Supply chain optimisation with assembly line balancing

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International Journal of Production Research

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Supply chain optimisation with assembly linebalancing

Turan Paksoy , Eren Özceylan & Hadi Gökçen

To cite this article: Turan Paksoy , Eren Özceylan & Hadi Gökçen (2012) Supply chainoptimisation with assembly line balancing, International Journal of Production Research, 50:11,3115-3136, DOI: 10.1080/00207543.2011.593052

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International Journal of Production ResearchVol. 50, No. 11, 1 June 2012, 3115–3136

Supply chain optimisation with assembly line balancing

Turan Paksoya, Eren Ozceylana* and Hadi Gokcenb

aSelcuk University, Department of Industrial Engineering, Campus, 42031 Konya, Turkey; bGazi University,Department of Industrial Engineering, Maltepe, 06570 Ankara, Turkey

(Received 7 January 2011; final version received 25 May 2011)

Supply chain management operates at three levels, strategic, tactical and operational. While the strategicapproach generally pertains to the optimisation of network resources such as designing networks, location anddetermination of the number of facilities, etc., tactical decisions deal with the mid-term, including productionlevels at all plants, assembly policy, inventory levels and lot sizes, and operational decisions are related to howto make the tactical decisions happen in the short term, such as production planning and scheduling. Thispaper mainly discusses and explores how to realise the optimisation of strategic and tactical decisions togetherin the supply chain. Thus, a supply chain network (SCN) design problem is considered as a strategic decisionand the assembly line balancing problem is handled as a tactical decision. The aim of this study is to optimiseand design the SCN, including manufacturers, assemblers and customers, that minimises the transportationcosts for determined periods while balancing the assembly lines in assemblers, which minimises the total fixedcosts of stations, simultaneously. A nonlinear mixed-integer model is developed to minimise the total costsand the number of assembly stations while minimising the total fixed costs. For illustrative purposes, anumerical example is given, the results and the scenarios that are obtained under various conditions arediscussed, and a sensitivity analysis is performed based on performance measures of the system, such as totalcost, number of stations, cycle times and distribution amounts.

Keywords: supply chain design; assembly line balancing; nonlinear mixed-integer programming

1. Introduction

Supply chain management is more than just innovation for the sake of being innovative. It is creating a uniquesupply chain configuration that drives objectives forward. To get the most from a supply chain, five criticalconfiguration components are needed for consideration under strategic, tactical and operational decisions (Cohenand Roussel 2005):

. operations strategy

. outsourcing strategy

. channel strategy

. customer service strategy

. asset network

While companies have tended to address these components singly, they are now considering a few or all of them.However, considering the configuration components or different decision levels together also forces companies into anumber of trade-offs, for example production planning, distribution costs, line balancing, working times, location offacilities, etc. (Schmidt and Wilhelm 2000). Since a supply chain deals with material flows and information flowsacross the entire chain, from suppliers of original components to final customers, it comprises at least two majorintegrated domains: production planning, which deals with manufacturing, warehousing and their interfaces, and thedistribution and logistics process, which determines how products are retrieved and transported from suppliers tocustomers (Xiaobo et al. 2007, Tuzkaya and Onut 2009). In order to realise these major domains, each SCN shouldidentify strategic and tactical decisions that minimise the total costs or maximise the overall value generated.

A supply chain may be considered as an integrated process in which a group of several organisations, such assuppliers, producers, distributors and retailers, work together to acquire raw materials with a view to convertingthem into end products which they distribute to retailers (Mula et al. 2010). Because there are several organisations,

*Corresponding author. Email: [email protected]

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the efficiency of the supply chain system is influenced by many factors, the most common of which is to determinethe location of facilities to be opened and the distribution network strategy in such a way that customer demand canbe satisfied at minimum cost or maximum profit (Syarif et al. 2002, Yan et al. 2003, Gen and Syarif 2005,Altiparmak et al. 2006). In addition to the above factor, the production operations should also be decisive factorsfor the optimisation of SCNs. Assembly line balancing operations, which are one of the decisive factors, are themost common situation in SCNs due to the large number of components. To construct an agile SCN, competentand compatible assembly line processes and supply–distribution processes have to be able to work simultaneously.To deal with these problems, SCN functions should be integrated in a comprehensive framework. This integrationshould basically be between two main SCN processes such as assembly line balancing and the above transportationfunctions. This situation can provide visibility, which will lead to greater accuracy, reliability, and customer servicelevels. At this point, two main aspects gain crucial importance in a SCN. First, companies try to add maximumvalue by minimising their own transportation costs at each stage of the SCN. Second, companies struggle tooptimise the operations of whole areas of the SCN such as line balancing and the fixed costs of opened stations(Tuzkaya and Onut 2009). Therefore, there is a close linkage between assembly and distribution that necessitates thecoordination of assembly and distribution operations in supply chain systems.

In this paper, we present a novel nonlinear mixed-integer mathematical model for a supply chain networkconsisting of multiple manufacturers that integrates multiple components and multiple assemblers, integratingassembly lines and multiple customers, that have multiple period time horizons with respect to the available capacityrestrictions. This model is used to optimise the assignments of tasks to assembly lines to determine optimum stationsaccording to fixed costs and transportation decisions for a multi-echelon supply chain in order to minimise the totaltransportation cost. Cycle times are determined as a decision variable to connect two problems (SCN and assemblyline balancing problems).

The paper is organised as follows. Section 2 reviews the supply chain network design and assembly line balancingproblems literature. The proposed nonlinear mixed-integer programming model that minimises the total cost of theoverall SCN and minimises the fixed costs of assembly stations and the individual functional units is presented inSection 3. For illustrative purposes, a numerical example is given, the results and the scenarios that are obtainedunder various conditions are discussed, and a sensitivity analysis is performed in Section 4. Finally, Section 5concludes the paper and proposes future directions for research.

2. Literature review

Supply chain management has received considerable attention from academicians, researchers and operators duringthe last several decades. Designing and optimising SCNs is one of the most popular problems in this research field.For that reason, many mathematical and heuristic models have been proposed. Most of these models are related tothe transportation/distribution networks with the following considerations (Paksoy and Chang 2010):

. location of the facilities (plants, distribution centres, etc.) to be opened;

. design of the network configuration; and

. satisfy customer demand with minimisation of the total cost, including purchasing cost, transportation cost,fixed operating cost, etc. (Cohen and Lee 1989, Pyke and Cohen 1993, Syarif et al. 2002, Paksoy et al. 2007,Altiparmak et al. 2009).

