Optimal Con Figs Of Platforms

Journal of Operations Management 23 (2005) 267–290 www.elsevier.com/locate/dsw

Towards integrated optimal configuration of platform products, manufacturing processes, and supply chains George Q. Huanga,*, X.Y. Zhanga, L. Liangb a

Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China b Business School, University of Science and Technology of China, PR China Available online 2 December 2004

Abstract This paper seeks to address the challenge of designing effective supply chain systems that integrate platform product decisions, manufacturing process decisions, and supply sourcing decisions. Specifically, this paper considers the specific scenario of optimizing the configuration of the supply chain system given commonality among platform products. The paper uses and extends the concept of Generic Bills of Materials (GBOM) of a product family as a unified framework for qualitatively capturing and representing the structure of its supply chain. This qualitative model is then enhanced by a mathematical model developed to quantify the relationships among various design decisions. Endeavoring to solve the mathematical model more efficiently, we propose an effective heuristic method using Genetic Algorithm (GA). Although GA generally does not guarantee the optimal solution, the best heuristic solutions obtained in this study are consistent with the optimal solutions obtained using Dynamic Programming. The resulting mathematical model and solution algorithm are then used to investigate the mutual impact between the design decisions of platform products and of processes in the supply chain through sensitivity analyses. Several useful managerial insights are generated and discussed. # 2004 Elsevier B.V. All rights reserved. Keywords: Platform product development; Supply chain configuration; Commonality; Modularity; Genetic Algorithm

1. Introduction Generally speaking, a supply chain is a network of nodes. These nodes can be contracted enterprises engaged in activities ranging from the supply of the raw materials to the production and delivery of end* Corresponding author. Tel.: +852 28592591; fax: +852 28586535. E-mail address: [email protected] (G.Q. Huang).

products to target customers to the provision of technical support and customer services. However, more narrowly, for a single manufacturing firm, these nodes can be organizational units that perform functions such as the procurement of raw materials, the fabrication of parts, the assembly of components and end-products, and the delivery of finished products to regional distribution centres/customers, etc. Each node in the supply chain network often has several alternative options for accomplishing its

0272-6963/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jom.2004.10.014

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function and is a potential stock-point for inventory. Deciding what option should be used at each node and deciding where inventory should be placed among these nodes is what Graves and Willems (2001) refer to as Supply Chain Configuration (SCC). The scope of SCC, as defined, covers the configuration of manufacturing processes both within and beyond a particular manufacturer. Accordingly, SCC decisions include not only what alternative supplier and delivery mode to select and where and how much inventory to hold at different levels of the given Bill of Material (BOM) of end-products but also such manufacturing process aspects as processing method to use, manufacturing lead-time or time to market, setups and changeovers. These SCC decisions should differ when the features of end-products change. Likewise, the availability of alternative manufacturing processes and supply sources could in turn affect the design decisions of the product and/ or product family. The challenge is therefore how to generate the optimal configuration of the products, manufacturing processes and supply sources in order to form an effective and efficient supply chain in a simultaneous and integrated manner. This challenge is further complicated by the fact that multiple products are often involved in a supply chain. Different products often share significant similarity in terms of the components, characteristics, and associated manufacturing processes despite distinctive features in terms of marketability and functionality. Such similarity and dissimilarity, also known as commonality and differentiability respectively, across the product range have significant impact on the optimal configuration of the supply chain. In this paper, we address the challenge of designing effective supply chain systems that integrate platform product decisions, manufacturing process decisions and supply sourcing decisions using a mathematical model. More specifically, we use the mathematical model to answer the following questions: (1) What are the optimal supply chain configurations for a product family with and without commonality? (2) What are the differences between the optimal configurations for a product family with and without commonality? (3) What is the impact (i.e., benefits and costs) of product platform commonality on supply chain performance? (4) What factors contribute most to such differences and

impact? (5) Under what circumstances would the impact of platform commonality become more significant? This paper is organized as follows. We first review, in Section 2, the literature related to supply chain configuration, product line design, platform product development, and their combinations. We then describe, in Section 3, the research problem using a specific application case and extending the concept of Generic Bills of Materials as a qualitative model to represent both the platform product and its supply chain structure. In Section 4, we develop and formulate a mathematical model to enhance the qualitative model. Section 5 explains the use of a heuristic algorithm, Genetic Algorithm, for solving the proposed mathematical model. We devote Section 6 to report and analyse the case simulation results and to discuss managerial implications for these results. We conclude, in Section 7, by identifying directions for further investigation.

