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Annual Distribution Budget in the Beverage Industry: ACase StudyLuis Guimarães, Pedro Amorim, Fabrício Sperandio, Fabío Moreira, Bernardo Almada-Lobo

To cite this article:Luis Guimarães, Pedro Amorim, Fabrício Sperandio, Fabío Moreira, Bernardo Almada-Lobo (2014) Annual Distribution Budgetin the Beverage Industry: A Case Study. Interfaces 44(6):605-626. http://dx.doi.org/10.1287/inte.2014.0747

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Vol. 44, No. 6, November–December 2014, pp. 605–626ISSN 0092-2102 (print) ó ISSN 1526-551X (online) http://dx.doi.org/10.1287/inte.2014.0747

©2014 INFORMS

Annual Distribution Budget in the BeverageIndustry: A Case Study

Luis Guimarães, Pedro Amorim, Fabrício Sperandio, Fabío Moreira,Bernardo Almada-Lobo

INESC TEC, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal{guimaraes.luis@fe.up.pt, amorim.pedro@fe.up.pt, frsperandio@fe.up.pt, fnssm@fe.up.pt, almada.lobo@fe.up.pt}

Unicer, a major Portuguese beverage company, improved its tactical distribution planning decisions and studyalternative scenarios for its supply strategies and network configuration as result of an operations research(OR)-driven process. In this paper, we present the decision support system responsible for this new methodology.At the core of this system is a mathematical programming-based heuristic that includes decision variables thataddress transportation and inventory management problems. Unicer runs a set of production and distributionplatforms with various characteristics to fulfill customers demand. The main challenge of our work was to developa tactical distribution plan, which Unicer calls an annual distribution budget, as realistically as possible withoutjeopardizing the nature of the strategic and tactical tool. The company had a complex tactical distribution planningproblem because of the increasing variety of its stock-keeping units and its need for a flexible distribution networkto satisfy its customers, who demand a very fragmented set of products. Atypical flows of finished products fromUnicer’s distribution centers to its production platforms are a major cause of this complexity, which yields anintricate supply chain. The quality of the solutions we provided and the implementation of a user-friendlyinterface and editable inputs and outputs for our decision support system motivated company practitioners to useit. Unicer saves approximately two million euros annually and provides better information to its decision makers.As a result, these decision makers now view their operations from a more OR-based perspective.

Keywords : tactical distribution planning; mixed-integer programming; decision support system; beverage industry;supply chain management.

History : This paper was refereed. Published online in Articles in Advance August 22, 2014.

The food and beverage industries have a huge impacton the European Union (EU) economy. The EU is

the largest producer of food and beverages, rankingfirst in terms of sales and exports. In Portugal, thebeverage industry generates revenues of over 2.3 billioneuros (Instituto Nacional de Estatistica 2012) and facesever-increasing competition. To survive, companiesmust strive to excel in price, quality, and customerservice. To that end, distribution efficiency has becomea major focus. Indeed, many authors (e.g., Fearne andHughes 1999) claim that supply-chain managementis a key factor in building a sustainable competitiveadvantage.Beverage companies typically supply a variety of

products, including wine, beer, soda, and water. Thesecompanies, which are in the more general fast-movingconsumer goods (FMCG) industry, face the sameissues—an increasing variety of stock-keeping units

(SKUs) and the need for flexible distribution networksto fulfill customer demands, which in turn producevery fragmented product sets (i.e., product baskets).The combination of a large portfolio of products, com-plex distribution networks, and demanding customersgives rise to very intricate supply chains. The problemsthat these companies face are multilevel. On a strategiclevel, they must know where to locate production ordistribution platforms; on a tactical level, they may befaced with decisions about selecting the right logisticsproviders, types of contracts to use, and selection ofclients to visit on given days; on an operational level,they must address the daily problem of designing andconsolidating routes to serve customers, some of whomwere previously assigned to a particular day based ontheir demand orders.

In this paper, we describe work we did with Unicer,a major Portuguese beverage company that is part of

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the Carlsberg Group. Unicer has annual revenues ofapproximately 500 million euros. Its operations includethe production, commercialization, and distribution ofbeer, plain and sparkling water, soft drinks, and wine.The project’s objective was to design, develop, andimplement an operations research (OR)-based process tosupport Unicer’s managers in making tactical decisionsabout distribution planning. However, we also had toconsider the operational complexities. The tool thatwe developed helped Unicer to (1) perform its annualbudgeting of the distribution operation at a tacticallevel, and (2) model and test alternative strategies forthe supply chain. On an operational level, Unicer usessoftware packages that are dedicated to vehicle routingand load planning.Next, we discuss the problem we addressed, the

solution approach we developed, and the impact ofour work within the company. We also discuss theapplication of OR to practical problems. We finish withsome concluding remarks and possible future projects.

The ChallengeUnicer produces, commercializes, and distributes someof the most popular brands of wine, beer, soft drinks,and plain and sparkling water in Portugal. It sells morethan 380 SKUs to over 19,000 clients worldwide.Tactical distribution planning is a vital step in its

planning tasks because transport costs are a significantshare of the total product cost. This process is theresponsibility of the logistics department director, themain stakeholder of the plans. The logistics directorreports the results achieved directly to the company’sboard (i.e., the chief operations office). Tactical distribu-tion planning is important in two phases of Unicer’splanning process.The first phase involves the creation of the annual

distribution budget (DB), which is part of Unicer’sannual budgeting process. Budgeting is a vital toolto align the company departments, which translatethe strategy into goals for the next 12 months. Thisprocess starts in mid-September and lasts until lateOctober. The first major task is the creation of an annualsales budget (SB). The SB is the responsibility of thesales department and defines a monthly sales forecastfor each SKU for the following year. Using the SBas input, the production planning department works

on the annual production budget, which defines thetotal production quantities of each product at eachproduction platform for the entire planning horizon ofthe 12 months. The results of these two steps definethe input required for the DB.The second phase involves validating strategy

changes in the supply chain configuration, productportfolio, and client supply strategy, and negotiatingwith the third-party logistics providers (3PLs) respon-sible for transports. Whenever a strategic change isunder consideration, Unicer studies its impact on futuredistribution costs. The process is similar to the creationof the DB; however the planning horizon is usuallylonger and the data are often more aggregated.The challenge we faced in this project is therefore

twofold. Our first objective was to create a tacticaldistribution plan for the next 12 months: the DB. Thisplan details the flow of the finished products amongthe locations in the supply chain; therefore, we mustknow the production plan for a set of productionfacilities and the customer demand during the nextyear. Simultaneously, the plan defines the supply chainconfiguration by determining which platforms areoperating and their respective activity levels. Oursecond objective was to provide a flexible tool; therefore,we had to develop an approach capable of modelingvarious scenarios for the supply chain network. In thefollowing sections, we describe the main entities andmovements in the supply chain (i.e., platforms, clients,and transports), and associate the expected outputs ineach area at both the tactical and strategic levels.

PlatformsUnicer has nine production platforms spread acrossPortugal (see Figure 1); each specializes in producingspecific product families. The production facilitiesdedicated to beer and soft drinks are strategicallylocated close to the geographical center of demand;however, mineral and sparkling water plants are placednear a water source that is often distant from the finalconsumer.

Distribution platforms are used for storage, consoli-dating shipments, and performing picking operations.The company has two major distribution platforms:one is located near the Oporto region and the other isin the Lisbon region. These regions are the two mainconsumption areas in Portugal. Unicer also has othersmaller distribution platforms across Portugal.

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Production platform(beer and soft drinks)

Production platform (water)

Distribution platform

Lisbon

Oporto

Figure 1: The map shows the geographic locations of Unicer’s main produc-tion and distribution platforms. The darker the area in the map, the higherthe population density of the region. Unicer also has smaller platforms thatthis figure does not show.