In addition to the studies mentioned above, a few of the proposed models focus on the integration of specificfunctions, such as warehousing (Ganeshan 1999, Monthatipkul and Yenradee 2008, Tuzkaya and Onut 2009),aggregated production planning (Singhvi et al. 2004, Foo et al. 2008) material requirement planning, etc. (Espositoand Passaro 1997, Yan et al. 2003). With respect to modelling, the vast majority of studies use the linearprogramming-based modelling approach (Martin et al. 1993, Chen and Wang 1997, Kanyalkar and Adil 2005),particularly mixed-integer linear programming models (Mcdonald and Karimi 1997, Dogan and Goetschalckx 1999,Sakawa et al. 2001, Rizk et al. 2008). Conversely, nonlinear programming is only used in a few studies (Lababidiet al. 2004, Altiparmak et al. 2006). Syarif et al. (2002) defined this kind of problem as being NP-hard because of thecombination of multiple choice Knapsack problems with the capacitated location–allocation problem simulta-neously. Thus, heuristic and meta-heuristic models have been developed and proposed by Jayaraman and Pirkul(2001), Syarif et al. (2002), Gen and Syarif (2005), and Altiparmak et al. (2009).

In supply chain optimisation models, costs, customer service and inventories are considered mostly forquantitative purposes. According to Mula et al. (2010), regarding costs, the minimisation of costs (Ozdamar and

3116 T. Paksoy et al.

Yazgac 1997, Azaron et al. 2008), the maximisation of revenues and the maximisation of benefit (Cohen and Lee

1989, Tsai et al. 2008) have been studied, while the maximisation of the service level (Chen and Lee 2004, Torabi andHassini 2008), the minimisation of backorders (Tuzkaya and Onut 2009, Paksoy and Chang 2010), flexibility involume or delivery dates (Sabri and Beamon 2000) or the maximisation of flow have been considered for customerservices. The maximisation of safety inventories has also been taken into account.

This section presents a review of mathematical programming models for SCN problems. The analysed papers aregiven by classification based on the analysis of the supply chain modelling approach and purpose. Conclusionsdrawn from this section affirm the following.

. Most of the models reviewed consider a supply chain network for production and transportation planningoriented towards the strategic or tactical decision level only. Studies that have integrated the hierarchicalstructure of the tactical and operative planning levels simultaneously are few in number.

. Because of the complexity of this kind of problem, nonlinear models are less useful than other mathematicalmodels.

. Inventory, backorder and warehouse functions are considered mostly as tactical decision levels.

Due to the above factors, we propose a nonlinear mixed-integer mathematical model that considers strategic andtactical decisions simultaneously. After reviewing past studies, we determined that assembly line balancing problemshave not been studied as a tactical decision while designing and optimising a supply chain network. An assembly lineconsists of several successive workstations, at which assembly operations of a particular product are performed.

A task is defined as the smallest portion of an assembly operation. The magnitude of the work content of aworkstation is the sum of the completion times of tasks assigned to the workstation. The largest work content of anassembly line is defined as the cycle time of the assembly line (Kara et al. 2009). Assembly lines can be classified interms of the shape of the line (straight or U-shaped) and also in terms of the number of different products producedon the line (single or mixed) (Gokcen and Agpak 2006). This paper focuses on straight and single assembly lines.

A single-model assembly line is limited to producing one variant (Figure 1) and is mainly used for massproduction of one homogeneous product (Hakansson et al. 2008). The problem of assigning tasks to workstations insuch a way that certain performance measures are optimised subject to the precedence relationships (Figure 2)

among tasks is known as the assembly line balancing (ALB) problem (Kara et al. 2009). Figure 2 shows aprecedence graph with n¼10 tasks with task times between 2 and 9 (time units). The precedence constraints for task5, for example, state that its processing requires that tasks 1 and 4 (direct predecessors) and 3 (indirect predecessor)be completed. In other words, task 5 must be completed before its (direct and indirect) successors 6, 8, 9, and 10 canbe started (Scholl and Becker 2006).

The simple assembly line balancing problem (SALBP) occurs when stations are equally equipped with respect toworkers and machines, alongside a paced line with fixed cycle time and deterministic operation times. Depending onthe performance measure considered, three versions of assembly line balancing can be identified (Scholl 1999).

. SALBP-1: Minimise the number of stations J for a given cycle time CT.

. SALBP-2: Minimise the cycle time CT for a given number of stations J.

. SALBP-E: Maximise the line efficiency E or, equivalently, minimise J*CT.

The ALB problem was first formulated mathematically by Salveson (1955). Following this study, many studieson assembly lines, including exact solution methods, heuristics and meta-heuristic approaches, have been reported inthe literature to date. Ozcan (2010) reported that reviews of such studies have been given by Baybars (1986), Ghoshand Gagnon (1989), Erel and Sarin (1998), Scholl (1999), Rekiek et al. (2002) and more recently by Scholl and

Figure 2. Precedence graph (Scholl and Becker 2006).Reprinted from European Journal of Operational Research,168, A. Scholl and C. Becker, State of the art exact andheuristic solution procedures for simple assembly line balan-cing, 666–693, � 2006, with permission from Elsevier.Figure 1. Straight and single assembly line.

International Journal of Production Research 3117

Becker (2006), Dolgui (2006), and Becker and Scholl (2006). Several techniques have been proposed for the solutionof SALB problems with different considerations of task times and configurations (Graves and Lamar 1983, Pinnoiand Wilhelm 1997, Nicosia et al. 2002, Yamada and Matsui 2003, Agpak and Gokcen 2005). According to thestudies quoted above, supply chain network design and assembly line balancing problems are always studiedseparately. However, Che et al. (2009) reported that the operation mechanism of a supply chain is similar to anassembly production line. Hence they attempted to adopt line balancing technology to complete co-operatorselection and industry assignment for the cooperation mechanism with the lower delivery delay loss of the supplychain network. But they applied assembly line balancing to the supply chain network problem, therefore they arenot considered simultaneously. Che and Chiang (2010) focused on performing supply chain planning for a build-to-order supply chain network. The planning is designed to integrate supplier selection, product assembly, as well asthe logistic distribution system of the supply chain in order to meet market demand. They consider three evaluationcriteria, namely costs, delivery time, and quality, and a multi-objective optimisation mathematical model isestablished for build-to-order supply chain planning. However, line balancing is not considered. Sawik (2009)considered the integration of supply, production and distribution in a customer-driven supply chain and proposedmixed-integer programming formulations for the long-term scheduling and coordination of parts manufacturingand supply and finished products assembly. Although the problem considered is how to coordinate themanufacturing and supply of parts and assembly of products such that the total supply chain inventory holding costand the production line start-up and parts shipping costs are minimised, there is no consideration of assembly linebalancing. Xiaobo et al. (2007) consider a supply–assembly–store chain with a produce-to-stock strategy. The chaincomprises a set of component suppliers, a mixed-model assembly line (MMAL) with a conveyor linking a set ofworkstations in series, and a set of finished product storehouses. The paper conducts a modelling and performanceanalysis in the design stage of the system in the sense of ‘long-term-behaviour’.

