293

34 1 1 1 1 1 329 304 272 268 604 665 505 637 788 681 310 1126 601 512 509 561 493 503 615 621 962 700 1486 1116 753 1420 217 1394 646 1096 466 469 476 421 413 698 728 348 353 403 446 459 2256 409 397 458 2456 698 850 431 388 649 686 653 1356 634 616 529 554 177

38 1 1 1 1 1 1 144 118 66.6 398 457 305 352 890 427 396 919 164 228 193 164 232 136 638 327 1056 458 1172 1196 498 1546 331 1522 470 1426 250 255 173 131 197 419 398 59.4 93 107 196 77.4 2389 162 196 244 2583 386 613 511 513 413 449 329 1102 778 447 336 346 265

49 1 1 1 1 1 1 1 118 143 313 372 220 551 868 480 388 1012 314 273 199 238 439 185 591 544 1023 498 1283 1205 551 1499 399 1475 383 1400 366 195 187 220 314 584 527 175 96 114 380 135 2297 158 118 158 2536 496 496 515 491 448 484 451 1154 722 377 250 270 294

53 1 1 1 1 1 1 1 1 98.4 398 465 293 487 835 474 355 1027 313 301 298 290 414 203 565 467 991 492 1278 1169 545 1491 304 1466 469 1369 334 279 239 212 282 528 496 140 152 170 378 148 2265 215 203 244 2528 490 541 484 458 442 478 445 1148 689 428 335 363 238

59 1 1 1 1 1 1 1 1 1 397 456 296 349 839 452 345 915 211 267 239 212 274 184 580 342 1005 485 1270 1145 524 1495 241 1470 468 1364 247 271 220 153 195 416 395 80.4 136 154 194 119 2338 212 202 234 2532 433 573 460 462 439 491 355 1128 733 460 334 355 205

4 1 1 1 1 1 1 1 1 1 1 237 167 644 1166 710 687 1147 443 362 350 396 591 424 962 643 1838 634 1419 1809 686 2321 643 2297 129 1366 620 256 375 474 568 720 626 429 350 368 539 374 2243 320 239 216 3359 632 316 822 790 583 620 587 916 1307 460 118 208 578

22 1 1 1 1 1 1 1 1 1 1 1 169 511 1530 698 748 1013 372 292 280 325 423 359 954 509 1889 500 1286 2215 553 2372 760 2348 155 1546 613 185 308 426 565 586 493 461 344 326 421 404 2294 276 295 248 3410 498 218 876 851 449 487 453 968 1361 355 136 102 655

32 1 1 1 1 1 1 1 1 1 1 1 1 426 1068 397 589 929 287 207 185 240 338 300 795 424 1224 415 1201 1406 468 1700 600 1675 195 1602 512 94.8 207 341 455 502 407 321 258 275 337 256 2316 172 136 85.8 2737 413 224 716 691 365 401 368 989 922 319 48.6 65.4 495

56 1 1 1 1 1 1 1 1 1 1 1 1 1 1214 269 634 623 224 232 246 182 119 317 927 66.6 1295 287 978 1435 316 1844 570 1820 576 1733 187 344 236 220 206 125 109 326 362 314 166 324 2681 400 449 465 2882 163 568 750 838 186 206 124 944 1071 403 463 409 505

44 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1244 536 1702 1164 1076 1073 1124 1054 1066 1184 1198 459 1263 2048 637 1315 847 635 821 1747 1906 1027 1032 1038 982 975 1349 1292 910 922 966 1007 1022 1776 971 960 1021 1984 1261 1414 417 603 1213 1249 1216 2347 412 1179 1091 1117 694

25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 764 613 274 278 291 278 226 371 971 260 1400 122 924 1583 176 1876 776 1852 662 1778 389 316 294 301 342 299 240 387 425 342 265 450 2782 371 421 437 2913 211 354 893 868 152 164 167 697 1099 340 434 380 671

17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1201 629 595 593 607 560 585 708 715 703 783 1568 842 835 1192 140 1167 730 1406 532 552 558 488 480 779 748 415 442 485 513 542 2035 492 480 541 2230 780 934 157 148 733 769 735 1439 387 698 611 637 182

64 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 692 744 716 736 673 811 1415 605 1862 567 373 2002 514 2333 1136 2308 1079 2222 700 848 706 706 765 571 499 893 802 784 720 818 3170 904 953 969 3370 502 1035 1317 1400 593 583 560 1014 1630 869 967 913 1072

3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 112 127 43.2 138 142 847 224 1269 305 961 1368 344 1735 503 1711 438 1697 218 206 96.6 85.8 170 264 204 153 206 195 81.6 154 2593 200 261 271 2773 232 447 683 787 242 278 175 949 1018 281 325 271 437

39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 45.6 64.8 163 122 802 276 1231 296 970 1414 349 1707 607 1682 357 1609 277 125 48 160 250 317 214 217 131 113 161 170 2505 119 188 190 2744 260 350 724 699 245 282 203 952 930 212 244 190 502

42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 79.2 177 113 799 248 1228 310 985 1411 362 1704 604 1680 335 1606 292 100 61.8 175 265 289 228 208 103 85.2 175 159 2502 88.2 157 164 2741 308 367 721 696 259 296 200 965 927 250 223 179 499

45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 89.4 115 824 185 1246 310 964 1414 349 1756 607 1731 391 1657 219 159 54 96 171 237 208 154 166 145 81.6 161 2554 153 232 224 2793 237 418 724 747 271 308 180 953 978 251 278 224 477

50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 179 882 116 1220 258 913 1360 298 1710 495 1685 488 1590 211 257 146 131 163 175 147 231 280 245 73.2 224 2552 347 447 322 2747 185 479 675 896 194 231 128 901 1127 314 376 321 430

51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 755 307 1222 458 1036 1403 442 1697 553 1673 439 1599 304 175 74.4 120 205 384 280 123 103 97.8 200 76.2 2495 122 194 226 2735 334 445 713 689 338 375 251 1083 920 323 333 259 423

43 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 1 2 1 1 1 1 1 1 911 1339 990 1775 1520 1042 1815 713 1790 1001 1238 804 759 765 725 865 988 1019 653 647 697 746 715 2201 699 687 748 2852 988 1022 830 807 940 976 943 1646 1037 905 818 844 584

0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1372 224 887 1527 269 1829 563 1804 574 1718 171 343 238 209 232 106 70.8 287 352 316 163 314 2666 399 448 464 2866 109 567 842 822 133 160 92.4 938 1162 401 462 407 498

