Abstract Mass customization efforts are challenged by anunpredictable growth or shrink in the market segments andshortened product life cycles which result in an opportunityloss and reduced profitability; hence we propose a concept ofsustainable mass customization to address these challengeswhere an economically infeasible product for a market seg-ment is replaced by an alternative superior product variantnearly at the cost of mass production. This concept providessufficient time to restructure the product family architecturefor the inclusion of a new innovative product variant whilefulfilling the market segments with the customer delight andan extended profitability. To implement the concept of sus-tainable mass customization we have proposed the notionsof generic-bill-Of-products (GBOP: list of product variantsagreed for the market segments), its interface with generic-supply-chain-structure and strategic decisions about open-ing or closing of a market segment as an optimization MILP(mixed integer linear program) model including logistics andGBOP constraints. Model is tested with the varying marketsegments demands, sales prices and production costs against1 to 40 market segments. Simulation results provide us anoptimum GBOP, its respective segments and decisions on theopening or closing of the market segments to sustain masscustomization efforts.
K. M. Shahzad · K. Hadj-Hamou (B)G-SCOP, Grenoble University of Technology, 46 Av. Felix Vialet,38000 Grenoble, Francee-mail: [email protected]
Introduction
On demand supply chain structures are challenged by anunpredictable growth and shrink in the market segmentdemands. They are striving hard for an operational busi-ness excellence focused on mass customization and logis-tics costs. Different approaches like design for assembly(DFA), make to order (MTO), just in time (JIT) and Post-ponement are being practiced to reduce the logistics costswithin supply chain under mass customization efforts. Theseapproaches take into account similarities and commonali-ties within product, process and components for the formula-tion of a product family to fulfill varying customer demandsefficiently with an optimal resource utilization. There hasbeen a considerable research on the logistics aspects cou-pled with the design of a single product family but notfor a product family architecture [generic-bill-of-products(GBOP)] to sustain the mass customization under unpredict-able market segment growth or shrink; hence to incorporatethe GBOP constraints an interface between generic-supply-chain-structure (GSCS) and GBOP is proposed that createsa balance between the levels of product variety to be offeredin a reconfigurable supply chain. An optimization MILPmodel is proposed that includes GSCS/GBOP interface andlogistics costs to decide the opening or closing of a mar-ket segment and identify an optimum GBOP with respectivesegments under varying market demands, sales prices andproduction costs to sustain mass customization efforts. Thismodel dynamically readjusts GBOP while fulfilling maxi-mum market segments with an alternative product variantat the mass production cost and customer delight. Strategicdecisions about opening or closing a market segment andselection of an alternative product variant allow restructur-ing of the product family architecture to support true masscustomization efforts.
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Fig. 1 Diversity optimization process
Dynamic readjustment of the GBOP under the given mar-ket conditions can be explained in three steps as proposed inFig. 1:
– Step-1: Customer needs are mapped to the functionalrequirements and modeled with a unified compact repre-sentation for a product family as generic-bill-of-material(GBOM) (Hegge and Wortmann 1991; Jiao et al. 2000) orproduct configuration (Aldanondo et al. 2003), to gener-ate all feasible product variants. It reduces the functionalproduct variety to a technical feasible product variety.
– Step-2: Marketing department based on step-1 performsa market segmentation (regrouping customer demandsinto similar service level market segments to be servedwith one variant). It results in the product variants agreedto be offered while satisfying the customer demands;however they are less than the technical feasible prod-uct variety (El Hadj Khalaf et al. 2010; Alberto Jose andTollenaere 2005; Jiao and Tseng 1999).
– Step-3: Output from the step-2 is fed to our proposedmodel to determine an optimum GBOP and strategicdecisions on the opening or closing of market segmentsassociated with the supply chain generic supply chainstructure (GSCS). The GBOP is an architecture thatresults in a set of product variants from those selectedin the step-2.
The research aim is to dynamically readjust the GBOPincorporating logistics constraints to support sustainablemass customization efforts. MILP model is tested under vary-ing market demands, sales prices and production costs toanalyze the impact of dynamic GBOP adjustment on GSCS;however the logistics constraints if included shall impact
GBOP and GSCS to provide equilibrium between productdiversity and an optimal logistics network. We have assumedunlimited supply from the suppliers at “0” lead times andadded logical market segments, categorized from highest tolowest service levels where each service level correspondsto a product variant. Sub-assemblies are produced at the pro-duction facilities whereas product variants are assembled atthe distribution centers; however final demand is collectedonly at the distribution centers. Opening or closing of a geo-graphical market segment is allowed in order to sustain masscustomization efforts if there is no alternative product var-iant to be offered at the mass production cost. This modelfocus on the identification of GBOP and LMS (logical mar-ket segment: demand of the similar product variant frommultiple physical segments) to serve geographical marketsegments based on the product variants and sub-assembliesportfolio at the production facilities and distribution cen-ters. This model empowers supply chain to gain the advan-tages of early sales and improved integrated value chain byquickly responding to the varying demands of the marketsegments.