According to assembly line managers, the most important goals related to assembly line balancing are theminimisation of the number of workstations or minimisation of the cycle time. In some studies, minimisation of thenumber of workstations is provided via minimisation of the fixed costs of each station in the assembly line. Askinand Zhou (1997), Amen (2000) and McMullen and Tarasewich (2006) consider cost parameters for stations, workersand equipment in assembly line balancing problem objectives. In the aforementioned objectives, the cycle times andnumber of stations should be constant and given. However, this situation can change and be complex in someassemblers that deal with a supply chain network. Decision makers cannot ignore supply chain activities whilebalancing assembly lines, or ignore assembly line balancing while designing a supply chain network for a supplychain that has assemblers. These two main problems are completely interactive. Transportation amount, thecapacity of facilities, and changing demand directly affect the cycle time and total stations in assemblers.

To the best of our knowledge, there is no published study dealing with supply chain network design andassembly line balancing problems simultaneously in the literature. Consequently, in this paper, simultaneousoptimisation of the supply chain and assembly lines is introduced and characterised. Therefore, the consideredproblem is a new problem and the problem becomes even more difficult in our case due to the NP-hard structure ofthe supply chain network and assembly line balancing problems. A nonlinear mixed-integer mathematical model isdeveloped to model and solve the problem. For integration of the two problems, cycle times are transformed intodecision variables. The results of computational experiments of the developed model on a set of test problems arereported.

3. Optimisation of supply chain networks with assembly lines

In this section, a nonlinear mixed-integer model is developed to solve the optimisation problem of a supply chainnetwork with assembly lines. First, the problem is described, and the problem assumptions are given.The mathematical formulation of a deterministic version of the problem is then presented.

3.1 Integration of supply chain network design and assembly line balancing

In this section, the optimisation of a supply chain network while balancing the assembly lines is discussed. A typicalsupply chain network design problem has typical inputs such as a set of customer zones to serve, a set of products tobe manufactured and distributed, demand projections for the different customer zones, and information concerningfuture conditions, costs (e.g., for production and transportation) and resources (e.g., capacities, available


raw materials). Supply chain network design problems deal directly with a set of products to be manufactured orassembled. To consider this relation, we embedded the assembly line balancing problem into a supply chain networkdesign problem. We determined the cycle time (CT) as the integration point of these two problems. The cycle time isthe time required to complete a given process. In our model, the working time is certain, but the number of productsneeded to be assembled is variable according to the obtained outputs of the network design problem. Equation (1)shows that the work content of workstation j does not exceed the cycle time of assembler a in period p. The cycletimes of assembler a in period p are determined by dividing the transported amount from assembler a to allcustomers c by the working time in period p:

XNi

ti:Vaijp � CTap 8a,j,p ð1Þ

CTap ¼Wtime

�XCc

Yacp 8a,p ð2Þ

Therefore, while the model determines the transported amounts between facilities to satisfy demand, it also balancesthe stations according to variable cycle times. We determined a fixed cost per period to open a station in theproposed model, therefore our objective is to minimise the transportation costs and minimise the total fixed costs ofthe stations simultaneously. Therefore, our proposed assembly line balancing problem is entirely different fromexisting SALB problems due to the simultaneous station and cycle time variability. The basic assumptions of theproposed model are as follows.

. The demand of each customer for a product is deterministic and must be fully satisfied (i.e. no shortages areallowed). The demands and the transported materials are divisible amounts, which is applicable in the caseof supply chains of gas or liquid products.

. The flow is only allowed to be transferred between two sequential echelons.

. The capacities of manufacturers and assemblers are limited and are known in advance.

. All parameters are deterministic and known.

. A single model of one product consisting of i–1 components is produced on an assembly line.

. The cycle time of each assembler is variable.

. The travel times of operators are ignored.

. No work-in-process inventory is allowed.

. A task cannot be split among two or more stations and all tasks must be processed.

. The precedence relations of the problem are known.

. All stations can process any of the tasks and all have the same associated costs.

. The task process time is independent of the station and, furthermore, they are not sequence dependent.

. Any task can be processed at any station.

. The line is serial, with no feeder or parallel subassembly lines and process times are additive at any station.

. The line is designed for a unique model of a single product.

The first four are standard assumptions for supply chain designs considered in other studies. The remainder ofthe assumptions, except for the cycle time, are defined by Baybars (1986).

3.2 Mathematical model

The indices, sets, parameters and decision variables used in the mathematical formulations are given as follows.

Indices

m index of manufacturersa index of assemblersc index of customersp index of periodsk index of components

i, r, s index of tasksj index of workstations


Sets and parameters

M number of manufacturersA number of assemblersC number of customersP number of periodsK number of componentsJ number of stations (upper bound) which can be estimated from a heuristic procedureN number of tasksL set of tasks that precedes from a task

(r,s)2L a precedence relationship; r is an immediate predecessor of sti task time of task i (time units)

Wtime working time in period p (time units)amkp capacity of manufacturer m for component k in period p (units)bap capacity of assembler a in period p (units)ucp demand of customer c in period p (units)

Cmap unit cost of shipping from manufacturer m to assembler a in period p (monetary units/distance

units*units)Cacp unit cost of shipping from assembler a to customer c in period p (monetary units/distance units*units)Dma distance between manufacturer m and assembler a (distance units)Dac distance between assembler a and customer c (distance units)O fixed cost to open a station in the assembly line in all periods (monetary units, MU)

Variables

Xmakp amount shipped from manufacturer m to assembler a for component k in period pYacp amount shipped from assembler a to customer c in period pVaijp 1, if task i is assigned to workstation j for assembler a in period p;

0, otherwiseZajp 1, if there is any task assigned to workstation j for assembler a in period p; 0, otherwiseCTap cycle time for assembler a in period p

Objective function:

Z1 ¼XMm

XAa

XKk

XPp

Xmakp�Dma CmapþXAa

XCc

XPp

Yacp�Dac Cacpþ ð3Þ

Z2 ¼XAa

XJj

XPp

Zajp:O ð4Þ

The objective function consists of two main parts (Z1,Z2). The first (Equation (3)) tries to minimise the total

shipping costs of the first and second stages in the supply chain network during any period. The second part

(Equation (4)) minimises the total fixed costs for operating the stations in the assemblers during any period.

