Project Scheduling Problem Based on Modular Outsourcing

Guo-rong Chai, Yin-li Bao, Guo-xing Zhang School of Management

Lanzhou University Lanzhou,China

chaigr@lzu.edu.cn, baoyl08@lzu.cn, guoxingzh@lzu.edu.cn

Ya-na Su Department of Management Lanzhou Polytechnical College

Lanzhou,China synatlz@163.com

Abstract—The market competition under globalization promotes enterprises to integrate resources all over the world, and the decision-making of outsourcing is becoming an important influencing factor of project scheduling. Taking subproject TCP/C1-3-1A-1 of Three Gorges Project for example, this paper constructs module network by design structure matrix, and chooses outsourcing module primarily by two levels, then formulates optimization model of project scheduling based on modular outsourcing. The results show that the income of the project is enhanced and the duration of the project is greatly shortened because of synergy effects with modular outsourcing.

Keywords-project scheduling; modular outsourcing; subproject TCP/C1-3-1A-1; Design Structure Matrix; synergy effects

I. INTRODUCTION

Due to conforming to individual market demand, Project management has begun to permeate through every aspect of management theory and practice and show great superiority. Previous research on the project scheduling problems（PSP）is to determine the starting time (completion time) of the project activities in order to minimize the overall project duration, subject to the precedence constraints among the activities [1]. In recent years, the research has introduced resource constraint and multiple execution modes which leaded us to the new area of multi-mode resource-constrained project scheduling problems（Multi-mode Resource-Constrained PSP, MRCPSP）[2]. A wide variety of optimality criteria are used for example: minimize makespan, maximize net present value [3], minimize total project costs [4], balance resources levels [5], cost/time trade-off [6] etc. The field again covers a wide variety of problem types such as bonus-penalty structure [7], payment scheduling [8,], stochastic problems [9], etc.

In recent years, with increasingly unique customer needs and gradually fierce market competition, there are contractors cutting the investment of specific assets to cope with lean and agile management concepts. On the other hand, the continuous pressure to cut lead times has also affected contractors. This contradiction forced contractors to search new means in order to break the limits of internal resources, including purchasing parts, renting resources, outsourcing operations [10]. Although purchasing from outside has been the primary focus of resources integration problem in the project scheduling literature, it is only suitable for standard parts. Over the few years, many scholars have studied resource renting in project scheduling and put

forward flexible- resource-constrained project scheduling problem [11]. To the best of our knowledge, the literature on outsourcing and scheduling is completely void.

Outsourcing in project level, differing from enterprise level, is more precise [12]. Due to complicated relations between project activities, outsourcing maybe split logic connection among activities and add coordinate and management costs between contractor and client. To solve the problem and in line with the practice, one can assemble relative activities as a whole process module to schedule by modularization. The resulting problem denoted as the project scheduling problem based on modular outsourcing（PSP-MO）.

This paper takes subproject TCP/C1-3-1A of Three Gorges Project for example to illustrate PSP-MO. The project started in July 2002 and included 726 activities [13]. Since the magnitude and complexity of the project, this paper chooses a relatively independent subproject TCP/C1-3-1A-1 as the object of the research. We deal with the PSP-MO by taking an activity-based method. The project is represented with Activity-on-Not (AON) network in which we consider dummy activities 0 and 16 as the start and end of the project (Fig 1).

Figure 1. Activity network of subproject TCP/C1-3-1A-1

II. PROJECT MODULARIZATION

Modularization is a dynamic integration process that aims to decompose a complex system or process into different modules according to connection rules, and to communicate information through standardized interfaces. With the development of information technology, modularization is an effective way of solving complex system problems. Modularization involves decomposition and integration. Partitioning system or process into independent module according to certain connection rules is defined as module’s decomposition; module’s integration is to unify modules as an integrated whole.

This work is supported by the National Natural Science Foundationof China (Project NO. 70702013), the Program for New CenturyExcellent Talents in University, and the Fundamental Research Funds forthe Central Universities.