Some production platforms have areas available forstoring products and supplying client orders. There-fore, they can act as both production and distributionsites. However, this is uncommon and introduces anadditional level of complexity to the supply chainmanagement.Platforms have limited capacity for storage, pallet

movement, picking operations, and loading of ship-ping containers. We can define storage capacity by:(1) drive-in, (2) rack, and (3) floor-stacking pallet stor-age. In drive-in and rack pallet storage, the number ofslots available for pallets is strictly defined. However,for the floor-stacking capacity, we must consider thenumber of stacking levels that a given product palletpermits. The available capacities are determined by theactivity level selected. An activity level can relate to acontract with an outsourced platform, which guaranteesdifferent capacities in a piecewise linear function, or tothe possibility of extending or reducing workforce andequipment in the internal platforms. Figure 2 depicts

possible cost curves for operations at various activitylevels. Furthermore, some platforms may operate onlyduring certain months and remain idle for the rest ofthe year. This corresponds to the filled dot depictedin each plot in Figure 2; the cost corresponds to thefixed cost without activity. Figures 2(a) and 2(b) mayrepresent an outsourced platform. In the first case—Figure 2(a)—the same unit cost is paid for any quantitymoved and (or) stored; the second case—Figure 2(b)—shows contracted levels of activity for which fixed anddifferent unit costs must be paid. Figure 2(c) depictsthe likely cost structure for Unicer-managed platforms.Both the definition of the operating platforms and

the adjustment of platform capacity are particularlyimportant in the beverage industry because sales arehighly seasonable. The sales profile of these prod-ucts shows peaks of demand during the Easter andChristmas seasons, and especially during summer.However, production capacity remains almost constantthroughout the year. This forces the industry to workon a make-to-stock basis because the capacity availableduring peak sales seasons is insufficient to match thedemand, thus stressing the supply chain. Traditionally,during the low season (January to March), Unicer usesthe idle platforms to store the seasonal stock, andadjusts the activity level of the remaining platforms toincrease their operational capacity during the summer.The tactical distribution plans should define the

following for each platform for each month:• Should it be operating?• If operating, what is its optimal activity level?• What is the utilization of each type of storage?• What is the total number of pallets handled?• What is the total number of picking operations?• How many containers are shipped?• What are the activity costs? Depending on the

cost function associated with the platform, activitycosts may be proportional to the number of prod-ucts stored, pallets handled, picking operations, orcontainers shipped.

From a simulation perspective, the approach shouldallow us to model new scenarios for opening andclosing production and distribution platforms.

CustomersWe categorize customers into four sales groups: capi-lar, retailer, strategic, and export. This distinction is

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Cost(a) (b) (c)Cost

Total quantityTotal quantityTotal quantity

Cost

Figure 2: The graphs show examples of possible cost functions for platform activities: (a) initial fixed-cost andlinear variable costs; (b) piecewise fixed-cost activity costs; and (c) initial fixed-cost and variable piecewise activitycosts.

important because each customer group has distinctrelationships within the supply chain.

Customers in the capilar group are located in Oportoand Lisbon regions; Unicer gives them door-to-doordelivery. They include small to large restaurants, coffeeshops, bakeries, bars, and related establishments thatserve food and beverages. Their orders are usuallysmall (less than a pallet); however, the products theyorder represent a diverse product basket that requiresa complex picking operation.

Retailers are companies that have special commercialcontracts with Unicer; they do their own door-to-door delivery, especially in the regions outside Oportoand Lisbon. Their deliveries are restricted in size to33 pallets or 25.5 metric tons that ensure the full use ofa large truck. Unicer does not allow picking operationsfor this customer type.Strategic clients consist of modern retail chains,

wholesalers, restaurant chains, hotels, and other busi-nesses dedicated to commercial food and beverages.Each strategic client has several stores spread over thecountry. This sales group is the most heterogeneous;thus, we cannot define a typical order for the group,neither in terms of quantity nor product mix. Never-theless, these clients are particularly important becausestockouts in their stores have a huge impact on brandvisibility and recognition.

Finally, export clients are located outside Portugal.This segment, of which Spain and Angola are the maindestinations, represents over 40 percent of Unicer’stotal sales volumes, although the company sells itsproducts to more than 40 countries. Most of thesecustomers order large amounts of one or two productsthat Unicer ships in containers.

For each customer, the tactical plans define (1) thequantity of each product sent from each platform, and(2) the supply costs. From a simulation point of view,studying the effect of adding a new set of customers tothe network or assessing the impact of changing theorder policy of a given group of customers is critical.

TransportsProduction platforms, distribution platforms, and cus-tomers form a three-echelon distribution network.The production sites comprise the first echelon and dis-tribution platforms comprise the second. Both upstreamechelons can supply customers in the downstreamechelon. The example in Figure 3 shows the dynamicsof Unicer’s supply chain. It considers two productionplatforms (PP1 and PP2), two distribution platforms(PD1 and PD2), and three customers (C1, C2, and C3).In this representation of the supply chain, nodes arelocations and arcs represent the flow of finished prod-ucts. The figure shows only the arcs used to supplyclient C2. We distinguish between two type of flows:direct supply transportation movements, which aim tosupply client orders (depicted as solid arcs), and trans-portation movements that are intended to reallocatethe stock among the facilities (hereafter depicted asdashed arcs and called inverse movements).Distribution planning usually does not consider

inverse movements because supply chains are oftenacyclic networks in which production platforms cansend their products only to a distribution platform ordirectly to a client, and distribution platforms deliveronly to clients. The situation in our case study ismore complex because the finished products can flowamong production and distribution platforms, anddistribution platforms can also send products back to

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PP1

PP2

PD1

PD2

C2

C1

C3

Figure 3: Unicer’s supply five chain is a three-echelon distribution network.The production platforms are in the first echelon, the distribution platformsare in the second, and the clients are in the third. Solid lines representsupply movements and dashed arcs depict stock reallocation movements.

production platforms. The objective of these inversemovements is to more efficiently deliver clients’ orders.Before introducing the supply strategies for the variouscustomer groups, we first introduce some generalaspects of their supply.

In addition to capilar customers who deliver ordersusing Unicer’s fleet, Unicer subcontracts the services oftrucking companies, or 3PLs, to deliver its products.These companies use trucks that can carry up to 33 pal-lets or a maximum weight of about 25.5 metric tons.Hereafter, we will use the term truck to refer to theselarge vehicles.

We use the term full pallet to refer to a pallet loadedwith a single product, and the term picking to representunits (boxes) of products or pallets with several prod-ucts. A picking operation, which is possible only at adistribution platform, takes full pallets that originatedat the production lines, converts them into separateproduct units or rearranges them to form pallets thatinclude several products, which we call mixed pallets.The supply process for capilar clients starts by

sending full pallets from production to distributionplatforms. At the distribution platforms, the small het-erogeneous orders are picked and loaded into Unicer’svehicles that have been assigned routes on which theywill visit several customers.

Retailers receive their large orders in trucks that arecompletely loaded with full pallets directly from aproduction platform. All the products in the order arecommonly produced in only one production centerfrom which the order will be shipped. If the order isfrom a single production center, no further transportmovements occur. Otherwise, these orders can also

include very small numbers of products producedin other platforms or they can include some pickingunits. In such a case, the following may occur: If someproducts are not produced at the platform, full palletsare sent from a distribution platform or from theproduction platform responsible for their production.If the order includes a picking unit, these operationsare performed at a distribution platform that sendsthe picking unit(s) back to the production platform todeliver the order.As a result of the diversity in the orders coming

from strategic clients, these orders trigger the mostcomplex movements in the supply chain because theseclients adopt both centralized and decentralized inven-tory management strategies. Clients with a centralizedstrategy have their own central distribution platforms.Stores send their requirements to these depots, whichare responsible for sending orders to Unicer and forreceiving the products to later send to the stores. Theseare large orders that, as in the retailer scenario, may beappropriate to supply directly from production plat-forms. However, if the product mix is too large and hasa high number of picking operations or no particularproduction platform producing the majority of theproducts, the orders are served from a distributionplatform. For clients who use a decentralized strategy,the stores send the orders directly to Unicer, whoassumes responsibility for shipping products directly tothem; the resulting orders are much smaller. Therefore,these orders must be consolidated at a distributionplatform to efficiently use the capacity of the truck thatwill be routed to several stores.

Shipments to export customer can travel by landor sea; in both cases, they are sent in containers, areshipped from the production platforms, and usuallycomprise full pallets. For these clients, the productionplatform can also perform limited picking operations.Table 1 summarizes the delivery modes for each cus-tomer group.