Therefore, Z2 finds a feasible assignment of tasks that minimises the sum of fixed costs.Constraints:

XAa

Xmakp � amkp 8m,k,p ð5Þ

XCc

Yacp � bap 8a,p ð6Þ


XAa

Yacp � ucp 8c,p ð7Þ

XMm

Xmakp �XCc

Yacp ¼ 0 8a,k,p ð8Þ

XJj

Vaijp ¼ 1 8a,i,p ð9Þ

XJj

Varjp �XJj

Vasjp � 0 8a,r,s2L,p ð10Þ

XNi

ti:Vaijp � CTap 8a,j,p ð11Þ

CTap ¼Wtime

.XCc

Yacp 8a,p ð12Þ

XNi

Vaijp � J:Zajp � 0 8a,j,p ð13Þ

Xmakp , Ycp , CTap � 0 8m,a,k,c,p ð14Þ

Vaijp , Zajp 2 0, 1f g 8a,i,j,p ð15Þ

Constraints (5) and (6) limit the total quantity of components shipped from the manufacturer to assemblers, and the

total quantity of product shipped from the assembler to customers cannot exceed the capacity of that manufacturer

and assembler during any period, respectively. Constraint (7) gives the satisfaction of customer demand for all

products during any period. Constraint (8) guarantees that the total component quantity that is shipped from

manufacturers to the assembler must be equal to the total shipped product quantity from that assembler to

customers that is able to satisfy the demand during any period. Constraint (9) is the assignment constraint and

ensures that each task is assigned to exactly one station in all assemblers during any period. Constraint (10) is

known as the precedence constraint and provides the precedence relationship by assigning task r as an immediate

predecessor of task s in all assemblers during any period. Constraint (11) is the cycle time constraint and prevents

the cycle time being exceeded for a station in all assemblers during any period. Constraint (12) shows that the cycle

time in all periods is equal to the total working time in all periods divided by the total product quantity that is

needed to be produced in all periods for all assemblers. Constraint (13) states that station j is used if any task is

assigned to it in all assemblers during any period. Constraint (14) imposes the non-negativity restriction on decision

variables (Xmakp, Yacp, CTap). Constraint (15) is the non-divisibility constraint and states that any task can be

assigned to a station as a whole or not.

4. Computational experiments

In this section we present a numerical example to illustrate the model. The application of the model is performed for

a hypothetical data set. The considered supply chain includes four manufacturers, two assemblers and four

customers. While determining the transportation amounts between manufacturers, assemblers and customers, the

model also attempts to balance the assembly lines in assemblers at the same time. The supply chain network is

shown in Figure 3.


Manufacturers produce seven different components and send them to assemblers to produce end-products. After

completion of the assemble processes in assemblers, end-products are transported to customers. As stated above, the

cycle time is defined as a decision variable. The model tries to find how many products will be transported from

assemblers to customers in addition to balancing the assembly lines according to the cycle time under fixed costs.

Seven different components are assembled in the assembler according to the precedence graph shown in Figure 4.

The figure also shows the precedence graph with N¼ 8 tasks with task times between 2 and 6 (minutes). Relevant

data are given below. Table 1 gives the distances and unit transportation costs, and Tables 2 and 3 give the capacities

and demands of each facility.We apply our proposed model to a supply chain network using the single model eight-task assembly line

balancing problem shown in Figure 4. A period is 3months (12weeks), and 5 days are worked in one week with

8 working hours in one day. Therefore, Wtime¼ 12*5*8*60¼ 28,800min. Data related to the example are M¼ 4,

C¼ 4, P¼ 2, K¼ 7, J¼ 6, N¼ 8, O¼ 0.3MU and Wtime¼ 28,800 minutes, and the set of tasks that precedes from a

task (L) are (1–2), (1–4), (2–5), (4–5), (3–6), (5–7), (6–7), (6–8) and (7–8). The proposed model is solved via LINGO,

which uses branch-and-bound algorithm (B and B) 11.0 on a Pentium IV PC running at 3.06GHz (3GB RAM) and

takes 2 minutes 20 seconds. The results obtained are shown in Table 4.According to the results obtained by LINGO, all customers are satisfied. The total transportation cost is

4,065,360.40MU. In total, 12 stations are opened with 12*0.3¼ 3.6MU during any period. The model balanced all

assembly stations in assemblers to satisfy customers in all periods. According to the optimal results, the cycle times

are determined as follows:

C11 ¼Wtime

ðY111 þ Y121 þ Y131 þ Y141Þ¼

28; 800

2720¼ 10:58min

C12 ¼Wtime

ðY112 þ Y122 þ Y132 þ Y142Þ¼

28; 800

3600¼ 8min

C21 ¼Wtime

ðY211 þ Y221 þ Y231 þ Y241Þ¼

28; 800

2800¼ 10:28min

C22 ¼Wtime

ðY212 þ Y222 þ Y232 þ Y242Þ¼

28; 800

1760¼ 16:36min

The optimal distribution between assemblers and customers is shown in Figure 5.All assembly lines are balanced in assemblers during any period. As can be seen from Figure 5,

1360þ 1360¼ 2720 units are transported from the first assembler to customers in the first period. To assemble

these units, the optimal line balance consists of three work stations with a cycle time of 10.58 minutes for the first

period in the first assembler. The work contents of the workstations for the optimal solution are given in Table 5.

Manufacturers (m) Assemblers (a) Customers (c)

Figure 3. Supply chain network.


In the second period, assembler 1 assembled 3600 units of product while balancing the line with four workstations with a cycle time of 8minutes. Table 6 gives the work contents of the first assembler in the second period.

Figure 6 shows the straight line layout for the optimal solution in assembler 1 for the first and second periods.At assembler 2, in total 2800 units of product are assembled and transported to customers. The optimal line

balance consists of three work stations with a cycle time of 10.28 minutes for the first period. This line is assembledwith no idle time. The work contents of the workstations for the optimal solution are given in Table 7 for the secondassembler in the first period

In the second period, the second assembler assembled 1760 units of product while balancing the line with twowork stations with a cycle time of 16.36minutes. Table 8 gives the work contents of the second assembler in thesecond period.

Figure 7 shows the straight line layout for the optimal solution in assembler 2 for the first and second periods.