This article is divided in four sections; “Introduction”presents state of the art on the supply chain configura-tion and influence of the product variety justifying theneed for sustainable mass customization efforts. “Litera-ture review” provides problem description and proposi-tion of the MILP model including GSCS/GBOP interfaceand logistics constraints. “Mathematical model” presentsa case study and the empirical findings on the influenceand dynamic readjustment of GBOP on GSCS for sus-tainable mass customization. Final section includes discus-sion on the open ended questions that can lead to futureresearch.
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Literature review
Supply chain configuration determines the structure and thelinks among the partners and covers both structural andcoordination decisions (Truong and Azadivar 2005). Thesedecisions are categorized as strategic and tactical decisions;however the most important network design decisions arefacility location, distribution center assignment, transportmode and production planning. There has been a consid-erable research along with models on this problem (Cohenand Lee 1988; Ganeshan et al. 1999; Goetschalckx 2000).
Benders method (Geoffrion and Graves 1974) providesan optimal solution to the large scale location-allocation inmulti commodity, single period, production and distributionproblems. There are many other models that take into accountthe effect of taxes and duties (Arntzen et al. 1995); scale ofeconomies and effect of uncertainties on the demand (Lucaset al. 1999; Santoso et al. 2005).
An invited review by Thomas and Griffin (1996) presentsall supply chain configuration and MILP models that serve asthe basis to understand two stage, single product and singleperiod network models whereas (Goetschalckx et al. 2002)provided an extensive literature review on dealing with theoptimization models and modeling issues including BOMconstraints along with the case studies.
Huang et al. (2005) propose a MILP model to investigatethe impact of a platform product with and without common-ality on the supply chain configuration decisions and perfor-mance. Authors took an example from Graves and Willems(2001) with multiple BOM to establish that the supply chaindesign for two product variants separately is more costlythen establishing a common supply chain based on the riskpooling of inventories. Further Lamothe et al. (2006) pro-pose concurrent design of market segmentation to select aproduct family while optimizing the supply chain cost. Ourwork is closely related to the work of Lamothe et al. (2006)but incorporates the investigation of dynamic adjustment ofGBOP architecture including GSCS/GBOP interface. A spe-cial issue on coordinating product, process and supply chaindesign by Rungtusanathama and Forza (2005) comprises ofthree research articles related to the concurrent product, pro-cess and supply chain design but it does not incorporate theGBOM constraints.
In mass customization, postponement strategy is impor-tant because in order to meet increasing demands for moreproduct variety, firms are revising their supply chain struc-tures to accommodate the mass customization. It results indelaying the delivery of the products (Sua et al. 2005) untilafter the customer orders arrive (time postponement), ordelaying the differentiation of the products until later pro-duction stages (form postponement). The results suggest thatonce the number of different products increases above somethreshold level the time postponement is preferred.
There is a significant research on the supply chain designproblems as MILP models (Truong and Azadivar 2005); how-ever special emphasis has been placed on the influence ofproduct architecture and process decisions on supply chainstructures (Blackhurst et al. 2005; Fixson 2005). Zhuo et al.(2006) provide a prospective on the product family archi-tectures with a mechanism for transferring the functionalrequirements in a compact representation based on tech-nical constraints. This helps in understanding the possibleconflicting constraints while creating a GSCS/GBOP inter-face.
Let us discuss some issues addressed regarding mass cus-tomization. A product family is a set of similar productsderived from a common platform having specific featuresto address market needs. Every product in a product fam-ily is called a variant and is subjected to address a spe-cific group of end users in the market that is coveredby the product family (Meyer and Lehnerd 1997). Ulrich(1995) explains that there are two basic issues, modular-ity and commonality associated with product families anddefined diversity of the products (functional and technical)that could be offered to a market. Functional variety, com-puted by the sales/marketing department, is the product diver-sity based on grouping of similar functional requirements;however the same is further processed for a technical vari-ety enforcing the design and manufacturing constraints thatreduces this product diversity to a reduced number of vari-ants.
Economies of scale and economies of scope (Jiao et al.2000; Tseng and Jiao 1996) are the core concepts towardsmass customization. In economies of scale, production vol-umes are very high to achieve mass customization benefitsand it can increase the sales but due to the setup change time,economies of scale are hard to achieve. Solution to this prob-lem lies in the economies of scope which can be achievedthrough the diversity reduction. As a hard rule by diversityreduction we can simply refuse any market segment to befulfilled; however product family initially based on the func-tionality is reduced by imposing technical constraints to aBOM. Authors presented the product family structure as amodel based on commonality to generate product familieshaving a common base, differentiation enabler and configu-ration mechanism. The concept of GBOM to formulate theproduct architecture is the key towards diversity reduction tomove from economies of scale to economies of scope. Untillast decade the product design and the supply chain werebeing treated separately but some guidelines to incorporatethe BOM in supply chain models are proposed. There havebeen much work in the product design to optimize the prod-uct offerings but efforts to incorporate the BOM with supplychain design have been rarely investigated.