2. Literature review The performance of a supply chain configured for a product or a product family is determined by design decisions of the products, manufacturing processes and supply chains. Supply chains are often modeled as a multi-stage production and inventory network under a periodically reviewed base-stock policy (Graves and Willems, 2001; Garg, 1999). Graves and Willems (2001), for example, developed a SCC optimization model that minimizes the total supply chain cost including safety stock cost, pipeline stock cost and cost of goods sold. Solved using a Dynamic Programming algorithm, their model included such decision variables as option selection and service time for each stage. Garg (1999), as another example, described a Supply Chain Modelling and Analysis Tool (SCMAT) for designing products and processes in the supply chain of a large electronics manufacturer—a tool that can be generalized to conduct analyses at the strategic level for other supply chains. Decisions considered in this tool include inventoryservice level, sourcing, location, transportation, capacity, and lot size. Like Graves and Willems (2001), we also consider two specific supply chain decision variables, namely, option selection and service time. The first variable is

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a sourcing decision. The second decision variable, service time, can be equated to an inventory location decision or, more specifically, the Average On-Hand (AOH) inventory at particular nodes in the supply chain and can be used to analyse the aggregate effects of safety stock level, stock holding cost rate and service time. Details are given in Section 3. In this paper, we are particularly interested in investigating the mutual impact between SCC decisions and product design decisions related to product variety. Chong et al. (1998) maintain that product variety is determined by market competition. The ever-increasing trend of globalization and product variety causes product proliferation, in turn leading to increased supply chain complexity, unacceptably high production and inventory costs, and long time to market. Thonemann and Bradley (2002) have investigated the impact of product variety on supply chain performance from several different perspectives. Their analyses showed that product variety has significant effect on supply chain lead-time especially when setup times are significant. It therefore becomes important to adjust the decision variables and parameters related to manufacturing processes and supply chains in order to improve performance under high product variety. In order to overcome the cost concerns of increased product variety, various models have been devised for extending and designing the product line instead of a single product. Related literature has been reviewed by Yano and Dobson (1998). Kohli and Sukumar (1990) formulated a joint problem of designing a set of candidate products by choosing the attribute levels for individual products and then choosing a subset among them to maximize the manufacturer’s profit margin. As indicated by Morgan et al. (2001), the product line design problem has typically been discussed from a marketing perspective focusing on how alternative sets of products interact and compete in the marketplace. They proposed a mathematical formulation including both marketing and manufacturing elements for identifying a profit-maximizing mix of products. With the model, they also investigated the impact of alternative manufacturing environment characteristics on the composition of the optimal product line. Raman and Chhajed (1995) formulated a more complicated problem—one that involved (a) choosing not only one or several products but also the appropriate manufacturing processes and (b) setting product prices.