14 2 2 2 2 2 2 2 2 2 2 3 3 2 2 1 2 1 3 2 2 2 2 2 2 2 2 1419 2204 367 1472 782 800 622 1784 2012 1193 1188 1195 1147 1141 1362 1387 1075 1103 1122 1173 1178 1814 1128 1117 1177 1820 1417 1736 607 773 1368 1405 1372 2384 424 1335 1552 1576 859

20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 878 1601 99.6 1895 795 1870 711 1796 433 334 326 333 374 253 216 419 444 361 296 469 2759 391 439 455 2932 165 419 908 887 109 118 140 763 1117 412 453 399 690

65 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 2 2 2 2 2 2 2 1 3 1 2386 825 2680 1563 2655 1351 2582 1054 1119 975 988 1069 881 785 1133 1070 1053 952 1173 3478 1176 1225 1241 3718 812 1307 1687 1672 862 828 829 1054 1903 1141 1238 1184 1433

54 2 2 2 2 2 2 2 2 2 2 3 3 2 2 1 2 1 3 2 2 2 2 2 2 2 2 1 2 3 1654 205 940 153 2110 2299 1333 1370 1377 1288 1281 1503 1555 1216 1258 1276 1313 1294 2106 1310 1300 1359 1256 1599 1751 748 933 1550 1587 1553 2450 743 1517 1430 1455 1000

41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1948 848 1922 796 1849 393 387 365 373 437 265 228 458 497 413 336 521 2878 443 492 508 2984 178 518 964 939 160 130 194 729 1169 418 506 452 743

15 2 2 2 2 2 2 2 2 2 2 3 3 2 3 1 3 2 3 2 2 2 2 2 2 3 3 1 3 3 1 3 1290 101 2267 2496 1682 1664 1670 1637 1630 1905 1924 1565 1561 1578 1663 1654 2297 1604 1592 1652 1185 1892 2452 1048 1235 1844 1881 1847 2867 907 1811 2019 2399 1349

40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1265 741 1313 467 564 544 423 416 638 748 350 395 412 448 487 2133 504 436 553 2327 793 945 256 257 744 781 747 1450 496 711 623 649 96

55 2 2 2 2 2 2 2 2 2 2 3 3 2 3 1 3 2 3 2 2 2 2 2 2 2 3 1 3 3 1 3 1 2 2243 2471 1658 1639 1645 1612 1606 1881 1898 1540 1536 1553 1638 1628 2273 1579 1567 1628 1252 1868 2427 1022 1210 1819 1856 1823 2843 882 1786 1994 2374 1325

57 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 2 1 2 3 1 3 1 3 1435 645 245 358 484 596 652 557 454 422 439 487 397 2189 326 304 243 3305 563 265 858 833 515 552 518 863 1324 421 127 181 637

63 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 3 2 3 3 3 3 2 3 2 1562 1566 1572 1517 1511 1794 1825 1445 1450 1499 1543 1555 978 1505 1494 1555 2969 1794 1768 1528 1441 1746 1783 1749 2452 1702 1712 1625 1650 1273

2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 447 256 222 115 201 199 224 308 322 164 277 2525 350 392 439 2720 251 612 647 650 268 283 229 1065 888 446 530 512 402

6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 122 260 386 419 326 245 158 141 220 196 2406 98.4 111 65.4 2701 332 242 680 656 284 320 286 990 886 211 134 84.6 459

13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 101 199 279 218 169 101 90.6 118 120 2468 94.8 163 187 2707 286 417 686 662 287 323 190 970 893 251 244 206 414

7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 148 292 231 124 172 163 84.6 116 2480 203 228 280 2674 260 500 603 709 269 305 203 977 969 335 374 325 357

8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 266 253 173 256 270 116 187 2473 332 340 386 2668 290 647 596 598 328 348 244 1017 1009 419 478 459 350

27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 2 1 1 1 1 1 71.4 394 374 356 234 390 2742 476 525 541 2942 124 607 818 972 166 155 132 978 1203 442 539 484 572

58 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 3 1 1 1 1 1 1 318 314 296 185 416 2722 382 431 447 2960 72.6 550 865 915 104 118 72 921 1145 384 445 391 618

9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 121 134 156 76.8 2407 163 200 247 2602 346 617 530 533 373 410 289 1063 770 451 339 355 285

12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 16.8 251 64.2 2398 87 135 196 2597 442 421 574 545 394 430 397 1100 775 353 288 242 329

30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 214 69 2396 69 134 214 2615 358 404 590 589 310 347 313 1017 820 266 305 225 347

46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 182 2506 234 388 311 2700 224 496 628 630 233 269 167 940 888 331 374 320 383

47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2452 113 143 183 2691 418 538 604 645 418 455 361 1109 876 371 283 298 358

60 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 4 3 4 3 3 3 3 3 3 3 3 3 4 4 3 4 3 3 3 3 2 3 3 3 3 3 4 4 3 3 3 3 3 2402 2390 2401 1658 2690 2374 1874 1834 2642 2679 2645 2789 1636 2609 2276 2320 2192

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 89.4 125 2641 388 353 620 595 340 377 343 1046 826 296 195 175 399

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 75 2629 437 350 615 584 389 425 392 1095 815 345 167 193 395

48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2690 453 306 669 644 404 442 408 1111 875 276 125 148 448

61 3 3 3 3 3 3 3 3 3 3 4 4 4 4 3 4 3 4 4 4 4 4 4 4 4 4 3 4 5 2 4 2 3 2 4 4 4 4 4 3 3 4 4 3 3 3 3 3 2 3 3 3 2930 3489 2084 2272 2881 2918 2885 3905 1944 2848 3056 3436 2386

52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 547 908 884 77.4 67.2 75.6 890 1115 385 451 397 688

35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 2 1 2 1 2 2 1 3 2 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1061 1037 499 535 494 759 1267 166 248 163 840

36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 2 2 244 860 897 863 1552 254 827 739 765 314

29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 1 2 1 1 1 1 1 2 2 1 1 1 1 1 3 1 1 1 3 1 2 1 835 872 839 1542 458 802 715 740 325

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 68.4 78.6 830 1066 361 403 348 639

18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 1 108 838 1103 398 439 385 676

26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 1 1 844 1070 328 406 351 642