Based on the above literature review it is quite evident thatthe questions established in this paper pertains to the research
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Fig. 2 GSCS/GBOP interface
area that has not yet been fully explored. Only Huang et al.(2005) and Lamothe et al. (2006) have worked in the domainof the supply chain design with the incorporation of GBOMconstraints. In this article we have proposed the concept ofGBOPs that offers closing or opening of the market seg-ments. Our work is different from others based on the GBOPconcept that fulfill the demands of the product variants witheconomically feasible high value products while ensuringprofitability at nearly mass customization cost. We haveproposed a MILP model with the maximization objectivefocused to keep intact all market segments with GBOP con-cept for the profit maximization. We have formulated ourproblem using only AND & XOR nodes instead of AND,OR, XOR nodes as commonly used. It is also evident fromthe literature that the global supply chain design models havebeen analytically solved using commercial solvers. Very fewauthors have used the Benders method and it is justified in theliterature that the adaptation of Benders Decomposition forsolving large scale MILP has been reduced due to recent ITdevelopments resulting in the commercial solvers like Cplex;hence we have implemented Benders method in the GAMSenvironment to solve our MILP model with the maximizationobjective instead of using commercially available solvers.
Mathematical model
Problem description
We have modeled a multi-stage, multi-period, multi-productand multi-objective (cost minimization and profit maximiza-tion) logistics network problem to investigate the dynamicGBOP adjustment and strategic decisions about opening orclosing of a market segment against varying market demands,sales prices and production costs. In this problem we have aset of production facilities PF (t), a set of distribution cen-ters DC (u) and a set of geographically distributed marketsegments GMS (v) with multiple product (i) demand port-folio (Fig. 2a). The market demand is further divided intological market segments LMS (v′) based on the service levelranging from the basic to the highest segment. Each servicelevel (v′) corresponds to one product variant (i) with possiblemultiple BOM (Fig. 2b). However each higher service levelproduct variant can fulfill the customer requirements of alllower service levels with the customer delight as representedwith the X O R nodes. Three nodes AN D, O R, X O R areused in the graphical representation of an example productfamily where:
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Fig. 3 Example of product family architecture
– AN D node (commonality): all the child nodes areselected if the parent article is selected,
– O R node (modularity): at least one of the child nodesmust be selected if the parent article is selected,
– X O R node (alternativity): one and only one of the childnodes can be selected if the parent article is selected.
The customers can place orders only at the distributioncenters and the demand is to be filled immediately with “0”lead time hence inventories (base stock + safety stock) areto be kept at the distribution centers. The product family isrepresented by a GBOP with logical market segments (v′),product variants (i), sub-assemblies ( j) and standard com-ponents (k). The standard components are supplied by thetier-1 suppliers to the production facilities and it is assumedthat the suppliers have an infinite capacity and “0” lead time.The sub-assemblies are produced at the production facili-ties and supplied to the multiple distribution centers for theassembly of the final variant. The distribution centers havethe capability of assembling the final variant as well as thedistribution of the same to the multiple market segments.
Huang et al. (2005) used an example to configure a supplychain for an example product family of laptops. The productfamily architecture represents the final assembly with AN Dnodes (2 sub-assemblies, 8 components) and O R nodes (2components) to formulate the architecture with two variantlaptops (one with CD-Writer and second with DVD). In orderto make the problem more complex, product family architec-ture of the laptops have been changed from two to five vari-ants, each represented by two architectures. In the originalexample the product family is represented using only AN Dand O R nodes whereas in our example (Fig. 3) it is rep-resented with AN D, O R and X O R nodes to generate theGBOP.
This product family detailed above (Fig. 3) representsfive variant laptops (basic, basic+CDR, basic+CDRW, basic+DVDR, basic+DVDW) represented through one structure(i1 to i5). Each variant corresponds to a logical market seg-ment marked with service levels ranging from the basic tothe highest one (v′
1 to v′5) such that: v′
5 � v′4 � v′
3 � v′2 � v′
1and i5 � i4 � i3 � i2 � i1. Each article is modeled withAi ′ j ′, Ai j for parent and child articles where A representsan article in the architecture [(i ′, j ′), (i, j)]. In this archi-tecture (i ′, i) represents the level and ( j ′, j) represents thenumber of corresponding article at the same level (logicalmarket segment, variant, sub-assembly or component) wherei ′ = 0, . . . , n − 1, i = 1, . . . , n − 1 and j ′, j = 0, . . . , m.
Further we have modified the product architecture of thebasic variant which is the common sub-assembly. In the mod-ified architecture (Fig. 2b), basic-1 contains 8 componentsand 2 sub-assemblies whereas the basic-2 contains 8 compo-nents and 1 sub-assembly.
The principal objective is to integrate dynamically theGBOP and the GSCS creating a seamless interface for opti-mization (Fig. 2). Decisions to be determined are optimalGBOP, final assembly portfolio, opening/closing of facilitiesand geographic market segments with profit/cost maximiza-tion/minimization objectives.