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Both models by Kohli and Sukumar (1990) and Raman and Chhajed (1995) are formulated for multiple products within the product line. However, these studies should ideally be extended in two directions. Firstly, their scope should be extended beyond that of the manufacturing environment to include supply chain decisions. Secondly, they should address the issue of sharing manufacturing resources and supply sources by taking advantage of common components and modular product structure shared across the individual products. The shared common components, product structure and manufacturing assets are often defined as the platform of a product family or line (Wheelwright and Clark, 1992; Meyer, 1997; Meyer and Lehnerd, 1997; Robertson and Ulrich, 1998; Sawhney, 1998). Commonality is a measure of the extent to which product variants share the resources and assets. The approach to developing new products based on the platform concept is therefore referred to as Platform Product Development (PPD). PPD is one of the most important means of realizing the Mass Customization (MC) strategy for creating necessary product variety for competitive success in the marketplace (Meyer and Lehnerd, 1997; Salvador et al., 2000). On the other hand, PPD dramatically controls and often reduces not only the cost but also the time to market to a competitive level. Leading manufacturers such as Black and Decker and Hewlett-Packard have applied some PPD strategies and techniques to rationalize their product lines (Meyer and Lehnerd, 1997). As a result, they have been able to increase the scope/ variety of the end-products while reducing the variety of the constituent components and raw materials. Rutenberg (1969) and Collier (1981) theoretically demonstrated the positive impact of platform (component) commonality on the component demand patterns, work-centre load, work-in-progress inventory, and delivery performance. Ramdas and Sawhney (2001) presented a crossfunctional approach to evaluating multiple line extensions that simultaneously considers revenue implications of component sharing at the product level and cost implications at the component level. Their activity-based costing procedure for estimating the life-cycle costs of line extensions that share components can be generalized to consider supply costs. They demonstrate that their proposed

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approach is most valuable when cannibalization dominates competitive draw as a source of volume, and discuss its relative merits under low and high parts-sharing. Having recognized and advocated the benefits of PPD, Krishnan and Gupta (2001) formulated a mathematical model for studying the appropriateness (costs and benefits) of PPD. Their results showed that PPD is not appropriate for extreme levels of market diversity or at high levels of non-platform scale economies. They have also shown that product platform has significant impact on the planning and the sequence of introducing multiple products to the market. In another effort, Gupta and Krishnan (1999) setup a model of component sharing to include multiple component types, with economies of scale in procuring one unique component type instead of multiple component types from a single supplier due to reduced vendor management. In the SCM literature, one of the most noticeable effects of platform (component) commonality of a product family or line is known as the ‘‘risk pooling’’ effect—the inventory levels of the common modules are generally reduced. Increased commonality generally encourages the risk pooling effect and then further improves material availability and reduces system complexity. High commonality results in simplified planning and scheduling (Berry et al., 1992), lower setup and holding costs (Collier, 1981, 1982), lower safety stock (Baker, 1985; Dogramaci, 1979), reduction of vendor lead-time uncertainty (Benton and Krajewski, 1990) and order quantity economies (Gerchak and Henig, 1989; Gerchak et al., 1988). Kim et al. (2002) developed a mathematical model and a solution algorithm for assisting the manufacturer to configure its supply chain for a mix of multiple products sharing some common raw materials and/or component parts. The model evaluates how much of each raw material and/or component part to order from which supplier (contract) under such constraints as the supplier’s capacity limit. They, however, did not use the model to investigate the impact of sharing common raw materials and/or component parts across multiple products although the model can be extended for this purpose (e.g. simply through a sensitivity analysis under different commonality levels). Gupta and Krishnan (1999) presented a decision support methodology for identifying and formalizing

the tradeoffs between the development costs and benefits of product platforms. Their methodology incorporated a supplier selection decision. An optimal set of components are determined and then the set of suppliers are chosen to supply them. Similarly, Chakravarty and Balakrishnan (2001) developed a mathematical model for investigating the tradeoffs in product design between manufacturing and development costs and the potential market value. Their model determined (1) how many product varieties in a product group should be best introduced in the market and (2) what the minimum numbers of module options are required to support the desired variety. They studied two extreme scenarios where module suppliers are independent enterprises whose module decisions are not coordinated with the manufacturer and where module suppliers are wholly owned subsidiaries of the manufacturer. At present, the literature dealing with product platform strategies and supply chain management in a comprehensive and systematic manner is limited. Salvador et al. (2002) is perhaps one of the most comprehensive studies dealing with the mutual interactions between product platform strategies (product modularity and variety), production processes and supply sources. Their insights were obtained from empirical case studies. While their findings play important roles in providing general guidance for the decision-making process, a quantitative decision is still needed at the tactical decision-making level. Park (2001) presented a comprehensive model of integrated product platform and global supply chain configuration with experimental simulations. This model has ambitiously incorporated multiple platform strategies and included a large number of supply chain decision variables and parameters along the whole product lifecycle, from the front-end global market segmentation to product design and manufacturing stages to raw material sourcing and transportation, manufacturing plant location, and end-product distribution. The resulting model, as such, was very sophisticated and presented difficulties in terms of realistic simulation experiments. Even if meaningful simulations were carried out, it would not be easy to independently derive focused findings and insights for decision parameters and variables of primary interest. In conclusion, the above literature falls into three categories. The first category includes studies related