To fulfill customer orders, a transportation movementmust be initiated at a production platform; orders canfollow one of three paths: (1) direct shipping from theproduction platform; (2) sending full pallets of prod-ucts to a distribution platform at which the order ispicked and sent, as mixed pallets, back to a productionplatform; from the production platform, mixed andfull pallets are shipped to the customers; (3) sending

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Customer group

Capilar Retailer Strategic Export

Delivery mode Door-to-door from Directly from production From both production and Directly fromdistribution platform platforms distribution platforms production platforms

Truck utilization LTLb FTLa FTLa/LTLb ContainersFull pallets No Yes Yes/no YesPicking Product units Rarely Product units and mixed pallets At the production platformProduct mix Complex Simple Complex Simple

Table 1: The table summarizes the main features of the supply strategies of each customer group.aFTL—Full truck load,bLTL—Less-than-full truck load.

products (full pallets) from various production plat-forms to a distribution platform that consolidates theorders and sends them to the customers.In addressing transports, we are particularly inter-

ested in capturing the flow among the platforms,including the inverse movements. The tactical distribu-tion plans created should define the following:• The quantities to be sent from the platforms (full

pallets and picking).• The total interplatform costs.Transportation management also gives rise to impor-

tant simulation questions, especially in relation to thedistribution network considered. By definition, Unicerdoes not use all possible transportation routes (i.e.,it does not consider the option of supplying a clientfrom some of the production platforms or distributionplatforms). Thus, we are interested in studying theeffect of this additional flexibility, which can lead torenegotiating existing 3PL transportation tariffs.

Initial SituationPrior to this project, the DB’s major purpose was toaid Unicer’s logistic department in estimating the costsit would incur in the following year. This departmentusually divided the DB into two budgets: platformsand transport. The platform budget included estimatesof the expenditures related to operating the platforms(i.e., activity costs); the transport budget projectedthe total costs in terms of interplatform movementsand client supply (i.e., costs incurred to meet clientorders). Both processes were performed manuallyusing spreadsheets and were highly dependent on themanagers’ experiences. These estimates were basedon past data, because no distribution plan had beencreated. Because a detailed sales budget per client

or per-client category was not available, managerslooked at total volumes per month and tried to detectdiscrepancies by comparing these volumes to thoseof the previous year. If they found discrepancies oracknowledged a significant change in past assumptions(e.g., important new clients or products, or changes inthe delivery mode for a set of customers), they wouldadapt the previous year’s budget to reflect the newreality.

To validate the various strategic choices, this processestimated future costs by looking at the past andcomparing past data to the data in the new scenario.Unicer was aware that its approach had some

drawbacks.1. It was heavily dependent on the experiences of

the managers assigned to the tasks.2. It was a difficult and time-consuming task because

the spreadsheet-based planning required significantmanual effort. This limited the number of scenarioanalyses that managers could perform to evaluate theperformance of various solutions or to assess a plan’ssensitivity to the input data.3. The plans generated did not ensure that the capac-

ity constraints identified at the platform level werefulfilled. Furthermore, because these plans did notdetail the flows of finished products, identifying andevaluating bottleneck activities was difficult.4. Finally, cost optimization, either in choosing the

platform activity level or selecting the delivery modeof clients, was not part of the process. These decisionsrequired trade-offs that were not being explicitly con-sidered. Examples of trade-offs include deciding toincrease the level of activity of one platform, openinga previously inactive platform for a short period, or

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changing the platform from which a given client issupplied.

The objective of this project was to develop a new pro-cess to correct the deficiencies in the existing methodol-ogy. However, this new process also had to providemore detail and better quality in the information avail-able to decision makers to improve their decisions.

Distribution Planning in theFast-Moving Consumer Goods IndustryIn the FMCG industry, 3PLs usually manage the trans-portation process. Companies in this industry acknowl-edge that they can increase their truck utilization byoutsourcing their transportation services to 3PLs thatcan consolidate shipments from different clients. More-over, efficiently using truck capacities can result inreduced freight costs (Stank and Goldsby 2000).Although Unicer has contracts with several 3PLs,

it controls its transportation planning. Crainic andLaporte (1997) distinguish between three levels oftransportation planning:• Strategic transportation planning encompasses a

long planning horizon and includes definitions of thedistribution network structure and customer servicelevels.• Tactical transportation planning uses aggregate

information to define the best allocation of resources.Hence, at this level, in which the distribution networkis fixed, the objective is to introduce activities aboutthe fixed facilities.• Operational transportation planning deals with

the detailed planning of vehicle loads, routing, andplatform management. At this planning level, agility inadapting to a very dynamic situation is necessary.

In our case study, the decision support system (DSS)helps to make decisions at the strategic and tacticallevels. However, its underlying mathematical modelhas a clear tactical scope. Many of the mathematicalmodels available in the literature for tactical trans-portation planning in a multiechelon network alsoinclude production decisions, as the review by Mulaet al. (2010) shows. Although these models capturemore upstream decisions, they provide a lower level ofdetail in the downstream echelons in comparison tothe formulation we present in this paper. For example,Timpe and Kallrath (2000) present an application in the

chemical process industry; in a multiplant productionsystem, they simultaneously plan distribution and mar-keting decisions with batch and campaign production.In this case study, the network consists of four plantsand four sales points that are significantly smaller thanours. We can find a distribution network similar to theone we discuss in this paper in the work of Bassettand Gardner (2010). These authors formulated twomathematical models; the first is for a three-echelondistribution network; the second adds an extra produc-tion echelon to form a four-echelon network. Althoughthe structure of their network and ours is similar, theirmodel’s decision level (strategic versus tactical) andthe distance between facility locations (long versusshort) clearly differ.The work by Kreipl and Pinedo (2004) seems to

share more common features with our project. It alsocovers a tactical problem that a beverage company(i.e., Carlsberg A/S in Denmark) faces, and the modelconsiders a three-echelon distribution network in whichcustomer orders can be supplied from both upstreamechelons. However, contrary to our work, it definesproduction decisions and allows no inverse movementsto occur. Furthermore, the second echelon is a single-distribution platform and inventory cannot be kept atproduction platforms. Finally, the activity level of theplatforms remains constant throughout the planninghorizon.For the aforementioned reasons, in addition to its

relevance in the context of the case study, we considerthe mathematical formulation we developed in thisproject to be important. Its major innovations rely onthe inverse movements in the network, the multipleactivity levels of the platforms, and the introduction ofoperational insights at a tactical level.

The Solution ApproachOur solution strategy to the tactical distribution plan-ning problem relies on a heuristic solution based on themathematical formulation of the problem, because thelarge scale of the instances in the case study prohibitedusing a commercial solver on the complete mathemati-cal formulation to achieve an optimal or quasi-optimalsolution. In our first experiments, (1) we could notload the complete model into the solver because ofinsufficient memory, or (2) the solver took prohibitively

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large computational time to generate the first feasiblesolution. Next, we describe the mixed-integer pro-gram (MIP) model for the tactical distribution planningproblem (see the appendix); later, we specify howwe heuristically solve it to find good solutions to theproblem.

A Model for the Tactical DistributionPlanning ProblemWe can describe the aforementioned three-echelondistribution network as a graph, G= 4V 1A5. The vertexset is composed of the reunion of the set P of availableproduction platforms (Echelon 1), the set D of distribu-tion platforms (Echelon 2), and the set C of customers(Echelon 3). The arc set explicitly defines the possiblepaths among vertices corresponding in practice to thetransportation routes that Unicer uses. These routescan be split into connections between platforms (I)and the paths linking platforms to customers (A).The problem is to define the flow of finished prod-

ucts K from the production platforms to the customersover the planning horizon T to satisfy the customerdemand at minimum cost. We can understand this asthe integration of two subproblems: transportation andinventory management. The first subproblem resem-bles a multicommodity, multiechelon, and multiperiodtransportation problem. Within this scope, the modelmust determine the quantity shipped in each periodfrom each platform to another platform, and fromeach platform to the set of final customers. The sec-ond subproblem handles all the activities within aplatform, subject to capacity constraints. Hence, themodel determines pallets handled, units of picking, andshipping containers, and also controls the inventoryand allocation of products to different storage types.These subproblems are deeply intertwined because thetransportation quantities determined will have a directimpact on the number of products handled and (or)stored.Next, we present the main decisions taken at each

entity of the supply chain.

PlatformsPlatforms can work on different activity levels (N ),which allow for different capacity restrictions. Thedefinition of these activity levels is crucial to attaininga realistic representation of the platform’s function-ing. Each activity level has a set of related costs and

capacities that incorporates the possibility of hiringadditional employees for picking or container-loadingoperations, using extra forklifts to increase pallet move-ment, or even creating additional working shifts. In ouroriginal case study formulation, we made additionaldistinctions on the abilities of each platform, such asthe ability to load (or not load) maritime containers.For brevity, we do not present these details.The major platform-related decision involves set-

ting the platform activity level in each period. To doso, we associate a binary variable with each activitylevel anit , which takes the value 1 if the (production ordistribution) platform i is at activity level n in period t.We model the inactivity of a platform using an artificialactivity level 0. At this level of activity, a fixed cost canbe incurred, but other costs and capacities are set to 0.