Mathematical notations, parameters and decision variables
The notations used in the model are discussed and detailedas under for reference:
Notations and parameters
t ∈ T : production facilities PF;
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u ∈ U : distribution centers DC;v ∈ V : geographical market segments GMS;v′ ∈ V ′: logical market segments LMS;i ∈ I : product variants;j ∈ J : sub-assemblies;Ai ′ j ′ : parent articles;Ai j : child articles;τ : time periods;N i
j : number of the sub-assemblies j in a variant i ;Di,v,τ : demand on LMS for variant i at GMS v for time periodτ ;Pmin/max
t+u : production capacity of the PF t ;
Qmin/maxt+u : inventory capacity of the DC u;
C Si,v,τ : unit cost of selling a variant i at GMS v during the
time period τ ;Ce
t , Ceu, Ce
v : fixed cost for opening a PF t , a DC u and a GMSv;Ch
t (Chu ): unit inventory cost of a subassembly or of a variant
at PF t (DC u);C p
j,t (C pi,u): unit cost for the production of the sub-assembly
j (variant i) at PF t (DC u);CT
j,t,u (CTi,u,v): unit cost of shipping (transport) of the sub-
assembly j (variant i) from PF t (DC u) to DC u (GMS v).
Decision variables
Y(t+u+v) ={
1 if(PF t, DC u, GMS v
)is opened
0 otherwise
X(t,u)
(X(u,v)
) =⎧⎨⎩
1 if link PF t → DC u(DC u → GMS v
)exist
0 otherwise
Yi(Yv′
) ={
1 if variant i(LMS v′) is selected
0 otherwise
Ai j(
Ai ′ j ′) =
⎧⎨⎩
1 if child article i j(parent article i ′ j ′
)exist
0 otherwise
Xi ′ j ′,i j =⎧⎨⎩
1 if the link parent article i ′ j ′ →child article i j exist
0 otherwise
W j,t =⎧⎨⎩
1 if the subassembly j is producedat the PF t
0 otherwise
Wi,u ={
1 if the variant i is produced at the DC u0 otherwise
Wv′,v ={
1 if the link LMS v′ → GMS v exist0 otherwise
Pj,t,τ = the production quantity of the sub-assembly j atthe PF t during the time period τ ;Pi,u,τ = the production quantity of the variant i at the DCu during the time period τ ;Z j,t,u,τ = the flow of the sub-assembly j from the PF t tothe DC u during the time period τ ;
Zi,u,v,τ = the flow of the variant i from the DC u to theGMS v during the time period τ ;Q j,t+u,τ = the inventory of the sub-assembly j at the PFt and the DC u during the time period τ ;Qi,u,τ = the inventory of the variant i at the DC u duringthe period τ .
Model constraints
The binary constraints define the GSCS, the generic bill ofproduct (GBOP) architecture and the GSCS/GBOP interface.
GSCS binary constraints
– A link PF → DC and a link DC → GMS may existonly if the corresponding PF, DC and GMS have beenrespectively established (Eq. 1);
⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩
Xt,u ≤ Yt , ∀t, u
Xt,u ≤ Yu, ∀t, u
Xu,v ≤ Yu, ∀u, v
Xu,v ≤ Yv, ∀u, v
(1)
– If a DC or a GMS has been established it can be servedby more than one PF or DC (Eq. 2);
⎧⎪⎪⎨⎪⎪⎩
∑t
Xt,u ≥ Yu, ∀u
∑u
Xu,v ≥ Yv, ∀v(2)
GBOP binary constraints
– AN D node: if a parent node exists it must have at leastone or more children nodes and the link to the child orto the children always exist (Eq. 3);
{Ai j ≥ Ai ′ j ′, ∀Ai j , Ai ′ j ′
Ai ′ j ′ = Xi ′ j ′,i j , ∀Ai j , Ai ′ j ′(3)
– X O R node: the parent-child link exists only if the parentnode exists; and if the parent node exists it can have onlyone parent-child link (Eq. 4);
∑i, j
Xi ′ j ′,i j = Ai ′ j ′ , ∀Ai ′ j ′ (4)
– O R node: if the parent node exists then at least one ormore than one links may exist and if the parent node
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doesn’t exist no links exist (Eq. 5);
Ai ′ j ′ ·∑i, j
Xi ′ j ′,i j ≥ Ai ′ j ′
⇒
⎧⎪⎪⎪⎨⎪⎪⎪⎩
∑i, j
Xi ′ j ′,i j ≥ 1 if Ai ′ j ′ = 1
∑i, j
Xi ′ j ′,i j ≥ 0 if Ai ′ j ′ = 0(5)
– Parent-child link: if the parent-child link exists then thechild node always exists and if the parent-child linkdoesn’t exist the child node may not exist, this constraintis common for the links between all the nodes consideredfrom the parent to the child (Eq. 6);
Ai j ≥ Xi ′ j ′,i j , ∀Ai j (6)
GSCS/GBOP binary constraints
These constraints ensure the relationship between the GSCSand the GBOP and act as interface as:
– The sub-assembly j is produced at the PF t if and onlyif the PF t is opened and the sub-assembly j has beenselected (Eq. 7);
{W j,t ≤ Yt , ∀ j, t
W j,t ≤ Y j , ∀ j, t(7)