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to supply chain configuration covering product and process design to some extent. These studies do not normally consider the product platform concept. The second category includes studies related to product line extension and design. Most models consider either upstream market attributes or downstream lifecycle cost elements, but the scope of these studies normally does not reach as far as the supply sources. In addition, they do not explicitly consider the product platform concept even if product family/ line is considered. The third category includes studies relating the product platform concept and supply chain performance. These studies often focus on only one product platform strategy—component commonality, although the scope of these studies sometimes does reach the supply sources. Other product platform strategies such as modularity, postponement, and scalability are not considered. Opportunities exist in all these three areas for further rigorous research.

3. Problem description In order to address the challenge of designing effective supply chain systems that integrate platform product decisions, manufacturing process decisions, and supply sourcing decisions, we employ a specific application case adapted from Graves and Willems (2001). This application case is concerned with the optimal configuration of different supply chains for a

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product family of two notebook computers, namely Notebook A and Notebook B, which are produced/ assembled by a manufacturer. While Notebook A is sold in both the US and European markets, Notebook B is only sold in the US market. In this paper, we make the assumption that the studied notebook computer manufacturer has finished its product development process, so that product development process/cost need not be considered as part of the application case context. 3.1. Representation of platform products using Generic Bills of Materials How to model and represent design decisions of platform products and platform strategies (e.g. commonality and modularity) is itself a major research area (Jiao et al., 1998; Huang et al., 2003). The concept of Generic Bills of Materials (GBOM) (Hegge and Wortmann, 1991; Jiao et al., 1998) is readily and widely applied for this purpose. Essentially, a GBOM is a tree consisting of AND/OR nodes. OR nodes represent somewhat platform modularity while AND nodes basically reflect platform commonality. Fig. 1 shows an example of the GBOM of the notebook product family considered in this paper. This product family is comprised of two major sub-nodes— one labelled ‘‘Subassembly’’ and another labelled ‘‘Dummy’’. The ‘‘Subassembly’’ node is an AND node with several end nodes and an AND sub-node.

Fig. 1. GBOM for representing platform commonality and modularity.

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This node reflects platform commonality such that each product variant in the family possesses a substructure represented by the ‘‘Subassembly’’ node. The ‘‘Dummy’’ node, on the other hand, is an OR node and represents platform modularity. That is, product variants in the family possesses either a DVD drive or a CD-RW drive. Therefore, the GBOM presented in Fig. 1 has two product variants. They share five common components and subassemblies, which formulate their product platform. They are distinguished by one unique component: Notebook A with a DVD drive and Notebook B with a CD-RW drive. Commonality and modularity at the parametric levels of individual nodes in the GBOM tree can also be easily incorporated. 3.2. Network representation of flexible supply chains While it is common practice to represent a supply chain as a network (Wu and O’Grady, 2001), the formality of doing so varies widely from one application to another. For practical purposes, this paper represents the supply chain as a conceptual multi-stage network. Nodes or stages of the network represent suppliers of the materials while the directed arcs represent the demand and supply relationships,