978-1-4244-5326-9/10/$26.00 ©2010 IEEE

A. decomposition of project

This paper adopts DSM（Design Structure Matrix）to partition project. DSM is a kind of square matrix to reflect the relationship between the activities (information flow) which can be used to describe sequence, parallel, and coupling. It makes up the deficiencies of tradition project scheduling focusing on work flows [14]. The DSM is a simple binary Boolean matrix whose elements of column and row are based on the same order of project activities. Diagonal on the figure indicates activities, i.e. iie i= . Matrix elements represent dependencies between activities, if there is dependence between activities i and activities j, i.e. 1ije = and

0ije = otherwise. Values of upper and lower triangular matrix indicates feedback information and feedforward information respectively.

DSM involves partitioning, clustering and sequencing of three basic operations [15]. Partitioning is to rearrange the order of column and row of the matrix, so as to eliminate circuit of the matrix. Clustering is to classify activities which have strong dependent relations with each other in one module and decrease the relations between modules and activities as far as possible. Sequencing is to adjust the sequence of activities and make activities in front of the matrix which have more inputs.

B. Module Integration of Project

Project module network is developed by clustering according to modularization theory. The nodes of network represent modules which lump together by interface rules. It is illustrated as Fig. 2 where the dummy module A and M mark the beginning and end of the project. We can reviews relationships between components around the project network from both static and dynamic perspective. By formal and informal contract, project module network forms a coordination mechanism of professional division and integration. The relation between outsourcing module and self-made module is built on the basis of explicit contract in the feature of contract and implicit contract in the feature of trust mechanism. The fundamental logic of the module network is to pursue synergy effects. Due to loose coupling and openness of module network, it is easier to achieve synergy and enhance flexibility of enterprise.

Figure 2. Module network of subproject TCP/C1-3-1A-1

III. PRELIMINARIES OF OUTSOURCING DECISION-MAKING

Correct decision-making for outsourcing is a prerequisite for success of outsourcing. In the study of outsourcing decision-making, the literature employed qualitative way in

which subjective factors of evaluation was strong. To a certain extent, it is affected the scientificity and can only get a preliminary program as a result of decision-making. When there are multiple candidates for outsourcing modules, the issue on whether all the modules are outsourcing and how to determine the module’s latest lead time is to be solved. Outsourcing cost, comparing to the cost of self-made cost, is in general relatively high. The contractor must make tradeoffs between the expense increment caused by outsourcing and advancing the project completion. This paper chooses outsourcing modules primarily by two levels, then formulates optimization model of PSP-MO. By solving the model, we can find an optimal schedule including outsourcing modules and their latest lead time.

First, we determine the approximate range of outsourcing modules by the contractor’s core competition. Project module can be divided into three parts i.e. strategic module, basic module and auxiliary module according to the correlation with the contractor core competence from high to low order. Strategic module is the core competitiveness of the contractor, and also is the main source of income. Though basic module doesn’t involve the contractor’s core technology, but it has higher extra value. Auxiliary module is a supporting and cohesion module between strategic module and basic module, and has no direct contributions to project income. In general strategic module and basic module take self-made model, while the auxiliary module can be outsourced.

According to technical factors and assets specificity, we can make a further reduction of the scope of outsourcing modules. Technical factors mainly refer to technology maturity. Assets specificity can be divided into entity assets specificity, personnel specificity and procedure specificity. The technology of module is more mature and assets specificity is weaker, so we can use more external resources. The module is suitable for outsourcing.

IV. PSP-MO MODELS Tradition RCPSP schedules activities with the objective of

minimizing the makespan of the project. To large-scale project of long duration, contractor always takes time value of capital into account and the objective is to maximize the net present value (NPV) of the contractor in real-life projects [16]. Once the interest rate per period is determined, the NPV is the cash flow which is associated with the outward cash flows and the inward cash flows in the project. In the perspectives of the contractor, a cash inflow is associated with the payment from client, and a cash outflow is associated with the expenditures of all the modules to be completed. Due to large equipment constraint, we only consider renewable resource constraint.