– The variant i is produced at the DC u if and only if the DCu is opened and the variant i has been selected (Eq. 8);
{Wi,u ≤ Yu, ∀i, u
Wi,u ≤ Yi , ∀i, u(8)
– The LMS v′ can serve the GMS v if and only if the GMSv exists and the LMS v′ have been selected (Eq. 9);
{Wv′,v ≤ Yv, ∀v, v′
Wv′,v ≤ Yv′ , ∀v, v′ (9)
Production constraints
These constraints validate that only the authorized sub-assemblies/variants are produced within the productioncapacities associated with the production facilities: the sumof all sub-assemblies j (variants i) produced at the PF t (DCu) must be less or equal to the max/min production capacityfor the given period τ if and only if the PF t (DC u) is opened(Eq. 10);
Pmin(t+u) · Y(t+u) ≤
∑j+i
P( j+i),(t+u),τ
≤ Pmax(t+u) · Y(t+u), ∀t, u, τ (10)
Material conservation constraints
The material conservation constraints ensure that the produc-tion + the inventory is always equal/less than what is shippedto ensure the minimization of the inventory cost as under:
– The production of the sub-assembly j at the PF t duringthe time period τ+ the inventory of the sub-assembly jcarry forward from the period (τ − 1) must be equal tothe flow of the sub-assembly j from the PF t to all DC+ the inventory of the sub-assembly j at the end of theperiod τ (Eq. 11);
Pj,t,τ + Q j,t,τ−1 =∑
u
Z j,t,u,τ + Q j,t,τ , ∀t, u, τ
(11)
– The sum of all sub-assembly j arriving at the DC u dur-ing the period τ+ the inventory of the sub-assembly jfrom the period (τ − 1) at the DC u the sum of thesub-assembly j used in the production of the variant iduring the period τ must be equal to the inventory of thesub-assembly j at the end of the period τ at the DC u(Eq. 12);
∑t
Z j,t,u,τ + Q j,u,τ−1 −∑
i
N ij · Pi,u,τ
= Q j,u,τ , ∀ j, u, τ (12)
– The inventory of the variant i at the DC u from the period(τ −1)+ the production of the variant i at the DC u dur-ing the period τ the flow of the variant i from the DC uto all GMS at the period τ must be equal to the inventoryof the variant i at the end of the period τ at the DC u(Eq. 13);
Qi,u,τ−1 + Pi,u,τ −∑
v
Zi,u,v,τ = Qi,u,τ , ∀i, u, τ
(13)
Inventory constraints
The inventory of the sub-assembly j at the PF t and theinventory of the sub-assembly j and the variant i at the DCu (Eq. 14);
Qmin(t+u) · Y(t+u) ≤
∑j+i
Q( j+i),(t+u),τ
≤ Qmax(t+u) · Y(t+u), ∀t, u, τ (14)
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Logical flow constraints
The parameter M is the capacity defined to ensure that if theabove constraint hold good the PF t and the DC u can shipmaximum capacities.
– The flow of the sub-assembly j from the PF t to the DCu can take place if and only if the link PF t → DC uexist and the sub-assembly j has been selected for theproduction (Eq. 15);
{Z j,t,u,τ ≤ Xt,u · M, ∀ j, t, u, τ
Z j,t,u,τ ≤ Y j · M, ∀ j, t, u, τ(15)
– The flow of the variant i from the DC u to the GMS v
can take place only if the link DC u → GMS v exist andthe variant i have been selected for the production at theDC u (Eq. 16);
{Zi,u,v,τ ≤ Xu,v · M, ∀i, u, v, τ
Zi,u,v,τ ≤ Yi · M, ∀i, u, v, τ(16)
Variables bound constraints
{integer variables ∈ {0, 1}real variables ≥ 0
(17)
Objective function
The cost objective function to minimize involves the fixedcost, the operational costs: production, distribution, trans-portation, material handling and the inventory cost (Eq. 18);∑t+u+v
Cet+u+v · Yt+u+v
+∑j,t,τ
C pj,t · Pj,t,τ +
∑i,u,τ
C pi,u · Pi,u,τ
+∑
j,t,u,τ
CTj,t,u · Z j,t,u,τ +
∑i,u,v,τ
CTi,u,v · Zi,u,v,τ
+∑j,t,τ
Cht · Q j,t,τ +
∑(i+ j),u,τ
Chu · Q(i+ j),u,τ
(18)
Empirical results and analysis
Implementation/scenario
The MILP model is formulated as a large scale location/allo-cation problem. It is apparent that the MILP models are hardto solve because they have a combination of integer and
continuous variables and as the number of integer variablesincreases model becomes harder to solve even under linearconstraints. Hence an efficient algorithm that result an opti-mal solution satisfying the constraints in the least iterationsis highly solicited. Two options could be used to solve theabove model (i) commercial solvers (Cplex) that uses intrin-sic libraries and (ii) an algorithm with an implementation ina programming language.