i.e. the flow of materials. Fig. 2 shows an example of the supply chain network for the product family shown in Fig. 1. Three sets of nodes or stages are easily observed in Fig. 2. One set includes the most upstream stages without any further predecessors. This set of stages perform procurement of raw material and are defined as procurement stages (set R). Another set includes all the most downstream stages without any further successors. This set of stages represent market demands of end customers and are defined as demand stages (set E). The last set includes intermediate stages with both up- and down-stream stages. They denote internal manufacturing/assembling processes and are defined as assembly stages (set P). These three kinds of stages or nodes form the nodes set N ¼ R [ P [ E of the directed graph G(N, A) which serves as the supply chain network representation model, where A is the set of directed arcs. A node where a common component is combined with differentiating parts/components is called a Differentiation Point (DFP), DFP 2 P. Node 10 in Fig. 2, for example, is a DFP. Certain similarity can be observed by comparing Figs. 1 and 2. Such similarity is largely due to the fact that all components in the GBOM are assumed to be bought from external vendors except for the three subassemblies and the manufacturer is only responsible

Fig. 2. Generic supply chain network of notebook family including variants A and B (GSC).

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Fig. 3. Instance supply chain networks for two variant notebook computers.

for assembling these bought-out components into subassemblies and ultimately into the end-products. Such similarity indicates that the GBOM platform representation can be used and extended to form the corresponding Generic Supply Chain (GSC) network representation. The GSC network for a product family in Fig. 2 can be decomposed into a set of two Instance Supply Chain (ISC) networks at the Differentia-

tion Point(s), e.g. Node 10 in Fig. 2. The resulting ISC networks, namely ISCA and ISCB for Notebook A and Notebook B, are shown in Fig. 3a and b, respectively. 3.3. Problem description In this paper, we do not introduce a commonality variable or index in the model. Instead, platform

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commonality is reflected by the supply chain network representation model. We consider two extremes. For the first extreme, we treat the two notebooks as two variants in a product family with commonality and their supply chains as jointly configured using the GSC network shown in Fig. 2. For the other extreme, we treat the two notebooks as a product family without commonality and assume that the supply chains for the two notebooks are configured independently using the two corresponding networks ISCA and ISCB shown in Fig. 3a and b, respectively. Hence, the ISC networks for individual product variants assume null commonality while the GSC network for the product family represents a certain degree of commonality. We conduct separate experiments with respect to these two extremes, after which we then compare and contrast the experimental results. As mentioned earlier, the optimization problem we define focuses on two decisions: option selection and service time. For each stage in our multi-stage supply chain network, there are several alternative options to select from, hence the option selection decision. The type of options available is determined by the type of stage to which the options belong. If stage i is a procurement stage, i.e. i 2 R, the options of this stage are alternative external raw material vendors; if stage i is a demand stage, i.e. i 2 E, the options are alternative end-product delivery modes; if stage i is an assembly stage, i.e. i 2 P, the options are alternative manufacturing/ assembling processing methods. The option selection decision, therefore, includes the configuration decisions of raw material vendor selection, endproduct delivery mode selection and manufacturing process selection. However, in this paper, different types of options are identified in the same way through their production cost and processing leadtime, and can, therefore, treated as one kind of decision in the optimization model. The second decision variable is that of service time. With respect to this decision variable, we assume that each stage guarantees a determined service time to its immediate successors. Following the terminology of Simpson (1958), service time is the time span between the time when an order for an item is placed and the order is filled. Accordingly, we can see that the service time decision of each stage determines the replenishment lead-time of its

corresponding stage. Therefore, we can equate the service time decision to that of inventory location, or more specifically AOH inventory location, and choose, in this paper, to present the service time decisions in terms of the results of AOH inventory level of each stage in the supply chain because the latter is more intuitive. Other factors such as demands and demand variances, inventory holding cost rates, and service levels are treated as parameters whose values are given as inputs into the optimization problem. Sensitivity analysis is then conducted to investigate the impact of these parameters under different level settings.