To capture the stock level at the end of each periodwe define seikt as the number of pallets of product kstored in platform i at storage type e in period t.

CustomersIn our mathematical formulation, we group customersbelonging to the set C according to transportationtype into maritime (M) or terrestrial (R) to capturethe container requirements. Using a second criterion,we categorize customers as national (F ) or interna-tional (E). We assume that D̄jkbt represents the demandof customer j for product k in the palletization (i.e.,use of pallets for transportation or storage) type b inperiod t. Palletization types correspond to the previ-ously defined full pallets (b= 1) and picking (b= 2).This immediately suggests the following decision vari-ables x̄ijkbt, which we define as the number of palletsof product k with palletization type b transported fromplatform i to customer j in period t to determine thesupply decisions. However, these variables are insuffi-cient to translate the reality into the model, becausethey do not capture the real operational moves in thetactical model, especially the inverse moves.To overcome this, we refine both the parameter

D̄jkbt and the decision variable x̄ijkbt . For this, we relyon the historical data for customer demand orders.We split the demand of customer j for each product kin a given period t into types of orders, in whichwe insert the demand. We then classify the ordersinto types according to order size (i.e., total orderweight measured in metric tons), production platform

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• Customer j• March•10,000 pallets

—9,000 full pallets—1,000 picking

• Product k

• 05–10 tons—Platform I—20%–30% | 1,000 full pallets• 10–15 tons—Platform I!—10%–20% | 4,000 full pallets• 10–15 tons—Platform I!—10%–20% | 500 pallets (in picking)• 20–25 tons—Platform I—80%–90% | 4,000 full pallets• 20–25 tons—Platform I—80%–90% | 500 pallets (in picking)

Demand by order typeq(tonnage) – i(majority of products) – p(percentage) | b(palletization)Demand

Figure 4: The figure illustrates possible demand decomposition into order types. Orders are grouped according tofour criteria: order size (tonnage), production platform of the majority of the products, magnitude of the majority(percentage), and palletization type.

producing the majority of products that are in this order,and the magnitude of this majority (i.e., a percentageof the total order weight). We define a finite set q 2 Qto classify orders according to their size and call ittonnage. Similarly, we also classify the magnitudeof the majority of products belonging to a singleproduction platform by intervals p 2G that we denoteas percentages. Figure 4 shows an example of thedemand conversion for a customer j for 10,000 palletsof product k in March.

Hence, we also must define x̄ in detail and introducea new decision variable f :

xijkbwt : number of pallets of product k with palletiza-tion b transported from platform i to customer jin period t to supply an order with the majorityof products from production platform w;

fqpjit : binary variable, which takes the value 1 if

demand orders of customer j in period t witha majority of products from production plat-form i having a percentage p and a tonnage q

are satisfied directly from i, or 0 if these ordersare satisfied through a distribution platformfrom the set D.

Ensuring the link between x and f allows us tocapture the operational behavior of deliveries in ourtactical model.

TransportsThe last decision variable details the interplatformmovements; ziwkbt represents the number of palletsof product k with palletization b transported fromplatform i to w in period t.

Having presented the main entities of our model,we can now describe the objective function and themain constraints.

Objective FunctionThe objective function minimizes the total distributioncosts over the entire planning horizon. These total costscorrespond to platform fixed-activity costs, platformstorage costs, pallet moving costs, picking movingcosts, shipping container loading costs, transportationcosts between platforms, and transportation costs todeliver orders to customers.All transportation costs consider the possibility of

dealing with returnable products in routes that maybe subject to such a consideration. Furthermore, tocalculate the FTL cost, we must consider the trans-portation mode used in a given transportation routefrom platform i to client j (i.e., trucks or containers).

ConstraintsIn the following, we describe the constraints used.Demand fulfillment constraints: All orders from

customers should be delivered without any delay (i.e.,in same period in which they were ordered). Backlogsare not allowed.

Demand supply strategy constraints: For each client,the model assigns demand order types 4i1 q1p5 either tothe corresponding production platform i or to the set ofdistribution platforms D. To make the plans coherentand comply with the judgments of the planners, wealso enforce the constraint that as soon as a given ordertype 4i1q1p5 is fulfilled through the correspondingproduction platform i, then all demand orders havingeither a heavier tonnage q or a higher percentage p

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Order sizes

0–5 tons 6–10 tons 11–15 tons 16–20 tons 21–25 tons

Percentages (%)100–80 DP DP PP PP PP80–60 DP DP PP PP PP60–40 DP DP DP DP DP

Table 2: The table presents the distributions paths for a given customer andperiod in production platform i, using a supply strategy defined by the cutoffpoint (i, 10–15 t, 80–60 percent). Order types whose size is bigger than10 t and with a percentage of product produced in i over 60 percent aresupplied directly from the production platform i, the remaining order typesare served by any distribution platform.

PP—Production platform; DP—Distribution platform.

must also be fulfilled from i. The supply strategycorresponds to the selection of a cutoff point, both interms of tonnage and percentage, above which ordersmust be supplied from a production platform. Table 2shows an example.

Inventory balance constraints (production platforms):The inventory balance constraints related to the pro-duction platforms characterize the movements that areallowed on these platforms. We distinguish betweenthe inventory balance constraints for products pro-duced (or not produced) in the respective productionplatform. We also consider that because of customsduties, picking at the production platforms can only bedone for international customers. Finally, each unit ofpicking entering the platform must leave the platformin the same period to satisfy Portuguese customerdemand.

Inventory balance constraints (distribution platforms):The inventory balance constraints at distribution plat-forms show their flexibility. In contrast to the produc-tion platforms, they can process any entering pallet intopicking units and dispatch in all palletization forms tothe customers with an associated transportation route.

Activity-level constraints: In each period, each plat-form can only operate at only one activity level.Platform activity cost constraints: Platform costs

depend on the activity level selected; thus, we mustlink them.Platform capacity constraints: Similar to the plat-

form costs, the amount of activity performed in eachplatform depends on the activity level determined.Hence, we impose the corresponding limits on thenumber of shipping containers loaded, pallets stored,

pallets moved, and picking operations performed inthe platforms.In this section and the appendix, we discuss the

general mathematical formulation for our problem.In this paper, we present the simplified version of themodel on top of which we built the heuristic embeddedin our optimization tool; therefore, we focus only onthe key modeling characteristics that can be applied insimilar situations.

The HeuristicsThe MIP model is not solvable for the large instances inour case study. Its computational intractability resultsparticularly from the large number of demand andflow variables. Therefore, solving this problem requiresthe use of efficient solution approaches. Mathemat-ical programming-based heuristics, also known asmatheuristics (James and Almada-Lobo 2011, Ball2011, Maniezzo et al. 2010), are algorithms that try tofind the best trade-offs between the effectiveness ofexact approaches and the efficiency of metaheuristics.We based our solution strategy on MIP-based heuristics,which are a class of matheuristics that rely on theheuristic solution of the mathematical formulation.

We designed the MIP-based heuristic in two phases:construction and improvement. Each phase uses adecomposition of the original mathematical formulationby period. In each iteration of the construction phase,we solve a single-period version of our MIP model.We start by solving the subproblem correspondingto the first period; we then fix the solution from thisperiod and set the final stock decisions as input to thenext subproblem (i.e., the second period). We repeatthis process and move progressively toward the endof the planning horizon. When we find the solution forthe last period, we have found a feasible solution tothe problem.The improvement phase of the heuristic seeks to

improve the solution quality of the feasible solutiondetermined. Solving a single-period version of ourmodel turns the final inventory decisions at each plat-form myopic, because the model does not consider anyadditional information about the demand. To overcomethis and other potential limitations of the single-periodmodel, we solve a two-period model at each iterationof the improvement phase. These two periods must beadjacent in time. We again start at the beginning of the

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Iteration 1

Iteration 2

Iteration 3

Iteration T

...

Construction phase

...