Benders Decomposition method is selected for the resolu-tion of the proposed model. It decomposes the MILP modelin such a way that it can be solved as an alternating sequenceof linear programs (LP) and pure integer programs (IP). Itinvolves sequentially solving the dual LP for specific valuesof integer variables and solving IP for the increasing valuesof this LP. At each iteration, the lower and upper bounds arecomputed; however algorithm terminates when the boundsbecome equal.
The Benders Decomposition method is implemented inthe programming platform G AM S however Cplex is usedfor the solution of decomposed IP/LP problems. The tests arecarried out using G AM S/Cplex 11.2.1 on a Pentium(R) 4CPU 2.80 GHz, 1GB RAM.
Geoffrion and Powers (1995) have stated that even theBenders algorithm have natural adaptability to the structureof the MILP; researchers are not using it because it requiresspecific application in terms of legal inequalities if the opti-mal results are required in least time. The reason for usingBenders Decomposition is to perform aggressive testing toreach to a conclusion with legal inequalities that result in theimproved performance of the algorithm; however at strate-gic level results obtained from a commercial solver even ifin 10 min does not make a big difference.
Initially the model proposed have been applied on a timehorizon of one semester and on a network consisting 5 pro-duction facilities, 5 distribution centers and 5 geographicmarket segments, 5 product variants with four optional mod-ules and five logical market segments. In this example thereare 325 binary variables, 541 continuous variables and 770constraints (see Table 1). This scenario is tested with twoobjective functions: cost minimization and profit maximi-zation. This scenario critically analyzes the opening/closingof the logical market segments i.e. the possible replacementof a product variant with a superior one. Other scenarios aretested on a same logistic network and a more complex GBOP(see Table 1).
We have used the time horizon one semester (= 6 months)as a short term planning based on the fact that product lifecycles are getting shorter and shorter with exponentiallyincreasing R&D investments for design and developmentof innovative products at mass customization costs. In themaster production plan we do planning for three semesterswhere 1st semester is always frozen. Potential BOP is gener-ated for the 2nd and 3rd semesters however 3rd semester is
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Table 1 MILP models parameters and experiment results
Fig. 4 MILP model parameters and associated product family scenario
improved against demand variations when the 2nd semesteris frozen for implementation. In todays business product lifecycles are getting shorter and shorter while competitivenessis forcing industries to reduce prices at constant intervals tokeep intact market segments while still being profitable. Wehave included demand as it is the key factor that influencesthe market segments whereas price is included to analyzethe impact of demand variations against profitability basedon the potentially selected BOP as a product replacementstrategy.
Before moving towards results and potential analysis let usfirst discuss the MILP model parameters. Figure 4a demon-strates that total number of variables and constraints linearlyincrease with the logical market segments (product variants)whereas Fig. 4b depicts that the ratio of total number of vari-ables and constraints to the total logical market segments(product variants) reduces significantly with the increasinglogical market segments (LMS) from 5 to 40 but seems stabi-lizing at the LMS-40. It is based on the fact that modularity
and commonality associated with a product family gener-ate maximum number of product variants with a commonbase and minimum number of sub-assemblies resulting inminimum number of associated binary variables, continuousvariables and constraints.
The cost minimization model with options to open or closea market segment and replace low service level market seg-ments with higher levels, might result in closing all the marketsegments to achieve zero cost. To avoid such result, follow-ing constraints (Eq. 19) are added to the model to ensure thatat least one production facility PF, one distribution center DCand one geographic market segment GMS is kept open; orat least one logical market segment LMS must be satisfied(Eq. 20):⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩
∑t
Yt ≥ 1
∑u
Yu ≥ 1
∑v
Yv ≥ 1
(19)
∑v′
Y ′v ≥ 1 (20)
An alternative to the zero cost model is to replace the costminimization function with the profit maximization function.The profit maximization objective is given by subtractingthe total costs derived from the cost minimization function(Eq. 18) from the total sales revenues expected from thedemand at the geographic market segments (Eq. 21):
T otal Sales Revenues
⎛⎝∑
i,v,τ
C Si,v,τ Di,v,τ
⎞⎠−T otal Cost
(21)
Model with the profit maximization as an objective isan interesting evaluation to find that GSCS is best servedwith the profit maximization or cost minimization objectivesalong with location/allocation decisions under the influenceof GBOP. In the literature studies it is observed that thereare few models that take profit maximization into account;however this is mainly used to undertake the effects of taxes,exchange rates and transfer prices. The profit maximization
Exponential growing trend inthe sales prices from LMS-1 toLMS-40
Demand 1 D1 Linear decreasing demand from LMS-1 to LMS-40 Test 1 Test 6
Demand 2 D2 Linear increasing demand from LMS-1 to LMS-40 Test 2 Test 7
Demand 3 D3 uniformly demand from LMS-1 to LMS-40 Test 3 Test 8
Demand 4 D4 concave demand pattern from LMS-1 to LMS-40 Test 4 Test 9
Demand 5 D5 convex demand pattern from LMS-1 to LMS-40 Test 5 Test 10
in this scenario shall result not only in the optimal utiliza-tion of the resources and the minimization of the inventorybut shall focus and strive to meet the maximum customerdemand by either offering customer with the product vari-ety asked or fulfilling customers demands with a superiorproduct variant.