62 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 2 2 2 2 2 2 2 2 2 2 3 1 2 3 1 4 2 4 1 3 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 5 1 1 2 2 1 1 1 1949 832 950 994 1345

37 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 3 1 2 2 1 1 2 2 1 1 1 2 2 2 2 1 1 1 1 1 2 1 1 1 3 2 2 1 1 2 2 2 3 1033 946 971 568

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 2 2 1 3 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 1 1 1 1 2 343 284 605

5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 1 1 1 2 2 1 89.4 518

24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 4 1 1 1 1 1 1 1 2 2 1 1 544

10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 2 1 1 1 1

(e) 36 clusters for relocation with vehicle

0 3 5 6 7 8 9 12 13 16 19 23 24 26 28 30 31 32 33 38 39 42 45 46 47 48 49 50 51 53 56 58 59 62 65 10 11 17 34 40 43 63 60 61 1 2 18 20 25 27 41 52 14 37 44 4 21 22 35 57 64 15 54 55 29 360 369 804 587 421 477 576 575 397 580 783 696 708 124 768 540 808 742 786 681 338 420 398 358 590 736 856 260 523 851 135 120 714 1705 1507 1053 919 1311 1176 1131 1401 3583 5701 5666 218 303 290 370 463 213 393 164 2639 2014 2330 1047 750 842 985 971 1004 3460 2926 3297 1649 1547

3 1 659 392 142 249 257 406 244 407 425 377 546 348 538 371 534 598 515 328 223 251 85.3 126 321 573 537 149 254 471 233 404 391 1797 1780 831 609 1089 924 909 1148 3331 5478 5444 486 344 566 568 544 483 689 433 2417 1792 2108 1011 639 680 945 827 1276 3238 2704 3075 1427 1325

5 1 1 251 624 832 768 534 484 360 606 615 173 783 348 513 730 97 580 648 456 431 538 686 649 234 510 776 536 682 847 840 678 2232 2215 1048 858 1306 1150 1125 1375 3557 5695 5660 921 1029 1001 1003 979 960 1124 868 2634 2009 2324 244 592 196 578 219 1712 3455 2921 3291 1644 1542

6 1 1 1 409 537 516 326 257 148 484 443 168 567 208 299 608 190 458 571 239 200 306 467 376 130 389 485 321 561 569 623 557 2015 1998 926 736 1184 1029 1004 1253 3435 5574 5539 704 676 784 787 763 744 907 651 2512 1887 2203 495 412 302 591 434 1495 3333 2799 3170 1522 1420

7 1 1 1 1 175 171 320 172 321 361 328 569 401 480 285 448 553 429 279 268 296 181 95.3 235 487 479 202 168 407 285 457 305 1849 1832 745 523 1002 837 822 1062 3244 5392 5357 538 352 618 621 597 536 741 485 2330 1706 2021 925 662 702 968 792 1329 3152 2618 2988 1341 1239

8 1 1 1 1 1 240 452 300 450 438 446 697 458 653 382 397 761 537 335 396 424 307 176 348 696 597 281 278 472 267 514 328 1906 1890 642 508 900 765 720 990 3172 5289 5254 596 204 676 678 654 553 799 543 2228 1603 1918 1014 790 830 1096 1000 1386 3049 2515 2886 1238 1136

9 1 1 1 1 1 1 234 279 307 216 204 676 556 431 243 302 697 314 118 375 403 288 239 117 579 374 361 216 263 441 612 161 2004 1987 585 378 843 679 663 904 3086 5232 5197 693 408 774 776 752 705 897 640 2171 1546 1861 883 769 809 1075 935 1484 2992 2458 2829 1181 1079

12 1 1 1 1 1 1 1 190 152 224 144 480 554 249 34.6 348 463 198 187 227 205 298 393 114 396 193 526 179 301 583 611 281 2003 1986 663 476 921 769 740 993 3175 5310 5282 692 645 772 774 750 769 895 639 2249 1624 1939 701 579 613 879 701 1483 3070 2536 2913 1259 1157

13 1 1 1 1 1 1 1 1 191 395 304 397 377 374 155 505 413 389 334 117 131 104 259 208 357 378 379 84.4 478 450 433 421 1825 1808 859 633 1117 948 937 1172 3354 5506 5472 514 477 594 597 573 554 717 461 2445 1820 2136 728 491 531 797 652 1305 3266 2732 3103 1455 1353

16 1 1 1 1 1 1 1 1 1 384 301 325 559 179 124 508 289 358 362 268 190 301 409 245 223 321 528 234 461 599 616 464 2008 1991 880 636 1138 983 958 1207 3389 5528 5493 697 626 777 780 756 771 900 644 2466 1841 2157 604 448 459 752 528 1488 3287 2753 3124 1476 1374

19 1 1 1 1 1 1 1 1 1 1 102 649 763 269 259 160 535 145 154 471 465 410 446 198 416 205 564 333 121 667 819 126 2211 2194 461 292 754 564 573 788 2970 5143 5108 900 606 980 983 959 903 1103 847 2082 1457 1772 721 839 764 1110 773 1691 2903 2369 2739 1092 990

23 1 1 1 1 1 1 1 1 1 1 1 624 675 277 171 226 544 176 73 377 342 362 413 102 425 221 484 245 179 567 732 143 2124 2107 555 354 813 647 633 871 3054 5203 5168 813 614 893 896 872 817 1016 760 2141 1516 1832 730 716 740 1016 782 1604 2962 2428 2799 1151 1049

24 1 1 1 1 1 1 1 1 1 1 1 1 688 372 445 772 131 623 695 360 327 447 634 597 288 553 625 481 725 710 744 721 2136 2120 1091 900 1348 1193 1168 1417 3600 5738 5701 826 843 906 908 884 865 1029 773 2676 2052 2367 417 480 134 411 340 1616 3498 2964 3334 1686 1584

26 1 1 1 1 1 1 1 1 1 1 1 1 1 747 520 788 722 766 660 318 399 374 338 570 715 836 240 503 831 183 144 694 1591 1518 1033 898 1291 1156 1110 1380 3563 5680 5645 152 411 249 266 338 264 318 103 2619 1994 2309 1027 678 822 913 951 1015 3440 2906 3276 1629 1527

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 283 392 277 243 310 345 309 470 567 288 156 173 646 369 345 828 804 341 2196 2179 711 520 968 813 788 1037 3220 5358 5323 885 821 965 968 944 889 1088 832 2296 1672 1987 477 537 506 778 515 1676 3117 2584 2954 1306 1204