Iteration 1

Iteration 2

Iteration T – 1

Iteration 3

Improvement phase

Stock at the end ofperiod 1

Stock at the end ofperiod 2

Stock at the end ofperiod 3

Stock at the end ofperiod 2

Stock at the end ofperiod T – 1

Stock at the end ofperiod T – 2

Initialsolution

Unsolvedperiod

Fixedperiod

Periodbeing solved

Figure 5: The figure outlines the solution strategy. The initial solution is obtained by applying a time decompositionperiod by period to the complete model, and is then improved by solving two periods at a time.

planning horizon and reoptimize the solution corre-sponding to the first two periods, which we obtained inthe construction phase. In the next iteration, we fix thesolution for the first period, reoptimize periods 2 and 3together, and continue until we again reach the finalperiod. By keeping some overlap among successiveiterations, we guarantee a less-myopic heuristic andpotentially reduce the solution cost. Figure 5 visuallyshows the heuristics.Using MIP-based heuristics offers several ad-

vantages:• Assuming the user has some relevant expertise,

these heuristics are more easily implemented (i.e.,require fewer parameters and less effort by the user totune parameters and validate solutions) than traditionalheuristic approaches. Moreover, we consider theseheuristics to be problem independent because we can

add new variables and constraints with limited or nochange to the heuristic.• They take advantage of the computational effi-

ciency of modern commercial solvers.• Although they are based on the model, they can

accept model extensions (e.g., new constraints or newdecisions variables) with limited or no change to theheuristic.• As discussed in the literature, their performance

often provides quasi-optimal solutions for a variety ofproblems; for the majority of the companies, this issufficient.

However, these heuristics rely on the decompositionof a larger problem, with the expectation that theresulting subproblems are easier to solve than the mainproblem. If this is not true, these heuristics can eitherlose their efficiency or fail to deliver a feasible solution.

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Optimizationtool

KPIs andreportsM

aste

r dat

a

Productionplan

Demandforecast byorder type

SAPR/3

SAPAPO

Oth

erso

ftw

are

Production constraints

Supply chainconfiguration

Financialdata

Clients andSKU list

Orderclassification

Demand forecast

Delivery history

Figure 6: The figure depicts the high-level framework of the DSS. The necessary data are extracted from Unicer’sinformation technology systems and consolidated in a spreadsheet. Both the demand by order type and theproduction plan come from other Unicer systems. The spreadsheet and the systems output are entered into theoptimization algorithm; after processing these data, the algorithm generates the plan reports and key performanceindicators (KPIs).

Summarizing the pros and cons of MIP-based heuris-tics, we believe that they provide a more flexibleapproach that adapts to problem changes.

Decision Support SystemIn this section, we describe the DSS that envelops theoptimization tool and uses the solution strategy wepreviously describe. Figure 6 shows the relationshipbetween the building blocks of this DSS, which wediscuss in the following sections, and other softwarethat Unicer uses.This DSS uses an online platform that is available

to any computer with Internet access. To developthis tool, we used several programming languages.We coded the browser interface in JavaScript andestablished the communications with the dedicatedserver through C#. The core optimization tool usesC++ to read the data, execute the solution strategy,and generate the solution. The mathematical modelsare solved by a commercial mathematical programmingsolver. Finally, an add-on module, which we codedin Visual Basic for Applications (VBA), uses the raw

output data to build user-friendly reports and extractinformation from the output data.

Master DataThe master data input is a spreadsheet that includesmost of the model’s parameters. The user enters a listof products with all the required characteristics, a listof clients and associated client information, a list ofplatforms and abilities, the allowable activity levelsfor each platform, and the possible transportation arcswith their respective costs. As Figure 6 shows, much ofthis information is gathered from Unicer’s enterpriseresource planning system, SAP R/3, and entered into aspreadsheet for further validation and modification.The SAP advanced planner and organizer can alsobe helpful for entering the current configuration ofthe supply chain (i.e., the production and distributionplatforms and transportation routes used).

This considerable amount of data that reside perma-nently on the DSS server, can be changed incrementally.Because of the significant interactions between thesedata fields, this input is prone to consistency errors, asFarasyn et al. (2008) discuss. To circumvent this, we

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implemented a VBA module that identifies all potentialerrors and missing data. It also provides suggestionsfor rectifying the incoherent and missing values. Forexample, this module might indicate that a client hasno transportation route from any platform and suggestsome possible corrections. This type of informationsaved considerable time for the analyst setting upthe DSS.

Finally, using spreadsheets to enter the required datais an easy and inexpensive way to define new planningscenarios—a goal of this project. Adding new productsis a straightforward operation. Adding new customersor platforms, or even changing their locations, canbe more time consuming because of the number oftransportation routes affected; however, the process isas simple as adding or editing lines in the master datatemplate.

Demand Forecast by Order TypeThis module is responsible for creating the demandparameter; calculating this parameter requires twoinputs: (1) the demand forecast per client and periodof the planning horizon, and (2) the deliveries historyduring a similar horizon in the past; this informationis available from SAP R/3. For the DB, the demandforecast corresponds to monthly estimates for the nextyear and the delivery history of the current year. Usingthe demand forecast, we obtain total demand per client,product, and period. The deliveries history allowsus, with the necessary preprocessing calculations, todetermine the disaggregation detail of demand byorder type, based on customers’ previous demandorders.

Production BudgetThe production plan entered into the distributionplanning defines product production quantities at eachproduction platform in each period. The core problemconsists of assigning and scheduling production lots ina multiplant environment, in which each plant has aset of filling lines to bottle and pack drinks. Guimarãeset al. (2012) propose a method to create these plans. Theoutput of this method (or other solution approaches) isentered directly as parameters into the spreadsheet fordistribution planning.

Optimization ToolThe optimization tool is responsible for entering theinformation into our solution strategy, applying the

heuristics, and generating the output to be decodedby the VBA module. During the execution, the usercan request feedback about the status of the currentsolution. After setting up the input, the user initiatesthe optimization tool through the online interface.The heuristic then links to the MIP.

Key Performance Indicators and ReportsAfter the raw output generated by the VBA module hasbeen processed, graphical key performance indicators(KPIs) and extensive reports are available to the deci-sion makers to allow them to perform their analysesand make informed decisions. We implemented thefollowing seven KPIs that cover the main areas thatthe DSS influences.• KPI 1 (aggregated costs: platforms versus trans-

portation): Shows the main division of total costsbetween platform and transportation costs.• KPI 2 (platform costs by process): Disaggregates

the overall platform costs by activity costs, storagecosts, pallet moving costs, picking moving costs, andshipping container loading costs.• KPI 3 (transportation costs by process): Decom-

poses the overall transportation costs into their maincomponents—transportation costs to serve customersand between platforms.• KPI 4 (platform usage): Based on the number of

pallets distributed by each platform, this KPI showstheir relative importance to satisfy customers demandamong all platforms; it also allows the user to identifythe major bottlenecks within the distribution network.• KPI 5 (platform costs by platform): Divides the

overall platform costs by platform, providing thedecision maker with an overview of the platforms thathave higher costs.• KPI 6 (transportation costs by client type): Disag-

gregates the transportation costs by client type.• KPI 7 (expeditions per platform): For each plat-

form, assesses the number of pallets sent to clients andto other platforms.

In addition to the general information that the KPIsprovide, we developed seven reports to allow decisionmakers to delve more deeply into the results.• Report 1 (total costs): Gives the same information

as KPIs 1, 2, and 3, and allows the user to see theperiod (monthly) evolution of these costs.

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• Report 2 (platform costs by process): Breaks downKPI 2 and splits the process costs by platform and bymonth.• Report 3 (transportation costs by client type):

Breaks down KPI 6 by month.• Report 4 (transportation costs by client): Expands

on the detail in Report 3, includes separate costs foreach client, and splits the costs by product transported.• Report 5 (movements report): Summarizes the

activity of all platforms, making it the most importantreport. For each platform, it includes the monthly evolu-tion of the activity levels, stock, entries, and deliveries.For each resource, it shows utilization rates. Figure 7shows the details of this report for one platform.• Report 6 (activity levels): Shows activity levels for

all platforms for all months.• Report 7 (stock report): Shows the amount of stock

at each platform and in each type of storage for allmonths.

InterfaceThe final block of our DSS is the online interface, whichhas three major areas: (1) data file upload, (2) toolexecution, and (3) solution history. Figures 8 and 9show screenshots of the graphical interface and theexpected interactions with it, respectively. In Figure 9,the left column shows how the user can manage thedata files of the run, the central column illustrates thatthe user can launch new runs of the tool and accessthe log of the present and previous runs, and the lastcolumn shows solution files available for the user todownload.

ValidationIn conjunction with Unicer’s planning team, we vali-dated our approach in October 2012, as Unicer was cre-ating the DB. During this period, we trained the futureusers of the DSS, helped them to define the master dataspreadsheet, and taught them to set up the requiredproduction plans and demand forecasts. In the mas-ter data spreadsheet, we reduced Unicer’s original380 SKUs to approximately 120 product clusters bymerging products with similar physical and demandproperties. Similarly, we also created client clustersby using the aforementioned customer categories andthe districts in which the clients are located. Thus, wereduced the original 19,000 clients to about 200 client

clusters. In our solution strategy, clustering guaranteesthe tractability of the MIP models.