Simulation results
Model is benchmarked with changes in the sales prices (2cases) and market segments demands (5 cases) to analyze itsimpact on the strategic decisions of opening or closing themarket segments as summarized below (Table 2).
– demand 1—D1: linear decreasing demand of the lowend products that meet the minimum needs; hence noincentive to invest and offer multiple products to the cus-tomers,
– demand 2—D2: linear increasing demand of the highend products as lower range products are not sufficientto meet with the customer needs,
– demand 3—D3: uniform demand (same for all seg-ments),
– demand 4—D4: increasing demand in the low or thehigh end product variants as for the customers it is betterto buy a basic product or add money to buy a high endproduct than buying a basic product,
– demand 5—D5: increasing demand for middle end prod-uct variants because they are cheaper than the high end
variants and contain more options as compared to thelow end product variants.
Opening or closing of a market segment
Opening or closing of a market segment is one of the mostcritical decisions to be made as a part of business strategyby an organization; hence several cases were treated with thefollowing results:
– The profit maximization always results same i.e. the totalsatisfaction of all market segments where each segmentis satisfied with a minimum production cost variant (e.g.variant 1 always responds to the segment low range, var-iant 2 responds to the segment average range 1…).
– The cost minimization objective’s results are analyzedunder the following specialized scenarios.
Closing costs are less than the cost of market entry
It was assumed that the entering costs into the market (pur-chase of new machinery, labor cost…) are higher than clos-ing various sites within the supply chain. Cost minimizationobjective result in the closure of all the sites; hence it is notworth to enter in any market segment regardless the quan-tity required, the sales price and the cost of production. Thisresult is quite logical, since the sum of the closure of sites isstill minimal.
Closing costs are higher than the cost of market entry
It was assumed that the costs of closing various sites (closingproduction lines, loss of market) are higher than entering intoa market. Results achieved with the changes in the demandare similar to those obtained with the assumption to meet thedemand of at least one segment (adding constraint equations19), with the cost minimization objective. It can be concludedthat it is better to enter in the market segment to minimize
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Fig. 5 Scenarios CPU time variations
overall costs because opening of a logistics network site sat-isfy the demand of a segment. This segment is chosen sothat the production cost of the variant fulfilling this segmentand the demand in this segment result in a minimal cost. Itexplains that each time a segment is chosen, it is answeredby the variant produced with minimal cost that cannot meetthe segment of the next line (the segment of the lower rangeis always satisfied by the variant 1, the segment of the aver-age range is satisfied with the variant 2…). Based on theassumption to meet demand of at least one segment, resultsare quite understandable because it minimizes the cost andstill responds to at least one segment.
Production of a single variant
For this example it is assumed that the company decidedto produce a single variant (minimal variety). The objec-tive function used is the profit maximization along with anassumption that the demand on a specific market segment canbe partially satisfied or not satisfied at all. Table 1 summarizesmultiple scenarios average Bender iterations and associatedaverage CPU times whereas Fig. 5 shows variations of totalscenarios CPU times. It is evident that the CPU time growsin an exponential trend based on the fact that when a MILPmodel parameters increase either LP/IP Cplex solving CPUtimes or associated total Benders iterations also increases.Note that Benders algorithm didn’t converge in a requiredfinite CPU time for some experimentation especially whentotal LMS is more than 35. To avoid this, Benders algorithmrequires a specific application in terms of legal inequalities.
In all the experiments presented, the Benders algorithmtermination test is ensured when U B ≤ L B+0.05L B; whereU B and L B define upper and the lower bounds of the solutionrespectively.
The following figures (Figs. 6, 7) include all the resultsconcerning the example of 40 logical market segments from
Fig. 6 Production of a single variant with maximizing profit: tests 1,6, 2, 7, 3, 8
the basic LMS-1 to the highest one LMS-40 with their cor-responding variants.
We can conclude from the tests 4, 7, 8 and 9 that the variantcorresponding to the highest range market segment (variant40) is selected to fulfill the market demand because both thetotal demand and the sales price of this variant is higher thanlowest range market one. This result is quite logical as totalrevenue combined with the minimum network cost is stillmaximum with this high demand and the sales price. Tests 4
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Fig. 7 Production of a single variant with maximizing profit: tests 4,9, 5, 10
and 9 conclude that the demand for a low range market seg-ment is not satisfied or just partially fulfilled by the variant 40because total production cost of the variant 40 is greater thanthe total revenue of the low range market segments. Fromtests 1 and 6 it is evident that the highest range variants arenot selected since the total demand for the correspondingmarket segments is less than the demand of the lowest rangesegments as highest range variants are not profitable. Tests 5and 10 demonstrate that the middle range market segmentsare more satisfied and model choose the closest variant tofulfill the total demand.