30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 383 442 232 214 192 171 261 355 123 403 227 492 162 335 545 576 316 1968 1951 698 510 955 803 775 1028 3210 5345 5310 657 558 737 740 716 735 860 604 2283 1659 1964 722 545 579 844 681 1448 3104 2571 2941 1293 1191

31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 659 267 227 601 589 513 476 322 540 319 630 437 194 660 844 159 2236 2219 343 163 624 435 443 659 2841 5013 4978 925 565 1005 1008 984 894 1128 872 1952 1327 1642 845 963 888 1233 897 1716 2773 2239 2610 962 860

32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 509 577 394 370 476 640 578 164 439 714 465 611 831 778 607 2170 2153 977 786 1235 1079 1054 1304 3486 5624 5589 859 958 939 942 918 898 1062 806 2563 1938 2253 341 552 265 536 264 1650 3384 2850 3220 1573 1471

33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 228 425 403 433 515 213 390 73.7 634 328 160 765 822 225 2214 2197 500 346 852 618 672 842 3024 5242 5207 903 705 984 986 962 973 1107 850 2180 1555 1871 695 777 738 1048 747 1694 3001 2467 2838 1061 1088

38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 430 458 343 398 139 458 254 435 266 231 552 717 97.1 2112 2092 502 313 759 605 579 830 3012 5149 5114 798 502 878 880 856 773 1001 745 2088 1463 1778 763 789 829 1095 815 1589 2909 2375 2745 1098 996

39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 71.9 130 334 297 395 420 235 180 548 336 374 519 1766 1749 955 729 1213 1043 1032 1268 3450 5602 5567 455 543 535 538 514 494 658 402 2541 1916 2231 699 446 494 760 623 1246 3362 2828 3198 1551 1449

42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 159 361 325 356 398 337 208 541 420 456 545 1848 1831 983 716 1241 1071 1060 1295 3478 5630 5595 537 570 617 620 596 576 740 484 2568 1944 2250 675 412 461 726 599 1328 3390 2860 3226 1579 1477

45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 162 254 466 474 178 190 487 263 434 430 1819 1809 868 641 1125 956 945 1180 3363 5515 5480 516 444 596 591 567 513 710 462 2453 1829 2144 782 532 581 847 705 1305 3274 2742 3111 1463 1361

46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 318 574 565 147 252 514 222 394 377 1786 1769 721 586 979 844 798 1068 3251 5368 5333 475 271 555 558 534 473 678 422 2307 1682 1997 1011 727 767 1033 879 1266 3128 2594 2964 1317 1215

47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 460 256 440 148 275 508 626 236 2018 2001 655 450 912 743 732 967 3150 5302 5267 707 534 787 790 766 772 910 654 2240 1616 1931 764 690 731 996 817 1498 3061 2528 2898 1250 1148

48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 321 694 399 493 765 772 489 2164 2147 858 668 1116 961 936 1185 3368 5506 5471 853 969 933 936 912 930 1056 800 2444 1819 2135 433 554 421 693 401 1644 3265 2731 3102 1454 1352

49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 644 344 236 825 892 285 2284 2267 619 412 912 683 732 907 3090 5301 5267 973 764 1053 1058 1032 983 1176 920 2240 1615 1931 625 716 669 958 677 1764 3061 2527 2898 1250 1148

50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 373 611 141 296 473 1688 1671 875 740 1132 998 952 1222 3404 5522 5487 378 378 458 460 436 375 581 324 2460 1836 2151 1130 588 759 846 998 1168 3281 2748 3118 1470 1368

51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 410 442 559 358 1951 1934 796 564 1054 879 873 1103 3286 5443 5408 640 455 720 723 699 705 843 662 2382 1757 2072 780 574 615 880 704 1431 3203 2669 3039 1392 1290

53 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 735 887 173 2279 2262 427 273 725 544 583 769 2951 5152 5118 968 640 1048 1051 1027 937 1171 915 2091 1466 1782 798 915 841 1186 850 1759 2912 2378 2749 987 999

56 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 232 590 1711 1607 905 770 1162 1028 982 1252 3434 5552 5517 315 168 395 453 475 305 483 262 2490 1866 2181 1201 732 843 967 1069 1104 3311 2778 3148 1500 1398

58 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 750 1734 1394 1089 955 1347 1212 1167 1436 3619 5736 5702 208 399 185 360 465 142 297 145 2675 2050 2366 1083 750 878 984 1007 891 3496 2962 3333 1685 1583

59 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2142 2125 416 248 695 539 514 763 2945 5084 5049 831 496 911 914 890 800 1034 778 2023 1398 1701 794 911 837 1175 846 1622 2844 2310 2681 1033 931

62 2 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 2 3 3 2 3 3 3 2 3 3 2 2 3 2488 2481 2347 2739 2604 2559 2829 5011 7129 7094 1561 2041 1634 1476 1334 1856 1353 1679 4067 3442 3758 2475 1566 1958 1387 2399 2607 4888 4354 4725 3077 2975

65 2 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 2 3 3 2 3 3 3 2 3 3 2 2 3 3 2464 2330 2722 2588 2542 2812 4994 7112 7077 1583 1774 1556 1735 1841 1433 1667 1486 4050 3425 3741 2458 2125 2253 2360 2382 720 4871 4337 4708 3060 2958

10 2 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 3 3 219 327 336 195 561 2743 4797 4763 1170 810 1251 1253 1229 1139 1374 1117 1736 1051 1427 1163 1349 1206 1566 1215 1961 2557 2023 2394 590 588

11 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 3 1 465 337 310 561 2744 4938 4903 1036 675 1116 1119 1095 1005 1239 983 1877 1217 1567 973 1090 1016 1361 1025 1827 2698 2164 2534 728 763

17 2 2 2 2 2 1 1 2 2 2 1 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 1 2 2 1 4 4 1 1 538 192 806 2989 4478 4443 1428 1068 1508 1511 1487 1397 1631 1375 1417 732 1107 1421 1607 1464 1824 1473 2219 2238 1704 2075 344 279

34 2 2 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 2 1 1 2 2 2 1 1 2 1 2 1 1 2 2 1 3 3 1 1 1 383 548 2413 4863 4952 1294 933 1374 1376 1352 1262 1497 1241 1925 1234 1616 1266 1437 1309 1654 1318 2084 2746 2212 2583 652 800