It is assumed that a project consists of N module. Oπ is defined as an set of outsourcing module which is composed of all outsourcing modules. Let q denote execution mode of module ( q M= represents self-made manufacturing, q O= represents outsourcing). Module n can be executed with iQ modes ( 1i OQ

π∉ = denotes that module can only be processed by

contractor ， 2i OQπ∈ = denotes that module can be either

processed by contractor or outsourced). When module i is performed with mode M, its duration and cost and resource requirements to contractor’s self-owned resource are iqd , iqc , iqsr

respectively (comparing with self-made manufacturing:

iM iOd d≥ , iM iOc c≤ , 0iOsr = ). iP represents the set of predecessor module i . t denotes period index defined in time interval ( ]1,t t− . [ ],i iE L is the time window under precedence constraints. sR is available quantity of resource s per period. The contractor gets lump-sum payment from the client at the end of the project. The contract price of project is P. The cost of module occurs at module starting times. All the parameters are deterministic and integral except α .

In PSP-MO we need to define two groups of decision variables for the problem as follow:

{1 if module is performed in mode0 otherwise ,iq

i qX i q = ∀ (1)

{1 if module is started at period0 otherwise ,it

i tY i t = ∀ (2)

Duration, resource requirements, starting time of module i represent

1iQ

iq iqqX d

=∑ , 1

( )iQiq iqsq

X r s=

∀∑ , i

i

Litt E

Y t=∑

respectively.

The objective of PSP-MO is to make an outsourcing decision making of project module based on primary selection results of outsourcing module and then to find an optimal schedule

{ , }S Q T= , defined by vector Q of module performing modes

q and vector T of module starting times it , so that precedence relations of module and the constraints of self-owned resources are satisfied and the NPV of the contractor is maximized.

Based on the analysis above, the optimization models of the PSP-MO can be formulated as follows:

( ) ( )1 1

1Max1 1

i i

Ni

Q LN

iq iq itT ti q t E

PNPV c X Yα α= = =

= −+ +

∑∑ ∑ (3)

. .s t

1

1iQ

iqq

X i=

= ∀∑ (4)

1i

i

L

itt E

Y i=

= ∀∑ (5)

1

,j j i

j i

L Q L

jt jq jq it it E q i E

tY d X tY j P i= = =

+ ≤ ∈ ∀∑ ∑ ∑ (6)

1,

i

t

Q

iqs iq li S q

r X R t s∈ =

≤ ∀∑∑ (7)

In the model above, objective function (3) maximizes the NPV of the project, where the first and second is discounted to the start of project of payment and expenditures of each module respectively, including decision variables iq itX Y、 ; (4) chooses a execution mode for each module in the project; (5) arranges an occurrence time for module i within its time window [ ],i iE L ; (6) represents finish-start precedence constraints

between each pair of modules ( )ji, , where j immediately

precedes i; (7) are resources constrains where tS is the set of module executed in period t.

Without any loss of generality, let module execution mode in PSP-MO corresponding to activity mode in MRCPSP-DCF（Table 1）, then PSP-MO are transformed to MRCPSP-DCF[16]. PSP-MO is NP-hard problem the same as MRCPSP-DCF and commonly used metaheuristic when scale of solution space is large [1, 11]. Comparing with optimal model of PSP-MO and MPPSP（Multi-Mode Project Payment Scheduling Problem）in literature [8], we developed simulated annealing proposed by literature [8] for solving.