We conclude from these tests that the demand, productioncosts and sales price have a strong influence on the choice ofa variant to produce. This choice depends on the segmentswhich can respond to this variant. It also depends on the salesprice segments because sometime we do not care to meet thedemand in a segment even if a variant can be produced toaddress this segment. It is based on the fact that total produc-tion cost of this variant is higher than the sales price segment.
Satisfaction of all applications in all segments
The company’s goal here is to respond to all segments. Weworked with the two objective functions and different cases
of variations in demand, sales prices and production costs.During these tests we obtained the same results and foundthat each segment is always satisfied by its correspondingvariant. This choice can be explained by the fact that this isthe best way to minimize costs and maximize profit. Productvariant for a high service level market segment can be deliv-ered to any customer as it can respond to all segments, butwith variant 1, the company can earn more because of thedifference between sales price and the cost of production ismaximum because the sales price is fixed and the productioncost of this variant is still minimum.
From these tests, we can draw two general conclusionsdepending on the strategy chosen by the company.
If the company’s strategy is to produce a single variant, wecan keep the type O R logical operator for binding segmentsand variants and it is interesting to produce a variant that canrespond to several segments (Fig. 6 and Fig. 7).
If the strategy is to produce more than one variant, it isinteresting to work with the exclusive logical X O R betweensegments and variants; firstly, because all the results obtainedwith the O R operator show that one and only one child arti-cle is selected that can be obtained by the logical X O R;secondly, because number of binary constraints are signifi-cantly reduced with the X O R operator. It can also minimizethe number of iterations generated by the Benders algorithm.
Conclusion and future perspective
Based on the mathematical model and case study it is evi-dent that GSCS/GBOP interface can provide the best solu-tion with economies of scope. Results of this model providea clear indication that interfacing GSCS and GBOP providean optimum GBOP for a given network but when solved overmultiple periods, it results in a trend where product variantis selected having more common sub-assemblies, suggestingthe redefinition of product family as well as its architecture.It is concluded that trends highlight modularization basedon commonality rather than standardization. Redefinition ofGBOP based on these trends is always in line with the GSCSto minimize total cost; hence it shall result in significantcost reduction without reconfiguring supply chain. It is evi-dent that the product architecture has a strong influence onthe supply chain configuration. Product family adjustmentsif carried out in line with the trends identified by the MILPmodel, shall not significantly influence supply chain structurebut shall reduce cost; however if redefinition of the productfamily is carried out separately from the supply network thenit requires reconfiguration and in some cases redesigning ofthe supply chain.
The notion of opening or closing of a market seg-ment is included to incorporate new global trends (uncer-tain increase in the oil prices) that has drastically affected
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the manufacturing supply chains; therefore in the longrun it might be a nice idea to either close a market seg-ment (geographical or logical) or shift logical market seg-ment demand to a higher service level market segment. Infuture this optional opening/closing can be coupled withthe capacitated market segments having an option to par-tially fulfill the customer demand on a specific logical marketsegment.
Literature studies reveal that models have been solvedwith cost minimization objective but in this paper the notionof profit maximization being appropriate has been added tocompare the trends. It is believed that with the notion ofopening or closing of a market segment and possibly replac-ing a lower service level market segment with a superiorproduct variant comply with the suitability of profit maximi-zation.
Interfacing GSCS/GBOP is a domain not fully exploredand its structure results in the explosion of binary variables,not only the interface variables but also GBOP architecturevariables; hence results in a large scale MILP. It is suggestedthat Benders Decomposition method is the best approach tounderstand the hidden aspects of the problem that could onlybe realized if studied with an algorithm appropriate to thestructure of the problem and solve it based on the divideand conquer rule. It could identify the legal inequalities notonly to reduce time and space but to investigate the structuralevolution of model solutions in depth.
Sensitivity analysis shall be performed on the above sce-narios for two purposes (i) GBOP inclusion into GSCS resultsin a problem with exploding binary variables (hard to solveMILP model), hence Benders Decomposition was specifi-cally adopted for ideas to be used in more generalized rep-resentation of GBOP that reduces number of binary vari-ables, (ii) identify the percentage variation in demand, salesprices and production costs to which the model can sus-tain for mass customization and rapid reconfiguration thanredesign.
Our proposed GBOP concept provides business organiza-tions an opportunity to keep intact maximum physical mar-ket segments by restructuring logical market segments whereeach logical market segment corresponds to a product variant.Proposed MILP model with profit maximization objectiveresult in the optimized bill of product as a short term strat-egy resulting in sufficient time for R&D efforts to design anddevelop new innovative products at mass customization costwhile keeping intact the market segments with delight andprofitability at nearly mass customization cost. In future thisGBOP concept for the sustainable mass customization can beused to further analyze the impact on the inventories, estima-tion of nearly mass customization costs for a given GBOPand investigate the supply chain design or reconfigurationagainst logical market segment restructuring
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