40 2 2 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 2 1 1 2 2 2 1 1 2 1 2 1 1 2 2 1 3 3 1 1 1 1 651 2833 4682 4647 1248 887 1328 1330 1306 1216 1451 1195 1621 996 1319 1240 1426 1284 1643 1293 2039 2442 1908 2278 412 529

43 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 1 2 2 1 4 4 1 1 1 1 1 2229 5253 5219 1518 1157 1598 1600 1576 1486 1721 1465 2192 1502 1883 1490 1661 1533 1878 1542 2309 3013 2479 2850 1069 1068

63 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 6 6 4 4 4 3 4 3 1683 7129 3700 3340 3780 3783 3759 3669 3903 3647 4102 3117 3737 3672 3844 3716 4061 3724 4491 4924 4390 4760 2992 3250

60 7 7 7 7 6 6 6 6 7 7 6 6 7 7 6 6 6 7 6 6 7 7 7 6 6 7 6 7 7 6 7 7 6 8 8 6 6 5 6 6 6 2 3006 5818 5457 5898 5900 5876 5786 6021 5765 3212 3364 3729 5810 5996 5854 6213 5863 6609 4880 4346 4717 3636 4134

61 7 7 7 7 6 6 6 6 7 7 6 6 7 7 6 6 6 7 6 6 7 7 7 6 6 7 6 7 7 6 7 7 6 8 8 6 6 5 6 6 6 8 4 5783 5422 5863 5865 5841 5751 5986 5730 3476 3934 3816 5775 5961 5819 6178 5828 6574 2195 2769 2423 4703 4248

1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 5 7 7 510 99 198 304 328 210 153 2756 2131 2447 1164 697 959 932 1088 1080 3577 3043 3414 1766 1664

2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 2 1 1 2 2 1 2 4 7 7 1 582 629 789 405 714 454 2396 1771 2086 1273 936 977 1242 1196 1271 3217 2683 3054 1406 1304

18 1 1 2 1 1 1 1 1 1 1 2 1 2 1 2 1 2 2 2 1 1 1 1 1 1 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 5 7 7 1 1 223 329 314 126 111 2836 2211 2527 1245 771 1039 1005 1168 1053 3657 3123 3494 1846 1744

20 1 1 2 1 1 1 1 1 1 1 2 1 2 1 2 1 2 2 2 1 1 1 1 1 1 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 5 7 7 1 1 1 177 480 126 323 2839 2214 2529 1247 779 1042 1014 1171 1232 3660 3126 3497 1849 1747

25 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 2 1 1 1 1 1 1 2 2 1 1 2 1 1 1 2 3 2 2 2 2 2 2 5 7 7 1 1 1 1 587 249 429 2815 2190 2505 1223 755 1018 990 1147 1338 3636 3102 3473 1825 1723

27 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 2 1 1 1 3 2 2 2 2 2 2 2 5 7 7 1 1 1 1 1 407 215 2725 2100 2415 1397 907 999 1142 1128 930 3546 3012 3383 1735 1633

41 1 1 2 2 1 1 1 1 1 1 2 2 2 1 2 1 2 2 2 2 1 1 1 1 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 5 7 7 1 1 1 1 1 1 231 2959 2334 2650 1368 912 1162 1147 1291 1164 3780 3246 3617 1969 1867

52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 5 7 7 1 1 1 1 1 1 1 2703 2078 2394 1111 762 906 997 1035 983 3524 2990 3361 1713 1611

14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 2 3 2 3 2 3 5 4 4 4 3 4 4 4 4 4 4 853 789 2749 2934 2792 3151 2801 3547 1292 856 1429 1542 1222

37 3 2 3 3 2 2 2 2 3 3 2 2 3 3 2 2 2 3 2 2 3 3 3 2 2 3 2 3 2 2 3 3 2 4 4 2 2 1 2 2 2 4 4 5 3 2 3 3 3 3 3 3 1 503 2124 2310 2167 2527 2176 2922 1728 1194 1565 847 473

44 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 2 3 3 2 3 3 3 3 3 3 3 3 3 2 3 3 2 5 5 2 2 2 2 2 3 5 5 5 3 3 3 3 3 3 3 3 1 1 2439 2625 2483 2842 2492 3238 1611 1077 1447 1275 878

4 2 2 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 2 1 3 3 2 2 2 2 2 2 5 7 7 2 2 2 2 2 2 2 2 4 3 3 835 425 616 195 1955 3570 3036 3407 1759 1657

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 3 2 2 2 2 2 2 5 7 7 1 2 1 1 1 2 2 1 4 3 3 1 595 289 705 1622 3756 3222 3592 1945 1843

22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 2 2 2 2 2 5 7 7 2 2 2 2 2 2 2 2 4 3 3 1 1 389 205 1750 3613 3079 3450 1802 1700

35 2 2 1 1 2 2 2 1 1 1 2 2 1 2 1 1 2 1 2 2 1 1 1 2 2 1 2 1 1 2 2 2 2 2 3 2 2 3 2 2 3 5 7 7 2 2 2 2 2 2 2 2 4 3 4 1 1 1 481 1857 3973 3439 3809 2162 2060

57 2 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 1 3 3 2 2 2 2 2 2 5 7 7 2 2 2 2 2 2 2 2 4 3 3 1 1 1 1 1879 3622 3088 3459 1811 1709

64 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 1 3 3 3 3 3 3 5 8 8 2 2 2 2 2 2 2 2 4 4 4 3 2 2 3 3 4368 3834 4205 2557 2455

15 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 6 3 3 3 4 3 4 6 6 3 4 4 5 5 5 4 5 4 2 2 2 4 5 5 5 5 5 517 148 2497 2043

54 4 4 4 4 3 3 3 3 4 4 3 3 4 4 3 3 3 4 3 3 4 4 4 3 3 4 3 4 3 3 4 4 3 5 5 3 3 2 3 3 3 5 5 4 4 3 4 4 4 4 4 4 1 2 2 4 4 4 4 4 5 1 401 1963 1509

55 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 6 6 3 3 3 3 3 4 6 6 3 4 4 4 4 4 4 5 4 2 2 2 4 4 4 5 4 5 1 1 2334 1879

29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 1 1 1 1 1 2 4 5 6 2 2 3 3 3 2 3 2 2 1 2 2 3 3 3 3 3 3 3 3 487

36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 1 1 1 1 1 2 4 5 5 2 2 2 2 2 2 3 2 2 1 1 2 3 2 3 2 3 3 2 3 1

(f) 10 clusters for relocation without vehicle

1 2 3 4 5 6 7 8

Figure 8: Output of clustering algorithm for different number of clusters

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0

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02468

101214161820

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ands

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Figure 9: Clustering score for different number of clusters

shorter run times. In order to decide the most suitable clustersizes, the clustering algorithm is executed for various numberof clusters. Scores of each run for relocations with (Fig. 9a)and without (Fig. 9b) are shown in Fig. 9. We have selected theelbows in both cases as the best trade-off points that are ableto decrease 90% of the error compared to 2 clusters: 6 clus-ters for relocations with vehicles (Fig. 8b) and 10 clusters forrelocations without vehicles (Fig. 8f). In Fig. 8, the results forthe different number of clusters can also be seen. The max-imum value in the x-axes (39 for driving and 66 for movingcase) shows that number of clusters needed to have 0 error inthe relocation times.