The 2012 DB included 21 platforms, nine productionplatforms, and two major distribution platforms; theremaining locations are auxiliary distribution platforms.Over 200 transportation routes were available amongthe platforms and more than 1,300 routes connectingplatforms and client clusters were defined as supplyalternatives. Larger platforms could operate using threeto four activity levels; however, the auxiliary platformsusually could operate with only two possible activitylevels (active or inactive).

Our DSS converted the SB per client into a detailedforecast by order typology, considering 180 possibletypes defined by the nine product platforms, fivetonnages, and four percentages. This process took300 seconds because 30,000 demand orders must beanalyzed each month. Our main goal was to evaluatethe plans that the DSS created from a business per-spective. We did this in several meetings with Unicermanagers and found that the costs we analyzed weresimilar in order of magnitude to the managers’ esti-mates. Moreover, as these managers analyzed the plansin more depth, they became more confident aboutthe tool, because its suggestions provided importantinsights on operating the distribution process.

We repeated this process at the beginning of 2013 tocompare the yearly plan as defined by Unicer (i.e., theplan defined without the DSS) to the DSS-generatedsolution from a cost-efficiency perspective. We eval-uated the plan defined by operations over the yearaccording to the costs defined in the master datafile and used it to set the operations base total costs.We then compared this plan with the ones we obtainedby solving the following:• The complete mathematical model formulation

(see the appendix).• The construction heuristic.• The construction heuristic followed by the

improvement heuristic.We used an Intel i7-3630QM Processor with 16 GB

RAM in our tests, and limited the run times of allthe heuristic approaches to one hour. The solutionto the complete model was inadequate because ofits poor quality. The solver stopped its search at avery early stage; it had explored only 55 nodes of thesearch tree when it reached the maximum running time

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Platform

Type

Jan

Fev

Mar

Abr

Mai

Jun

Jul

Ago

Set

Out

Nov

Dez

Total

Activity

Platform

XLe

vel

22

22

22

33

22

22

Stock

Platform

XDrive

inCap

acity

Platform

XDrive

inStock

Platform

XDrive

inUtilization

Platform

XRacks

Cap

acity

511

511

511

511

511

511

511

511

511

511

511

511

Platform

XRacks

Stock

409

409

409

409

409

409

409

409

409

409

409

409

Platform

XRacks

Utilization

(%)

8080

8080

8080

8080

8080

8080

80Platform

XFloo

rCap

acity

201000

201000

201000

201000

201000

201000

201000

201000

201000

201000

201000

201000

Platform

XFloo

rStock

61041

61041

61041

61041

61882

81215

111743

141131

161522

151930

161818

141739

Platform

XFloo

rStock(Pal)

161697

161818

161705

161303

181732

221300

311212

371196

431230

411801

441058

381955

Platform

XFloo

rUtilization

(%)

3030

3030

3441

5971

8380

8474

54Platform

XTo

tal

Totalstock

61450

61450

61450

61450

71291

81624

121152

141540

161931

161339

171227

151148

Entries

Platform

XPA

LTo

tal

345

514

523

436

825

647

662

763

618

691

593

687

71304

platform

sPlatform

XPicking

Total

11530

1711445

161565

131426

291711

361511

411003

381661

201537

201685

141404

161205

4201683

platform

sPlatform

XPicking

Totalp

latforms

1921126

187

144

426

527

595

587

230

242

167

163

51413

(PAL)

Platform

XPA

LTo

tal

481195

421173

511172

561921

721139

661392

691500

731885

661921

641512

541150

501070

7161030

prod

uctio

nPlatform

XPA

LInitial

stock

131444

171105

171227

171114

161712

191141

221708

311621

371604

431639

421210

441467

Platform

XTo

tal

Totalen

tries

621003

611918

691109

741615

901102

861707

931465

1061856

1051373

1091084

971120

951387

110511739

Expe

ditio

nsPlatform

XPA

LTo

tal

251619

161237

121461

221598

241720

241577

191906

201885

191275

201241

151676

211059

2431254

platform

sPlatform

XPA

LTo

talc

lients

131395

211793

231911

261349

361516

301867

361686

491115

291657

341623

301311

271158

3601381

Platform

XPA

LCap

acity

701000

701000

701000

701000

701000

701000

701000

701000

701000

701000

701000

701000

Platform

XPA

LUtilization

(%)

5654

5270

8779

81100

7078

6669

72Platform

XPicking

Totalp

latforms

Platform

XPicking

Totalp

latforms

(PAL)

Platform

XPicking

Totalc

lients

4471903

6801541

112161565

8731367

8041146

7361656

5681342

9161367

111171337

9111346

5121528

6241854

914091952

Platform

XPicking

Total

51898

81487

171338

101673

101578

101142

71572

111839

141677

121870

61677

81033

1241784

clients(PAL)

Platform

XPicking

Cap

acity

112001000

112001000

112001000

112001000

112001000

112001000

112001000

112001000

112001000

112001000

112001000

112001000

Platform

XPick

ing

Utilization

(%)

3742

100

7265

5844

7391

7442

5162

Platform

XCon

tainers

Totalc

lients

648

661

11100

868

11019

704

755

11031

964

11100

984

843

101677

Platform

XCon

tainers

Total

161294

161678

281197

221017

251901

171860

191087

261156

241522

301924

251055

211408

2741099

clients(PAL)

Platform

XCon

tainers

Cap

acity

11100

11100

11100

11100

11100

11100

11100

11100

11100

11100

11100

11100

Platform

XCon

tainersUtilization

(%)

5960

100

7993

6469

9488

100

8977

81Platform

XTo

tal

Total

441912

461517

531710

591620

711814

651586

641164

811839

631609

671734

521664

561250

7281419

expe

dition

s

Figu

re7:

Thefigurepresentsan

exam

pleof

themovem

entsreport(Report5

).Thisreport

allowsusersto

analyzethestockho

ldat

each

platform

andthelogistic

flows,

enab

lingthem

toiden

tifybo

ttlen

ecks.

Note.Fo

rthe

row“U

tilization”

(%),the“Total”columncorrespo

ndsto

averag

eutilizatio

n.Bo

ldface

high

lightsmainKP

Is.

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Preprocessing(*.exe)

Optimizer(*.exe)

Report solution(*.xlsx)

Warnings and errors(*.txt)

Execute

Master data(*.xlsx)

Production plan(*.txt)/(*.xlsx)

Demand forecast#T (*.txt)/(*.xlsx)

Deliveries history#T (*.txt)/(*.xlsx)

User

Decision support system

Yes

No

Figure 8: This figure illustrates the interactions between the user and the DSS. The user is responsible for enteringinformation into the DSS by uploading the master data spreadsheet and other files from Unicer’s informationtechnology systems. The DSS analyzes the input data and provides feedback about possible data mismatches orerrors. If it finds no errors, it executes the algorithm and produces a spreadsheet that includes the solution.

Figure 9: The user-DSS interaction uses an online interface divided into three areas (columns): data management(left), tool execution (center), and solution history (right).

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Avg. solutionVariables (binary) Constraints Nonzeros time (secs)

Complete model 8301000 (30,000) 3351000 319001000 281800a

Single-period 661000 (2,400) 261000 3001000 30model

Two-period 1351000 (4,900) 511000 5951000 115model

Table 3: The table shows the increase in size and running time of the MIPmodels.

aMaximum time limit.

(eight hours); the solution had no value. Table 3 presentsthe average model size and solution time for the variousmodels. The single-period model corresponds to themodel used in the construction phase and the two-period model to the one used in the improvementphase.Both versions of our heuristic procedures finished

long before the time limit and delivered better solutionsthan Unicer’s. The plan obtained by the constructiveheuristic took 354 seconds to generate and reduced thecost of the company’s plan by 5.25 percent. Applyingthe improving heuristic on top of the initial solutionfurther reduced the total cost, making it 6.8 percent lessthan Unicer’s original plan. These cost improvementscorrespond to reductions of approximately 1.7 million

Transportationamong platforms

Transportationto clients

Fixedactivity

Storage Pickingmoving

Palletmoving

Shippingcontainerloading

Storagecapacityviolation

Movementcapacityviolation

ActualConst. heu.Const. heu. + Imp. heu.