Table 2. Component capacities of manufacturers during any period.

M1 M2 M3 M4

Components P1 P2 P1 P2 P1 P2 P1 P2

1 7000 7000 7200 7200 6700 6700 6500 65002 7000 7000 7200 7200 6700 6700 6500 65003 7000 7000 7200 7200 6700 6700 6500 65004 7000 7000 7200 7200 6700 6700 6500 65005 7000 7000 7200 7200 6700 6700 6500 65006 7000 7000 7200 7200 6700 6700 6500 65007 7000 7000 7200 7200 6700 6700 6500 6500

2

2

54

31

3

4 4

4

2

8

7

6

65

Figure 4. Precedence diagram for the eight-task example problem.

Table 1. Distances and unit transportation costs between facilities (Dma/Cmap)(Dac/Cacp).

A P M1 M2 M3 M4 C1 C2 C3 C4

1 1 280/0.15 350/0.137 300/0.13 250/0.18 530/0.141 480/0.168 460/0.182 510/0.1532 280/0.161 350/0.146 300/0.16 250/0.192 530/0.147 480/0.175 460/0.189 510/0.153

2 1 200/0.195 260/0.161 310/0.135 330/0.118 450/0.18 500/0.156 520/0.161 430/0.1742 200/0.24 260/0.173 310/0.164 330/0.136 450/0.193 500/0.168 520/0.167 430/0.188

Table 3. Capacities of assemblers and demands of customers during any period.

P A1 A2 C1 C2 C3 C4

1 4200 6900 1360 1440 1360 13602 4300 6100 1360 1280 1520 1200


Figure 6. Balanced assembly diagram of assembler 1 in the first and second periods.

Table 4. Optimal results for the test problem.

Variable Value Variable Value Variable Value Variable Value Variable Value

X1112 3600 X4222 1760 Y222 1280 V1211 1 V2212 1X1122 3600 X4231 2800 Y232 480 V1242 1 V2321 1X1132 3600 X4232 1760 Y241 1360 V1321 1 V2322 1X1142 3600 X4241 2800 Z111 1 V1332 1 V2411 1X1152 3600 X4242 1760 Z112 1 V1411 1 V2412 1X1162 3600 X4251 2800 Z121 1 V1412 1 V2521 1X1172 3600 X4252 1760 Z132 1 V1521 1 V2512 1X3111 2720 X4261 2800 Z141 1 V1542 1 V2651 1X3121 2720 X4262 1760 Z142 1 V1641 1 V2622 1X3131 2720 X4271 2800 Z152 1 V1632 1 V2751 1X3141 2720 X4272 1760 Z211 1 V1741 1 V2722 1X3151 2720 Y111 1360 Z212 1 V1752 1 V2851 1X3161 2720 Y112 1360 Z221 1 V1841 1 V2822 1X3171 2720 Y131 1360 Z222 1 V1852 1X4211 2800 Y132 1040 Z251 1 V2111 1X4212 1760 Y142 1200 V1111 1 V2112 1X4221 2800 Y221 1440 V1112 1 V2211 1

Figure 5. Distribution amounts between assemblers and customers during any period.

Table 5. Optimal line balancing for the first assembler in thefirst period.

WorkstationTasks

assignedWorkstationtime (min)

Idletime (min)

1 1–2–4 10 0.582 3–5 10 0.583 6–7–8 10 0.58

Total 30 1.74

Table 6. Optimal line balancing for the first assembler in thesecond period.

WorkstationTasks


Idletime (min)

1 1–4 8 02 3–6 8 03 2–5 8 04 7–8 6 2

Total 30 2


Figure 8 shows the determined cycle time, total assigned stations and idle time of each assembler during anyperiod. According to Figure 8, the maximum cycle time (16.36) and minimum stations are calculated in assembler 2in period 2. The best balanced assembly line is assembler 2 in period 1 with three stations and 0.84minutes idle time.The minimum cycle time and maximum stations are obtained in assembler 1 in period 2.

The solution to the test problem shows that the proposed model is valid and useful for optimising supply chaindesign and assembly lines simultaneously. While all customers are satisfied with the design of the whole supplychain, assembly lines in assemblers are also balanced.

4.1 Scenario analyses for managerial insights

The integration of assembly line balancing and supply chain network design is the key point of this paper. This ishandled by defining the cycle time (Cap) as a decision variable. As mentioned above, the cycle time of each assemblerduring any period can be calculated by dividing the total transported amount between assembler and customers bythe total working time of each period. Therefore, the demand is a decisive factor. When the results are examined, it isseen that each customer’s demand affects both the supply chain network and assembly lines directly. By changing

10,6

31,74

8

42

10,28

30,84

16,36

2 2,72

0

5

10

15

20

Val

ue

Assembler 1

Period 1

Assembler 1

Period 2

Assembler 2

Period 1

Assembler 2

Period 2

Cycle time Stations Idle time

Figure 8. Cycle time, stations and idle time of each assembler during any period.

Figure 7. Balanced assembly diagram of assembler 2 in the first and second periods.

Table 7. Optimal line balancing for the second assembler inthe first period.

WorkstationTasks


Idletime (min)

1 1–2–4 10 0.282 3–5 10 0.283 6–7–8 10 0.28

Total 30 0.84

Table 8. Optimal line balancing for the second assembler inthe second period.

WorkstationTasks


Idletime (min)

1 1–3–4–6 16 0.362 2–5–7–8 14 2.36

Total 30 2.72


the demand limitations of customers, different scenarios can be applied to the model to examine the relations andtrade-offs among model variables. Also, scenario analyses are considered in this section to examine the affects ofcycle time with respect to different daily working hours on product distribution amounts from assemblers tocustomers. Therefore, the solution of the model without any scenario (the current solution) and the results of the sixmain scenarios and 56 sub-scenarios are compared in this section. Because the main objective of assembly lines isbalancing and minimising the stations, the total fixed costs are not considered in the scenarios. Only the number ofopened stations, cycle times, assigned tasks and total transportation costs are considered in the scenarios. The mainscenarios are listed in Table 9.

The first scenario (A) considered is the effect of decreasing and increasing demand for products on theperformance measures (total transportation cost, total stations, assigned tasks, CPU time and cycle time). ScenarioA, which is applied to reflect real-life problems, is given in Table 10 together with its sub-scenarios.

We present the results of Scenario A with its sub-scenarios in Table 11 and Figures 9–11. Demands are modifiedfrom –25 to þ25% on current demand to examine the changes in total transportation costs, assigned stations andCPU time (Table 11). Figures 11(a) and (b) give the cycle time and assigned tasks of each assembler during anyperiod according to the sub-scenarios of Scenario A.