After all experiments, the error of using 6 and 10 clustersfor relocations with/without vehicle for each run is also calcu-lated. On average, the duration of relocations with vehicles isoverestimated by 5.97% more. The 95th percentile of the errorat each instance was 13.82%. These values were 10.93% and19.10% respectively for relocations without vehicles. Regard-ing the problem size and the efficiency of the method, theseerrors are acceptable. Note also that, this error could be de-creased if more clusters were used but this was not preferred to

have solutions within reasonable run times. Definitely there isa trade-off between the accuracy of the solution obtained andthe time needed to solve the problem. For this particular casewe have opted to use a number of clusters that yields a fairlyaccurate solution in order to have a reasonable solution timefor the operational decisions. In general it is up to the decisionmaker to select the number of clusters that will be used and theassociated accuracy.

4.2. Case Study Settings

After deciding on the clusters, demand samples with differentnumber of rentals were created. We tested samples of size 200,250 and 300 rentals per day. For each demand level, 30 differentsamples were created. Each sample is tested with two differentrunning configurations (type 1 and 2). In Type 1 configuration,the entire demand is considered known a priori and it was fed tothe model all at once and solved all in a single step. In Type 2configuration, the demand is received by the model one by oneand accepted/rejected after each iteration without reconsideringthe past decisions. Every rental request is accepted or rejectedin the iteration it is received. These decisions are ultimate andcannot be changed in further iterations. Type 1 configurationimplies that all requests for trips are known through an advancereservation system that has a cut-off time for accepting reserva-tions (e.g. 24 hours in advance). Type 2 configuration sits onthe assumption that the demand is handled as it arrives in thereservation system.

In all scenarios of type 1 and type 2 configurations, it wasassumed that there are three parking spots at each station one ofwhich has a fully charged parked vehicle at the beginning of theruns. Since there were not many demand realized from 22:00 inthe evening to 6:00 in the morning, all scenarios were started at6:00 and ended at 22:00. We set three different working shiftsthroughout the day: (1) morning shift from 6:00 to 12:00, (2)afternoon shift from 11:00 to 17:00 and (3) evening shift from16:00 to 22:00. Personnel cost was set to e18 per hour whichmakes the cost of each personnel in any shift e108 per person.

The system operating in Nice is a system with electric vehi-cles. Range of a vehicle with full charge is around 120 kilome-tres. It takes 8 hours to fully charge a vehicle with an emptybattery, i.e. for every kilometres of driving, 4 minutes of charg-ing is required. It is assumed that rented vehicles were driven30 kilometres per hour. The maximum trip length is set to 40kilometres. Some important values of the parameters used inthe model representing the operating environment of our runsare summarized in Table 1.

4.3. Results

The comparison of different performance measures for runswith different demand levels (200, 250 and 300 demands perday), safety gaps (0, 15, 30 and 45min) and configurations(Type 1 and 2) is shown in Fig. 10. Each set of parameterswas repeated with 30 different samples. In all figures, the reddots show individual runs. In all figures, x-axes show the con-figuration and the level of demand. y-axes take different valuesdepending on the performance measures they represent. These

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relocation personnel cost (e/shift): 108relocation fuel cost (e/km): .02maximum charging length (sec): 28800charging length (sec/km): 240maximum range without charging (km): 120min-max (mean) trip distance (km): 3-40 (18)min-max (mean) trip duration (hour): .2-10 (.8)relocation speed with vehicle (km/h): 30relocation speed without vehicle (km/h): 15number of rentals per sample: 200-300minimum trip start charging level: 40%

Table 1: Some important values of the parameters used in the model

values are counts (in Figs. 10b and 10c), percentages (in Figs.10a, 10e and 10f) or ratios (in Fig. 10d).

Fig. 10a shows the percentage of unserved demand to totaldemand for different configurations, safety gaps and demandlevels. In runs with demand 200 or less, there is no differencebetween the runs of type 1 and 2. If the same set of demand re-quests is accepted to be served by the three configurations, thesolutions of three runs should be the same. Because of that, forthe lower level of demand, the algorithm returns the same solu-tions for both types of running configurations. Having the in-formation of all demand requests before deciding in type 1 con-figuration gives the algorithm freedom to choose rental requestswhich are matching better to each other. In other words, sincetype 1 runs have additional information about the requests, type2 runs cannot outperform type 1 runs if all the other settings arethe same. Note that the uncertainty of the future demand fortype 2 runs create a system which is less robust. Even if theaverage fraction of loss demand is similar (3% instead of 2%for demand 300), there are a few days with significant losses(in the range of 10-15%). This analysis suggests that differentpricing strategies could be implemented in an operating systemfor short- and long-term reservations. This should be a researchpriority. For type 2 runs, the accepted requests to be served inprevious iterations affect the decision to serve or not to servean additional demand. On the other hand, type 1 runs try tofind the largest subset of demands that can be served with thecurrent system. Because of that, as the system is more stressedwith increased demand levels, type 1 runs perform slightly bet-ter than type 2 runs in terms of number of requests served. How-ever, it should be stressed that this is on the expense of the cer-tainty provided to the user that his/her request for service willbe granted.