Table 1 Synchronous Mapping from MPPS to PSP-MO

Network nod Decision variable Payment Expense

MPPSP event kmx nqy mtz k Kp ≠ Kp me

PSP-MO module 1 iqX itY 0 P iqc

V. ANALYSIS OF PSP-MO

The contract price of subproject TCP/C1-3-1A-1 is 352,460 and the deadline is 150 [13]. The project after modularization is decomposed into thirteen modules and activity 0, 1, {2, 4, 5}, 3, 6, 7, 8, 9, {10, 15}, {11, 12}, 13, 14 and 16 corresponds to module A, B, C, D, E, F, G, H, I, J, K, L and M. Fig. 2 is a module network. From the analysis of the project, the scope of outsourcing module is reduced to {B, C, E, H, J, K}. The durations and costs and resource requirements are all listed in Table 2. According to statistics of the Three Gorges project area, outsourcing cost is 1.9 times than self-made cost. According to China Construction Bank’s lending rates, the rate of interest per period is 0.00105.

Table 2 Parameters of Subproject TCP/C1-3-1A-1

Module Self-made/ outsourcing

duration(week)

Self-made cost

Equipment requirement

1 2 3 4 5 6 7 8

B 12/8 2156 0 30 0 7 8 35 0 0C 20/16 451 0 15 0 7 0 0 0 3D 36 7135 0 30 0 7 8 35 20 0E 10/8 513 0 0 0 7 8 0 0 0F 8 411 0 0 0 7 0 25 0 0G 12 41 0 0 0 0 0 0 0 3H 12/8 2140 0 30 0 7 8 35 0 0I 40 7791 2 30 7 7 8 35 20 0J 42/34 2156 0 0 0 7 8 25 0 0K 8/6 668 8 30 14 0 0 0 0 0L 4 36 0 0 0 0 0 0 0 3

Available

resource - - 8 60 15 15 16 60 20 3

The obtained optimal solution is presented in Tables 3. We can find that module B, D, F, G, I, K and L are all carried out with

self-made manufacturing, but module C, E, H and J are performed with their latest lead time 28, 8, 56 and 50 respectively. The NPV in schedule is 61,880 and the total duration is 100.

Table 3 Schedule of Subproject TCP/C1-3-1A-1 A B C D E F G H I J K L M q - M O M O M M O M O M M - t 0 0 12 12 0 8 16 48 60 16 8 50 100 t′ - - 28 - 8 - - 56 - 50 - - -

If there is not outsourcing, the contractor’s NPV will decrease to 58,920 and the project completion is delayed to period 152. The result shows that NPV ascends 5.04% and the total duration shorts down 32.43%. With the analysis of the resources utility of contractor, we can find the reason why the project duration makes such a drastic compression is that outsourcing eliminates contractor’s resource bottlenecks and decreases the idle ratios of resource to some extent, which results in a good synthetic effect.

Based on the results, we can depict the curve of average idle ratios of different resources and the idle ratios of resource 2 varying with project time showed in Fig.3 and Fig.4. Comparing with resource idle ratios of tradition RCPSP, average idle ratios of resources throughout project declined 4.12%, 22.31%, 7.87%, -11.3%, 0%, 17.35%, 50.52% and -6.4% respectively with an average of 10.56% falling. Outsourcing not only reduces the resource idle ratios, but also makes the resource usage reach a more stable and balances resource level.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

resource

average idle ratios

of resources

RCPSP PSP-MO

Figure 3. Average idle ratios of resources

0

0.2

0.4

0.6

0.8

1

0 12 24 36 48 60 72 84 96 108

120

132

144

156

T

idle ratios of resource

RCPSP

PSP-MO

Figure 4. Idle ratios of resource 2

VI. CONCLUSIONS

In the condition of globalization, the competitive power of enterprises depends largely on their ability to integrate resources. This paper constructs module network by design structure matrix, and chooses outsourcing modules primarily by two levels, then formulates optimization model of project scheduling based on modular outsourcing. By solving the model, we can find an optimal schedule, including execution modes of the modules (self-made or outsourcing), starting time of the self-made modules, and latest lead time of the outsourcing modules. The results show that the income of the project is enhanced and the duration of the project is greatly shortened. By analyzing the utilization ratio of the resources, we find the reason why the project duration is compressed greatly is outsourcing eliminates contractor’s resource bottlenecks and decreases the idle ratios of resources, which play a good synthetic effect.

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