The results presented in Table 11 and Figures 9 and 10 have the following implications. First, the increase indemand results in a linear increase in transportation costs (Figure 9). The main reason for this result is that theincreasing demand of customers will result in the transportation of many more products from manufacturers tocustomers via assemblers. The same situation is also valid and observed for opened stations. The increasing demandsystematically decreases the cycle time in each assembler while Wtime is constant. Therefore, the model selected toopen new assembly stations to satisfy each customer under diminishing cycle times. The total opened stations isbetween 11 and 16 (Figure 9). According to Scenario A, if the decision maker encounters a 25% decrease in demand,

Table 10. Scenario A with sub-scenarios for decreased and increased demand.

ChangeCustomer 1 Customer 2 Customer 3 Customer 4

Scenario A (%) Period 1 Period 2 Period 1 Period 2 Period 1 Period 2 Period 1 Period 2

1 –25 1020 1020 1080 960 1020 1140 1020 9002 –20 1088 1088 1152 1024 1088 1216 1088 9603 –15 1156 1156 1224 1088 1156 1292 1156 10204 –10 1224 1224 1296 1152 1224 1368 1224 10805 –5 1292 1292 1368 1216 1292 1444 1292 1140Current 0 1360 1360 1440 1280 1360 1520 1360 12006 þ5 1428 1428 1512 1344 1428 1596 1428 12607 þ10 1496 1496 1584 1408 1496 1672 1496 13208 þ15 1564 1564 1656 1472 1564 1748 1564 13809 þ20 1632 1632 1728 1536 1632 1824 1632 144010 þ25 1700 1700 1800 1600 1700 1900 1700 1500

Table 9. Main scenarios.

Scenario Definition

A Decreasing and increasing five times the customers’ demand from 5 to 25% during any periodB Decreasing and increasing five times the demands of the first customer from 5 to 25% during any period while the other

customer demands are constantC Decreasing and increasing five times the demands of the second customer from 5 to 25% during any period while the

other customer demands are constantD Decreasing and increasing five times the demands of the third customer from 5 to 25% during any period while the

other customer demands are constantE Decreasing and increasing five times the demands of the fourth customer from 5 to 25% during any period while the

other customer demands are constantF Decreasing and increasing totally six times the daily working hours of each period from 7 to 10 hours while the other

parameters are constant


he/she should reduce the total opened stations from 12 (current) to 11. In contrast, if there is a 25% increase indemand, the decision maker has to open four more stations to meet the demand. Due to the complexity of themodel, the CPU time is also increasing while demand is increasing. In particular, there is a remarkable gap in CPUtime between the eighth and ninth sub-scenarios of Scenario A.

The amount of products outgoing from each assembler changes in each sub-scenario of Scenario A due to thenature of the supply chain design problem. Therefore, changes in stations in each assembler are also variable(Figure 10). As a result, in these scenario clusters, while the demand is increasing, total transportation costs, totalopened stations and CPU time also increase linearly.

All assigned tasks, stations and cycle times of each assembler during any period are shown in Figures 10(a)and (b). Cycle times are changed between 7 and 25.26minutes (Figures 11(a) and (b)). The minimum station numberis two and the maximum is five in all sub-scenarios of Scenario A.

Table 11. Results for Scenario A for the total transportation cost, stations and CPU time.

Scenario A

1 2 3 4 5

Cost (MU) 3,049,019.70 3,252,288.40 3,490,356.40 3,658,824.40 3,862,092.40Total stationsa (unit) 2þ3þ4þ2: 11 2þ3þ4þ3: 12 2þ4þ4þ2: 12 3þ3þ3þ3: 12 3þ3þ3þ3: 12CPU time (seconds) 11 10 11 41 62

6 7 8 9 10

Cost (MU) 4,268,628.10 4,471,895.80 4,675,163.80 4,878,431.50 5,081,700.20Total stationsa (unit) 2þ3þ5þ3: 13 3þ4þ4þ3: 14 3þ4þ4þ3: 14 4þ4þ4þ3: 15 4þ5þ4þ3: 16CPU time (seconds) 55 788 37 15,576 29,403

Note: aAssembler 1 in period 1þassembler 1 in period 2þassembler 2 in period 1þassembler 2 in period 2.

0

1

2

3

4

5

6

4 5 Current 61 2 3 7 8 9 10Sub-scenarios of A

Sta

tions

Assembler 1 in Period 1 Assembler 1 in Period 2Assembler 2 in Period 1 Assembler 2 in Period 2

Figure 10. Comparison of opened stations in each assembler during any period according to Scenario A.

8

11

14

17

20

23

5 Current1 2 3 4 6 7 8 9 10

Sub-scenarios of A

Val

ues

Total cost (1/240000) Total station

Figure 9. Relationship between total stations and total transportation costs according to Scenario A.


While the total demand is increasing, the cycle time distribution narrows, as seen in sub-scenarios 8–10(Figure 12). The main reason for this situation is that the transportation amounts between assemblers and customershave a balancing distribution while the demands are increasing. For example, while the transportation quantitiesbetween assemblers and customers are 1260, 2880, 2880, and 1140, respectively, in sub-scenario 1, these quantitiesare 3300, 3953, 3600, and 2746, respectively, in sub-scenario 2. Therefore, the change in the cycle time distribution,which is associated with the transportation amounts between assemblers and customers, is an expected situationwhile the percentage of demands increases.

In this section, the simultaneous effect of all customer demand changes on transportation cost, openedstations and assigned tasks is investigated. Scenarios B, C, D and E examine the effect of each customer demand

Figure 11. Assigned tasks and cycle times of each assembler during any period.


increase on total transportation costs and assigned stations while the other customer demands are constant(Tables 12 and 13).

Tables 12 and 13 show that increasing each customer’s demand while the other customers’ demands remainconstant results in an increase in the total transportation cost. This relationship is linear, as shown in Figure 13.A 25% increase in demand of customers 1, 2, 3 and 4 during any period increases the total transportation costs by6.19, 6.25, 6.74 and 5.81%, respectively, with respect to the current situation. This shows that if the decision makeris obliged to reduce or give up part of the demand, he/she should use his/her preference for customer 3, orcustomer 4 should be chosen if the decision maker wishes to minimise the total cost while increasing demand.