The effect of the parameters on the number of relocations isshown in Fig. 10b. In these figures, we see a trend of increaseof the number of relocations with the increase in demand. Therelationship between the number of relocations and the num-ber of requests show almost a linear relationship: For every8-10 rental requests, approximately 3 relocation operations areneeded. Slightly more relocations are needed with higher lev-els of demand. As the system becomes congested and parkingspaces and/or vehicles are not available at the right stations,more resources are used for relocations. The safety gap does

not influence significantly relocations up to a value of 30 min-utes. Nevertheless, we observe a significant decrease in relo-cations if a safety gap of 45 minutes is applied. This comeswith a significant cost for the loss demand and highlights thathigh safety gaps should not be allowed (or late returns shouldbe penalized).

In the same figure, we also observe some differences betweentwo configurations. As expected, type 1 runs required less num-ber of relocations compared to type 2 runs for the same level ofdemand requests. Type 2 runs usually serve less demand whendemand is high. The difference in the number of relocations be-tween configurations shows the effect of selecting better subsetsof requests: If the requests are selected with more information,more demand can be served with less number of relocations. Asexpected, more relocation means more number of personnel. InFig. 10c, the total number of personnel from all shifts is shown.Very similar trends with Fig. 10b are observed.

In Fig. 10d, we see the average number of relocations per per-sonnel in different scenarios. While this value does not vary sig-nificantly (ranges between 5 and 5.3), it is clear that for highersafety gaps that increase the ratio of unserved demand (in Fig.10a), a slightly smaller number of relocations per personnel isperformed. This is an interesting observation as the operatorcan plan in advance the personnel needs if he has a good pre-diction of the demand level.

In the last two figures, Figs. 10e and 10f, utilization of vehi-cles under rental and relocation are shown respectively: An in-crease in the demand of about 50% (from 200 to 300 requests)increases the vehicle utilization for about the same amount(from 19% to 28%). This is reasonable given that for the safetygap not more than 30 minutes, unserved demand is little. Ve-hicle utilization during relocation increases more sharply, from3% to 6% as demand increases from 200 to 300. This highlightsthe need for a larger number of relocations (and personnel) tokeep the quality of service high. As expected, the increase inthe number of demand requests increases the vehicle utilizationunder rental and relocation. The difference between utilizationfor rental operations is more evident with the demand level 250and 300. But this difference is not as severe as Fig. 10a. Thismay be because of the way we selected the first objective func-tion (see Objective 1) in the operations minimization model(see Sec. 3.2.4). In our first objective function, the durationof the requests was not considered in the objective. Demandrequests with longer duration were not given higher weight ascompared to shorter ones. As a result, type 1 runs are inclinedto select shorter requests in case of high demand levels to servemore demand with the same system resources. Final figure,Fig. 10f, shows the power of freedom to choose demand subsetagainst accepting/rejecting requests with limited information.Especially for higher demand levels, although more demand re-quests were served, type 1 runs keep vehicles less busy withrelocations.

The remaining analysis focuses on a specific instance with300 demand and type 1 run. In Fig. 11, the movements of ve-hicles between stations are shown. In Fig. 12, movements ofrelocation personnel on different working shifts can be seen. InFig. 13, two separate scenarios are applied on the same prob-

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0%

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(a) Ratio of lost demand to total demand.

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(e) Average vehicle utilization without relocation.

2%

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vehicle utilization in relocation

(f) Average vehicle utilization in relocation.

Figure 10: Some important performance measures of runs with different request counts (200, 250, 300) and configurations (type 1 and type 2). Upper and lowerwhiskers show the boundaries for the 95th and the 5th percentiles whereas the box shows the values between the 25th and the 75th percentiles. The median is shownwith a line in the box and the mean with a blue diamond.

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HH

mm

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Figure 11: Chart showing movements of vehicles and relocation routes for the case with 300 rental requests.

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lem instance with additional constraints. Constraints 23 wereapplied to limit the maximum number of personnel at each shift(see Fig. 13a). Constraint 24 was applied to type 1 runs to limitthe number of demand served.

vs ≤ maximum number of personnel per shift ∀s (23)∑i

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In Fig. 11, the two leftmost vertical columns show the stationnumber and the number of spots of this station (3 per station).The uppermost horizontal numbers are the starting hour andminute of the intervals. Each colour shows a different state forthe parking spot. The legend for colour coding is shown inthe legend on the same figure. Note that, for all states except“spot available”, the number inside the cell identifies the vehicleaffected with this state. For this instance, since only the 0th spotof every station has an available vehicle at the beginning of theday, each vehicle is numbered with the station parked at thebeginning of the day.

Fig. 11 also enables to see the detailed relocation operations.Each orange line shows the relocations starting/ending timeand origin/destination stations. One of the expected results ob-served from this figure is to see the relocations of vehicles fromstations with no/low demand to stations with high demand atthe beginning of the day and the opposite movement at the endof the day. Vehicles from stations without demand (i.e. 61, 62,63, 64 and 65) were relocated to stations with high demand (i.e.14, 35 and 55 then 42 and 55) at the beginning.

The identification of numbers enables to track the daily as-signments of each vehicle. For instance, vehicle 0 started fromthe 0th spot of Station 0. Between 8:00 - 8:15, it was relocatedto the 1st spot of Station 25. The vehicle was charged for onetime interval and rented at 8:45. The vehicle was returned to the0th spot of Station 54 at 9:45. At 12:00, it was rented again witha partial charge. At 12:30, the vehicle was returned to the 0th

spot of Station 30. The vehicle stayed and fully charged thereuntil it was rented again at 19:15. At 20:45, the vehicle wasreturned to the 1st spot of Station 29 and stayed there until theend of the planning period.

To see the detailed movements (i.e. relocations with/withoutvehicle) of each personnel, separate charts for each workingshift are created (see Fig. 12). Each set of the connected quad-rants represents a separate station. Area of each quadrant isdirectly proportional to the number of demand originating from(gray, left top), demand destined to (blue, right top), relocationdestined to (green, bottom left) and relocation destined from(red, right bottom) the station they are representing. Each lineset with different colors represents different personnel. Solidlines show relocations with vehicles and dotted lines show relo-cations without vehicles. For instance, the person representedwith red firstly relocated a vehicle from an outer station (fromFig. 11 we can see it is Station 61) to Station 14. Then he movedto Station 10 without vehicle. After that, he relocated a vehi-cle to Station 16. Then he moved to Station 23 and relocated avehicle to Station 33. He then relocated a vehicle from Station33 to 36. And finally he moved back to Station 29 and relo-

cated another vehicle to Station 36. Regarding the size of eachquadrant per station, note that there are some repetitive trendsby looking at the aggregated values. For example, stations withhigh demand of origins, usually have a high number of reloca-tions destined to this station. Stations that have high demandboth as origins and destinations do not have a clear trend withrespect to relocations as the temporal distribution of demandmatters.