Figure 10: In this figure, we compare the two heuristic plans and the original Unicer plan in various cost categories.Both the storage capacity and the movement capacity violations are depicted by considering a secondary axis tohighlight the differences between plans.

and 2.2 million euros, respectively. Figures 10 and 11give more detail about the differences in the alternativeplans. Both heuristic procedures provide cost-categorytrade-offs that differ from Unicer’s perspective: theyincrease the transportation costs among platforms andthe storage costs to significantly reduce the customers’supply costs (see Figure 10) that represent the greatestshare of costs. Essentially, the plans we recommendedshow that repositioning the stock along the supplychain can lead to significant savings and meet clientdemands. We stress that the total stock in the supplychain is the same across the plans; the differences instorage costs result from the increased use of moreexpensive facilities. Moreover, as Figure 11 shows, wecan explain the cost differences between plans by theoperations behavior in the peak months of summer,when the capacity of the supply chain is tighter and thedecisions made have a higher impact, a situation thatpersists until the end of the year. Another importantaspect to emphasize is that both plans obtained bythe heuristics resulted in less transgression of both thestorage and the movement capacities (see Figure 10).We had to allow these violations in the model, butpenalized them in the objective function; otherwise themodel would be infeasible because of the low capaci-ties defined for these resources in the master data file.

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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

ActualConst. heu.Const. heu. + Imp. heu.YTD actualYTD const. heu.YTD const. heu. + Imp. heu.

Figure 11: The graph shows year-to-date cost and monthly cost for the three plans (see Figure 10).

These low capacities, which are the result of managersunderestimating capacities, ensure feasibility whenperforming the operational planning of the distribu-tion, as their level of overutilization in the actual planshows. Figure 12 highlights the benefits of the heuristicsover the planning horizon, considering only tangiblecosts. The apparent bad performance of the plans sug-gested by the heuristics in April (see Figure 12) occursbecause algorithms within the tool attempt to lower thestorage and movement capacity violations, which aresubstantially lower than in the Unicer plan.

Conclusions and Future WorkIn this paper, we describe the real-world tactical dis-tribution problem that Unicer, a major Portuguesebeverage production company, faces. The literature thataddresses tactical distribution problems with the fea-tures of this real-world application is sparse. However,we built on existing concepts addressing transportationand inventory and developed a new MIP model thathas as a key feature the insights of operational practiceat a tactical level. The model is the basis of our solutionstrategy, which we designed and implemented in a DSSthat Unicer is now using. We examined the componentsof the main building blocks of the DSS to help readersunderstand its most important factors; thus, we hope togive readers a basis to build a similar DSS and achievecomparable cost reductions.Today, Unicer uses OR in its tactical distribution

decisions, which are now based on automated, detailed,

and accurate tactical distribution plans. The companyis using our DSS to evaluate various logistic scenariosand prepare its annual budget. It validated its 2013budget using this new tool. The benefits attained fromusing the DSS are evident by cost reductions, easeof simulating multiple logistic scenarios, and timesaved in preparing the annual budget. Unicer cananalyze virtually all possible distribution scenarios, agreat advantage to a company that must frequentlychallenge its practices. Moreover, the new planningmethodology makes the process more transparentand substantially decreases the lead time requiredto deliver the plans. Unicer analysts recognize thatthe DSS has an underlying optimization model thatretrieves solutions that were difficult to generate usingthe previous empirical methods.

We built the DSS as modules using blocks that couldbe easily modified; therefore, it has the potential toaddress similar real-world problems. The most straight-forward application is adapting this approach to otherbeverage companies with similar distribution problems.However, other FMCG companies are a natural exten-sion because they also have vast product portfolios,many clients, and dynamic distribution networks.Future work could involve the integration of dis-

tribution and production tactical planning becausethey are related intrinsically. Extending the DSS toaccommodate customer service levels and empoweringthe decision makers with more knowledge about thesolution are also possibilities for future research.

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€

Figure 12: In the graphs, we compare the savings the heuristics provide vs. the company plan; (a) absolute value;(b) percentage value.

AcknowledgmentsWe would like to express our gratitude to Unicer and espe-cially to its logistic department for the strong cooperation wereceived throughout this project. This work is financed by theERDF—European Regional Development Fund—throughthe ON.2 Programme and by National Funds through theFCT—Fundação para a Ciência e a Tecnologia (PortugueseFoundation for Science and Technology)—within Smart Man-ufacturing and Logistics [Project NORTE-07-0124-FEDER-000057].

Appendix. The MIP FormulationThe parameters related to the platforms needed to formu-

late the problem are as follows.Costs

F ni Fixed activity cost in platform i 2P [D for activity

level n.

uHni

Unit storage cost in platform i 2P [D for activitylevel n.

uMni

Unit pallet moving cost in platform i 2 P [D foractivity level n.

uPni

Unit picking moving cost in platform i 2P [D foractivity level n.

uCni

Unit shipping container loading cost in platformi 2P [D for activity level n.

Capacities

rHein

Storage capacity in number of stack positions inplatform i 2P [D for activity level n and storagetype e.

rMni

Capacity for pallet movements in platform i 2P [Dfor activity level n.

rPni

Capacity for picking movements in platform i 2P [Dfor activity level n.

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rCni

Capacity for loading shipping containers in platformi 2P [D for activity level n.

To correctly assess the available storage capacity, we mustconsider the number of pallets that we can stack becausethis number depends on the product and storage type.The parameter çek sets the maximum number of pallet stackinglevels of product k at storage type e. For production platforms,the planned production quantities are also an input to themodel. Let Pjkt define the quantity of product k produced atplatform j 2P in period t.

The demand parameter used in the mathematical model isas follows:

Dqpjkbit Demand of client j in period t for product k with

palletization b within an order in which the majorityof products from i 2P have a percentage p and atonnage q.

The following parameters are necessary to capture the trans-portation costs among the different locations of the supplychain:

fTij Full truck load (FTL) cost for traveling from i to j .vTij

Less-than-full truck load (LTL) cost for traveling from ito j .

To describe the MIP model formulated for the tacticaldistribution problems, the following additional parametersare required:

Åk Cost factor to account for the inverse logistics of prod-uct k.

Çij Cost factor to account for the inverse logistics of passingin arc 4i1 j5 2A[I .

ÉRk Land-container capacity if only product k is transported.

ÉMk Maritime-container capacity if only product k is trans-

ported.Ük Weight of each pallet of product k.Ñk Number of product units in a pallet of product k.åk Factor for converting pallets of product k into full

pallets of product k.

We also must introduce auxiliary decision variables to lin-earize the piecewise cost functions at platforms, which wedefine as follows:

cHitStorage cost in platform i 2P [D in period t.

cMitPallet moving cost in platform i 2P [D in period t.

cPit Picking moving cost in platform i 2P [D in period t.cCit

Shipping container loading cost in platform i 2P [Din period t.

The MIP model reads:

min⇢ X

i2P[D1n1 t

F ni a

nit +

X

i2P[D1 t

4cHit+ cMit

+ cPit + cCit5

·X

4i1 j52I1k1 b1 t

fTij /ÉRk 41+ÅkÇij5zijkbt

+X

4i1 j52I1k1 b1 t

vTijÑkÜk41+ÅkÇij5zijkbt

+X

4i1 j52A2 j2R1k1 b1w1 t

fTij /ÉRk 41+ÅkÇij5xijkbwt

+X

4i1 j52A2 j2M1k1 b1w1 t

fTij /ÉMk 41+ÅkÇij5xijkbwt

+X

4i1 j52A1k1 b1w1 t

vTijÑkÜk41+ÅkÇij5xijkbwt

�0 (1)

The following auxiliary constraints quantify the variousplatform costs, which depend on the platform activity level.Constraints (2) quantify the storage cost of each platform ineach period. This cost is incurred for every full pallet storedand depends on the platform activity level. Note that Mdenotes a large number:

cHit�

X

k1 e

unHi

seiktåk

+M4anit É 15

8 i 2P [D1 n 2N 1 t 2T 0 (2)

Constraints (3) account for the full-pallet moving costs.These costs must consider all pallets handled either whenreceiving or sending products:

cMit�

X

4i1 j52A1k1 b1wuMn

i

xijkbwt

åk

+X

4i1 j52I1k1 b

uMni

zijkbt

åk

+X

4j1 i52I1k1 b

uMni

zjikbt

åk

+M4anit É 15

8 i 2P [D1 n 2N 1 t 2T 0 (3)