6

10

14

18

22

26

1 2 3 4 5 Current 6 7 8 9 10

Sub-scenarios of A

Cyc

le ti

mes

Assembler 1 in Period 1 Assembler 1 in Period 2

Assembler 2 in Period 1 Assembler 2 in Period 2

Figure 12. Cycle time distribution in each assembler during any period according to Scenario A.

Table 12. Results for Scenarios B and C for transportation costs, stations and CPU time.

Customer 1 demand

Scenario B Change (%) Period 1 Period 2 Cost Total stations CPU time

1 –25 1020 1020 3,813,420.10 4þ3þ3þ3: 13 1092 –20 1088 1088 3,863,807.50 3þ4þ4þ4: 15 163 –15 1156 1156 3,914,194.40 3þ3þ3þ3: 12 1214 –10 1224 1224 3,964,584.40 2þ4þ4þ2: 12 375 –5 1292 1292 4,014,972.40 3þ4þ3þ2: 12 215Current 0 1360 1360 4,065,360.40 3þ4þ3þ2: 12 1406 þ5 1428 1428 4,115,748.40 3þ3þ3þ3: 12 1177 þ10 1496 1496 4,166,136.40 3þ3þ3þ3: 12 4078 þ15 1564 1564 4,216,524.40 3þ3þ3þ3: 12 2159 þ20 1632 1632 4,266,912.10 4þ3þ3þ3: 13 32110 þ25 1700 1700 4,317,299.80 3þ4þ4þ3: 14 244

Customer 2 demand

Scenario C Change (%) Period 1 Period 2 Cost Total stations CPU time

1 –25 1080 960 3,811,320.40 2þ3þ4þ3: 12 822 –20 1152 1024 3,862,128.40 3þ3þ3þ3: 12 1173 –15 1224 1088 3,912,936.40 3þ3þ3þ3: 12 674 –10 1296 1152 3,963,744.40 3þ3þ3þ3: 12 775 –5 1368 1216 4,014,552.40 3þ4þ3þ2: 12 188Current 0 1440 1280 4,065,360.40 3þ4þ3þ2: 12 1406 þ5 1512 1344 4,116,168.40 3þ3þ3þ3: 12 627 þ10 1584 1408 4,166,976.10 3þ3þ4þ3: 13 4818 þ15 1656 1472 4,217,784.10 3þ3þ4þ3: 13 7379 þ20 1728 1536 4,268,592.20 3þ5þ4þ4: 16 1610 þ25 1800 1600 4,319,400.10 3þ3þ4þ3: 13 195


The mean values of opened stations in each of Scenarios B, C, D and E are 12.64, 12.64, 12.73 and 11.91(Tables 12 and 13), respectively. From this, scenario sets B, C, D and E show that changing the third customer’sdemand mostly leads to open assemble stations, then comes customer 2, 1 and 4, respectively. There is an additionalmanagerial insight that can be obtained from Tables 12 and 13 – the frequency of change of the stations in allassemblers during any period. Figures 14–17 show these frequencies according to different customer demand.

Table 13. Results for Scenarios D and E for transportation costs, stations and CPU time.

Customer 3 demand

Scenario D Change (%) Period 1 Period 2 Cost Total stations CPU time

1 �25 1020 1140 3,791,220.10 2þ5þ4þ2: 13 132 �20 1088 1216 3,846,047.80 2þ4þ5þ3: 14 273 �15 1156 1292 3,900,876.10 3þ3þ3þ4: 13 954 �10 1224 1368 3,955,704.40 3þ3þ3þ3: 12 955 �5 1292 1444 4,010,532.40 3þ3þ3þ3: 12 255Current 0 1360 1520 4,065,360.40 3þ4þ3þ2: 12 1406 þ5 1428 1596 4,120,188.40 3þ3þ3þ3: 12 5347 þ10 1496 1672 4,175,016.40 3þ3þ3þ3: 12 8738 þ15 1564 1748 4,229,844.40 3þ3þ3þ3: 12 2849 þ20 1632 1824 4,284,672.10 3þ3þ4þ3: 13 13210 þ25 1700 1900 4,339,499.50 2þ4þ5þ4: 15 5

Customer 4 demand

Scenario EChange(%) Period 1 Period 2 Cost Total stations CPU time

1 �25 1020 900 3,829,140.40 2þ4þ4þ2: 12 192 �20 1088 960 3,876,384.40 3þ3þ3þ3: 12 863 �15 1156 1020 3,923,627.80 2þ4þ4þ4: 14 144 �10 1224 1080 3,970,872.40 3þ3þ3þ3: 12 855 �5 1292 1140 4,018,116.40 3þ3þ3þ3: 12 198Current 0 1360 1200 4,065,360.40 3þ4þ3þ2: 12 1406 þ5 1428 1260 4,112,603.50 3þ6þ4þ2: 15 177 þ10 1496 1320 4,159,848.10 3þ3þ4þ3: 13 2348 þ15 1564 1380 4,207,092.10 3þ3þ4þ3: 13 5439 þ20 1632 1440 4,254,336.10 3þ3þ4þ3: 13 55710 þ25 1700 1500 4,301,580.10 3þ3þ4þ3: 13 783

Scenario B

3,600,000

3,700,000

3,800,000

3,900,000

4,000,000

4,100,000

4,200,000

4,300,000

4,400,000

–25% –20% –15% –10% –5% Current

D mand changes

5% 10% 15% 20% 25%

Tot

al T

rans

port

atio

n C

ost (

MU

)

e

Scenario C Scenario D Scenario E

Figure 13. Changes in total cost according to Scenarios B, C, D and E.


It can be seen that there are variations in the number of stations when the demand changes between –25% and þ5%in each assembler for all scenarios. In contrast, there is a more or less regular station distribution for changes indemand between þ5% and þ15%. A possible reason for this situation may be the balanced distribution between theassembler and the customers after a þ5% increase in demand. Increasing the first customer’s demand (Scenario B)

0

1

2

3

4

5

6

Scenario E

Num

ber

of s

tatio

n

Assembler 1 Period 1 Assembler 1 Period 2 Assembler 2 Period 1 Assembler 2 Period 2

–25% –20% –15% –10% –5% Current 5% 10% 15% 20% 25%

Figure 17. Number of stations according to Scenario E.

0

1

2

3

4

5

6

–25% –20% –15% –10% –5% Current 5% 10% 15% 20% 25%

Scenario C

Num

ber

of s

tatio

n


Figure 15. Number of stations according to Scenario C.

0

1

2

3

4

5

6

Scenario B

Num

ber

of s

tatio

n


–25% –20% –15% –10% –5% Current 5% 10% 15% 20% 25%

Figure 14. Number of stations according to Scenario B.