In Fig. 13a type 1 and type 2 runs are compared for the samesingle instance with 300 demand. Different than the previousruns, the maximum number of available relocation personnelat each shift is limited to different values from 0 to 8. Thedark (i.e. black) lines and (darker) columns (on the left) showthe run results for type 1 runs. The light (i.e. gray) lines and(lighter) columns (on the right) show results for type 2 runs.The left vertical axis shows the number of personnel (columns)and the number of relocations per personnel (lines with trianglemarkers). The right vertical axis is for the total demand served(lines with square markers) and the demand per personnel (lineswith diamond markers).

Note the difference between the number of demand servedwith type 1 and type 2 runs. This difference shows that a car-sharing system can serve more demand if it is able to choosea specific subset. This analysis suggest that different businessmodels can be used for offering carsharing services with differ-ent implications for the users in terms of service provision andassociated costs. Specifically a business model that requires ad-vance reservation and notification regarding acceptance or notof the requested services at the end of the reservation period(type 1 configuration) may provide benefits to the operator onthe expense of uncertainty to the user’s request. In contrast, asystem that will provide immediate (within minutes) responseif a trip request is granted or not (type 2 configuration) requiresmore resources for the same level of demand. These results canalso create intuition with respect to the development of pricingstrategies to deal with the emerging business models. It is alsoclear that short term reservations can contribute in system im-balances and loss demand. In other words, if the demand to beserved is selected with full knowledge of total demand, the pro-ductivity of the system can be improved for the same level ofresources. In our case, we see an improvement ranging from 0to 60% depending on the maximum number of personnel avail-able per shift.

In Fig. 13b, the type 1 run has given freedom to choose anumber of demand to be served (170 to 300 in every 5) from aset of 300 demand. 170 is selected as the starting point becausefrom Fig. 13a we can see that 174 rental requests of the se-lected instance can be served without any relocation personnel.We could not have the same test for the other running config-uration since in type 2 runs, the requests become available andare accepted/rejected iteratively as they appear in the system.In this figure, the horizontal axis shows the number of rentalrequests that needs to be served among 300 demand. Columnsshow the number of personnel from different shifts. The purpleline shows the number of relocations per personnel. Both thenumber of personnel and relocations per personnel are shownon the left vertical axis. The blue line shows the demand per

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Figure 12: Movements of different personnel with (straight line) and without (dashed line) vehicles at each shift for the selected case with 300 rental requests.

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Figure 13: The effect of limited number of personnel and number of demandserved on the selected case with 300 rental requests.

personnel with the values on the right vertical axis.

From this figure, we can see how the demand per personnelconverges to a specific value. Although, this value is highly re-lated to the system parameters, it is worth noting such a valuemay exist for carsharing systems. This ratio could help in car-sharing systems to determine the number of personnel neededfor any demand level. Similarly, with the increase in the num-ber of demands served, relocation per personnel reaches to 6. Inother words, every member of staff needs one hour per reloca-tion on average since in these runs we assumed personnel shiftsof 6 hours. Note that, these 6 hours include not only relocationswith vehicles but also relocations without vehicles. Betweenevery two relocations with vehicles, the personnel in charge of

the relocations needs to travel from the destination station ofthe previous relocation to the origin station of the next reloca-tion. This value probably depends on the topology of the systemand the relocation strategy, but if known (or estimated), it canbe utilized to develop simpler formulations for the tactical andstrategic problems of the system (see for example Boyacı et al.,2015).

In Fig. 14, various system states during the day are comparedfor the two different types of runs. Figures on the left show thenumber of stations with a specific number of vehicles (0 to 3)for each time period. Figures on the right, show the number ofvehicles providing service, under relocation and the charginglevel of vehicles at stations over time. The same 300-demandset is used for all cases. In all figures, x-axes show the time ofthe day during simulation. y-axes represents either the numberof vehicles (Figs. 14b and 14d) or the number of stations (Fig.14a and 14c). Note that the distribution of the number of vehi-cles per station converges to very similar values independentlyof the run type.

5. Conclusions and Future Work

In this paper, we developed an integrated optimization-simulation framework to deal with the operational decisions ofone-way (electric) carsharing systems with reservations. Wedeveloped a clustering algorithm to decrease the computationalcomplexity of the model, an event-based simulator to test thefeasibility of charging levels during the optimization procedureand MILP models to handle the operational decisions. Thethree modules are interacting iteratively to guarantee close-to-optimal solutions. Experimental results showed that, the devel-oped framework is efficient. We have tested two types of runsrelated to reservation confirmation policy: Type 1 is with fullinformation about the system, as it might happen in the case ofreservations in advance. In type 2, requests are appearing oneper time and the system does not know the future demand dur-ing optimization. We also tested various demand levels to seethe performance differences and applicability range for differ-ent settings.

Experimental results showed the importance of efficient al-gorithms for relocation operations. Comparison between differ-ent configurations also showed that especially in congested sys-tems, forecasting the future demand or optimizing the initial lo-cations of vehicles in the beginning of each day is quite impor-tant to utilize system resources efficiently. To serve higher num-ber of requests without increasing system resources, demandshould be managed through the use of incentives/disincentives(e.g. pricing). Specifically, business models that require reser-vations with an advanced cut-off point for confirming them maylead to a more efficient use of the system resources on the ex-pense of not receiving immediate confirmation for serving theexpressed demand (less flexible). The business models that re-quire reservations based on type 2 runs provide higher flexibil-ity to users in terms of making advanced reservations, but theyare less efficient in terms of the utilization of resources.

A field test to investigate the optimization results in real con-ditions is also under preparation. Future work is looking to

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Figure 14: Comparison of the states of vehicles and stations for three different approaches for the selected case with 300 rental requests. Left figures represent thestations with different number of vehicles whereas right figures represent the number of vehicles with different charging levels.

expand these models to systems without reservations. Whileresearch work (e.g. Correia et al., 2014) dealt with system im-balances through trip pricing, a combination of pricing and re-location strategies should be another research priority.

Acknowledgements

This work has been partially supported by the (European Re-search Council) ERC Starting Grant METAFERW: Modelingand controlling traffic congestion and propagation in large-scaleurban multimodal networks. We also thank the VENAP AutoBleue, the carsharing system in the city of Nice, for providingthe data for this study.

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