In contrast to the full-pallet moving costs, the picking costsare obtained considering only the number of units of pickingexiting the platform (constraints (4)):

cPit �X

4i1 j52A1k1wuPn

ixijk2wtúk +

X

4i1 j52I1k

uPnizijk2túk

ÉX

4j1 i52I1k

uPnizjik2túk +M4anit É 15

8 i 2P [D1 n 2N 1 t 2T 0 (4)

The final cost constraints refer to the loading shippingcontainers cost, which we obtain through constraints (5):

cCit�

X

4i1 j52A2 j2M1k1 b1w

uCni

xijkbwt

ÉMk

+M4anit É 15

8 i 2P [D1 n 2N 1 t 2T 0 (5)

Next, we introduce demand fulfillment constraints. The firstconstraints of this group, constraint (6), state that the cus-tomer’s demand must be satisfied completely:

X

4i1 j52Axijkbwt =

X

q1p

Dqpjkbwt

8 j 2C1 k 2K1 b 2B1 w 2P1 t 2T 0 (6)

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Constraints (7) and (8) use decision variables fqpjit to assign

demand order typologies to a certain distribution echelon(i.e., production or distribution platforms):

xijkbit =X

q1p

Dqpjkbitf

qpjit

8 4i1 j5 2A2 i 2P1 j 2C1 k 2K1 b 2B1 t 2T 1 (7)X

4i1 j52A2 i2Dxijkbwt =

X

q1p

Dqpjkbit41É f

qpjit 5

8 j 2C1 k 2K1 b 2B1 w 2P1 t 2T 0 (8)

Constraints (9) and (10) define the cutoff point for supply-ing orders from the production platforms:

fq0pjit É f

qpjit � 0

8 j 2C1 i 2P1 q1 q0 2 Q2 q0 � q1 p 2G1 t 2T 1 (9)

fqp0jit É f

qpjit � 0

8 j 2C1 i 2P1 q 2 Q1 p1p0 2G2 p0 � p1 t 2T 0 (10)

The inventory balance constraints related to the produc-tion platforms are expressed in constraints (11)–(13). Con-straints (11) and (12) distinguish between the inventory balanceconstraints for products produced (or not produced) in therespective production platform (using set Kj , which representsthe set of products belonging to platform j 2P), respectively.These equations show that picking at the production platformscan only be done to satisfy international customers.

Pjkt +X

e

sejk1 tÉ1 +X

4i1 j52Izijk1t =

X

e

sejkt +X

4j1 i52Izjikbt

+X

4j1 i52A2 i2N 1k1 j

xjik1jt +X

4j1 i52A2 i2E1k1 b1 jxjikbjt

8 j 2P1 k 2Kj1 t 2T 1 (11)X

e

sejk1 tÉ1 +X

4i1 j52I1 b

zijk1t =X

e

sejkt +X

4j1 i52Izjikbt

+X

4j1 i52A2 i2N 1k1 j

xjik1jt +X

4j1 i52A2 i2E1k1 b1 jxjikbjt

8 j 2P1 k 2K\Kj1 t 2T 0 (12)

Constraints (13) force each picking unit that enters theplatform to leave the platform in the same period to satisfythe demands of Portuguese customers:

X

4i1 j52I 2 i2Dzijk2t =

X

4j1 i52A2 i2N 1 j

xjik2jt

8 j 2P1 k 2K1 t 2T 0 (13)

The inventory balance constraints at distribution platformsis given in constraint (14):

X

e

sejk1 tÉ1 +X

4i1 j52I 2 i2D1 b

zijkbt +X

4i1 j52I 2 i2Pzijk1t

=X

e

sejkt +X

4j1 i52Izjikbt +

X

4j1 i52A1 b1 jxjikbjt

8 j 2D1 k 2K1 t 2T 0 (14)

The following capacity constraints limit the amountof activity performed in each platform depending onthe decided activity level: shipping containers loaded—constraint (15), pallets stored—constraint (16), pallets moved—constraint (17), picking performed in production platforms—constraint (18), and picking performed in distributionplatforms—constraint (19):

X

4j1 i52A2 i2M\YD1k1 b1w

xjikbwt/ÉMk

X

n

rCjnanjt

8 j 2P [D1 t 2T 1 (15)

X

k2Ksejkt/åk/ç

ek

X

n

rHejnanjt 8 j 2P [D1 t 2T 1 (16)

X

4i1 j52A1k1wxjik1wt/åk +

X

4i1 j52I1k

zjik1t/åk X

n

rMjnanjt

8 j 2P [D1 t 2T 1 (17)X

4i1 j52A2 i2E1k1wxjik2wtúk

X

n

rPjnanjt 8 j 2P1 t 2T 1 (18)

X

4i1 j52A2 i2N 1k1w

xjik2wtúk +X

4i1 j52I1k

zjik2túk ÉX

4j1 i52I1k

zijk2túk

X

n

rPjnanjt 8 j 2D1 t 2T 0 (19)

Finally, Equation (20) ensures that each platform onlyoperates at a single activity level in each period:

X

n

anjt = 1 8 j 2P [D1 t 2T 0 (20)

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Surveys Oper. Res. Management Sci. 16(1):21–38.Bassett M, Gardner L (2010) Optimizing the design of global supply

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Verification LetterCarlos Caiado, Director of Logistics Department of Unicer,Bebidas, SA, Via Norte-Leça do Balio, Matosinhos, Apartado1044, 4466-955 S. Mamede de Infesta, writes:

“I hereby certify that the Decision Support System devel-oped by the authors of the manuscript ‘Annual DistributionBudget in the Beverage Industry: A Case Study’ is being usedby my team at Unicer. Unicer is one the two biggest beveragecompanies in Portugal. As any company with this size, it hasseveral challenges in its supply chain management. This toolallows having a strategic and optimized perspective of ourdistribution process, keeping at the same time a high level ofreality.

“Currently, this Decision Support System is being used toevaluate different logistic scenarios and to help in prepar-ing the annual budget of the department that I am running.The attained benefits are evident by the easiness of simulationof multiple logistic scenarios and by the time saved in prepar-ing the annual budget. Moreover, this decision support systemhas an underlying optimization model that retrieves solutionsthat were hard to grasp with the previous empirical methods.”

Luis Guimarães has an MSc and PhD in industrial engi-neering and management from the Faculty of Engineering ofthe University of Porto (FEUP), where he is currently a post-doctoral researcher. His main research interests are alignedwith both supply chain planning optimization and mathe-matical programming based heuristics. He has published inrefereed international journals in the fields of engineeringapplications and operations research. Most of his researchis problem-driven and aims to develop advanced analyticsolutions to be applied in real-world problems. In this context,he has worked on several consultancy projects with privateinstitutions.

Pedro Amorim graduated with a degree in industrialengineering from the Faculty of Engineering of Universityof Porto (FEUP). He has a PhD from the same universityand is an assistant invited professor at the Departmentof Industrial Engineering and Management at FEUP. Hisresearch activities are focused on production and distri-bution planning of perishable goods. In this area, he haspublished several papers in refereed international journals.He has been researcher of over 10 research and consultancyprojects supported by European Commission, Science andTechnology Foundations of several countries and privateinstitutions.

Fabrício Sperandio is a PhD candidate in the Faculty ofin Engineering at the University of Porto, Porto, Portugal,where he is a research assistant. As a software engineer, hehas 10 years of experience with design and implementationof information systems for hospitals and private clinics, par-ticularly Web-based applications. His main research interestsare operating room planning and scheduling and medicalstaff rostering. He is currently working on a novel simulationoptimization approach to the operating room schedulingproblem under uncertainty.

Fábio Moreira is a PhD candidate in industrial engineeringand management at the Faculty of Engineering of the Univer-sity of Porto (FEUP) from which he has received an MSc inthe same field. In the past, he developed analytic tools as aresearcher at both the Institute of Mechanical Engineeringand Industrial Management to assist project management andin a pharmaceutical company to solve its route schedulingand crew assignment problem. His current research interestsare combinatorial and supply chain optimization.

Bernardo Almada-Lobo is an associate professor at Fac-ulty of Engineering of UP, head of the Industrial Engi-neering and Management Research Unit of INESC-TEC,and vice director of the IBM Center of Advanced Stud-ies Portugal. His main area of activity is management sci-ence/operations research. He develops and applies advancedanalytical models and methods to help make better deci-sions, solving managerial problems in various domains(industry, health, retail, and transportation), with a spe-cial focus on operations management. He has conductedover 30 industry-based research and consulting projects.He has published in a number of journals in the field ofindustrial engineering, operations research, and computerscience.

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