0123456

Scenario D

Num

ber

of s

tatio

n

–25% –20% –15% –10% –5% Current 5% 10% 15% 20% 25%

Figure 16. Number of stations according to Scenario D.


results in most variability in the station number. Then changes, respectively, in the third, fourth and secondcustomer’s demand has most effect. In other words, it can be stated that the variability or uncertainty in the firstcustomer’s demand leads to the maximum variability in the stations. While Scenario B changes stations 19 times,Scenario D changes 17 times, Scenario E 16 times and Scenario C 10 times.

Scenario F provides managerial insight for decision makers if the daily working time changes. Inferences fordecision makers concerning cycle times and transported quantities between facilities can be obtained. Figure 18shows the transported amount between assemblers and customers during any period when the daily working timechanges from 7 to 10 hours step by step. According to these scenarios, increasing the daily working hours alsoincreases the product amount outgoing from the first assembler in the second period and from the second assemblerin the first period. Therefore, if the decision maker increases the daily working time, assembly line balancing inassembler 1 in period 2 and assembler 2 in period 1 becomes difficult. Also, increasing the daily working timeprevents a balanced distribution between assemblers and customers. With a 7-hour working period, the distributionis 2210 and 3150 units. When it is set at 10 hours, it oscillates between 1360 and 4160 units. Therefore, the decisionmaker has to keep the working hours low to distribute the total load to the assembler equally under the samedemand.

The above situation concerning transported amounts between assemblers and customers can also be seen inFigure 19. This figure shows the calculated cycle times in the assembler during any period according to differentdaily working times. Although the daily working time increases, it should be noted that the cycle times aredistributed differently. The reason for this situation can be explain by referring to Figure 18. Because of theincreased transported amounts from assembler 1 in period 2 and assembler 2 in period 1 to customers, the cycletimes are short in these assemblers during those times. In contrast, the cycle times increase in assembler 1 in period 1and assembler 2 in period 2 because of the decreasing transported amounts between these assemblers and customersduring those times.

0500

10001500200025003000350040004500

7 7.5 8 (Current) 8.5 9 9.5 10

Daily working time (hour)

Tra

nspo

rted

am

ount

Assembler 1 Period 1 Assembler 1 Period 2


Figure 18. Transported amount from each assembler according to different shift times.

0

5

10

15

20

25

30

7 7.5 8 (Current) 8.5 9 9.5 10

Daily working time (hour)

Cyc

le ti

me

(min

utes

)



Figure 19. Obtained cycle times according to different shift times.


5. Conclusion

This paper addresses an important issue concerning the application of strategic and tactical decisions in supply chain

management. The main objective of this paper is to introduce and characterise the problem of integrating supplychain network design and assembly line balancing problems. For this purpose, in this paper, a novel nonlinear

mixed-integer programming formulation is developed to model and solve the problem. The proposed mathematical

model considers the optimum distribution network while balancing the assembly lines in each assembler

simultaneously. An illustrative example problem is solved using the proposed approach, and a numerical experimentis conducted to demonstrate the efficiency of the proposed approach. The model results were compared using

different scenarios. Sensitivity analyses were then performed to measure the sensitivity of the model results for

different parameter values. The presented study is almost the first study of the simultaneous optimisation of thesupply chain network and assembly lines.

This study shows that assembly lines and supply chain networks should be optimised simultaneously. The

contributions of this paper are as follows. (i) It describes a modelling approach for incorporating straight assembly

line balancing into existing design methods for supply chain networks. (ii) It presents a nonlinear mixed-integerprogramming formulation for supply chain network design, which, in contrast to all existing studies, minimises total

costs composed of transportation and assembly line balancing. (iii) It presents extensive computational analyses that

capture the trade-off between various performance measures. The results of the computational experiments onhypothetical instances yielded the following.

. Increasing or decreasing demand directly affects the amounts transported between facilities and theopened assembly stations. A 25% increase in demand results in a 24.97% increase in the overall cost

and a 33% increase in the total number of opened stations. In contrast, a reduction of 25% in demand

causes a reduction of 25.03% in the overall cost and a decrease of 8.33% in the total number ofopened stations.

. A 25% increase in demand of customers 1, 2, 3 and 4 during any period increases the total transportation

costs by 6.19%, 6.25%, 6.74% and 5.81%, respectively. This shows that if the decision maker is obliged to

reduce or give up part of the demand, he/she should use his/her preference for customer 3, or, in contrast,customer 4 should be chosen if the decision maker wishes to minimise the total cost while increasing

demand.. A similar situation is observed for the assembly lines. The mean values for opened stations are 12.64, 12.64,

12.73 and 11.91, respectively, while the demands of each customer change. From this viewpoint, thescenario sets show that changing the third customer’s demand leads to most open assembly stations,

followed by customer 2, 1 and 4, respectively.. The proposed model also shows that increasing the daily working time in assemblers leads to an unbalanced

distribution between assemblers and customers. Therefore, the decision maker has to maintain shortworking hours to distribute the total load to the assemblers equally under the same demand.

. Finally, increasing the daily working time by 42% (from 7 to 10 hours) also results in an increase of 72.42%

in the total cycle times in assemblers.

Overall, the model developed here can help a manager quickly respond to costumers’ needs, and determine

the correct policies to order raw materials, deliver finished goods, balance the assembly lines and efficientlymanage their operations. As a result, an organisation can benefit economically by effectively managing the

supply chain.Supply chain network design and assembly line balancing problems are defined as being NP-hard,

indicating that the number of computational steps increases exponentially with the number of inputs. Thus, theintegration of these problems becomes even more difficult in our case. Therefore, efficient heuristic and

meta-heuristic approaches such as genetic algorithms, tabu search, and ant colony optimisation need to be

developed to solve the problem. Several extensions are possible for the integration of assembly lines and supplychain networks. Different types of assembly lines such as U-shaped, parallel and disassembly lines, and also

different types of networks such as reverse, closed-loop and decentralised supply chains, should be studied

simultaneously to observe the different interactions. Also, studying multiple-criteria decision-making techniques

such as the goal programming and fuzzy goal programming approaches may be good subjects for considering morestrategic and tactical decisions. Finally, applying the planning models to real case studies is suggested for

future work.


Acknowledgements

The authors express their gratitude to the three anonymous reviewers for their valuable comments on the paper. In carrying outthis research, the first and second authors were supported by the Selcuk University Scientific Research Project Fund (BAP).These funds are hereby gratefully acknowledged.

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Supply chain optimisation with assembly line balancing