4. The mathematical model This section develops a mathematical model to quantify the relationships between the product platform decisions (e.g. component commonality) and supply chain decisions in terms of a chosen supply chain performance indicator (e.g. total cost, inventory level, etc.). Before developing the model, several assumptions have to be stated as follows: (1) any arriving order is processed immediately; (2) average backorders are quite small (which will always happen when service levels are chosen to be high) and, therefore, the backorder cost is negligible; (3) capacity is not restricted at each stage. The objective function of the model is to minimize the total supply chain cost consisting of inventory cost, production cost, procurement cost and transportation cost within the supply chain, as shown in Fig. 4. The inventory cost at each stage of the multi-stage production/inventory system, in turn, consists of Average On-Hand (AOH) inventory and Work-InProcess (WIP) inventory. Therefore, the aim of the model is to determine the optimal option and service time at each stage in order to minimize the total supply chain cost presented in Fig. 4. In this particular multi-stage production/inventory system, all operations take place at stages. Raw materials are purchased from outside suppliers at procurement stages (set R). Assembly stages (set P) transform raw materials into subassemblies and endproducts, after which end-products are transported to regional distribution centres or customers through demand stages (set E) in order to satisfy customer

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Fig. 4. The structure of total SCC cost.

demands. In addition to performing specific operations, every stage also serves as a potential stock point for the item finished at this stage. The optimal inventory level of each stock point is determined by the optimization model. Customer demands only occur at demand stages (set E). We assume that at each demand stage i 2 E, the demand zi is stationary and follows a normal distribution, that is, zi  Nðmi ; s i Þ, for i 2 E, and demand zi is uncorrelated in time. Correlations between customer demands are permitted and denoted by the correlation coefficient rij (i, j 2 E, i 6¼ j). This multi-stage production/inventory system operates following a periodically reviewed base-stock policy. At the beginning of each common review period, demand stages (set E) review their local inventory positions and place orders from their immediate predecessors to bring the inventory position up to a fixed base-stock level. For the upstream stages, so-called dependent demands are derived from the requirements of the BOM. Let nij denote the number of items finished at stage i needed to produce one unit of item at stage j. Hence, the requirements of the BOM can be represented by nij for i, j 2 N. Let E(i) denote the set of demand stages which require the item produced at stage i. For an upstream (procurement and assembly) stage i 2 RP [ P, the demand is normally P distributed 2 ¼ 2 2 with m ¼ n m and s ie i P e 2 EðiÞ e i e 2 EðiÞ nie s e þ P e 2 EðiÞ j 2 EðiÞ;j 6¼ e nie nij s e s j rej : One decision variable of the optimization problem is service time. Each upstream stage i 2 R [ P

guarantees a service time Si to its immediate successors. For demand stage i 2 E, the service time Si is determined and given by the outside customer. If it is equal to zero, the outside customer order has to be satisfied immediately. Each stage i is also guaranteed an input service time Sv(i) determined by its immediate predecessors. The input service time Sv(i) is the time period after which all the orders placed by stage i to its immediate predecessors can be filled. We assume that the quoted input service time for any procurement stage i 2 R is zero. This happens when there is an infinite supply of materials available to the outside raw material suppliers. In practice, any assembly stage i 2 P cannot start processing until all inputs are available. Therefore, the quoted input service time Sv(i) should be equal to the maximum service time of all its immediate predecessors, that is, SvðiÞ ¼ maxfSj g

for i 2 P [ E; j 2 vðiÞ

(1)

Another decision variable of the optimization problem is option selection. For each stage i, several alternative options (set S(i)) are available for selection. We assume that every alternative option has a deterministic production cost, namely CiOi (Oi 2 S(i)) and processing lead-time, namely TiOi (Oi 2 SðiÞ). Let ci and Ti denote the production cost and processing lead-time of each stage respectively. Once an option selection decision has been made at stage i, Ti would be set to TiOi ; ci would be set to CiOi . Thus, the processing time and production cost of each stage are deterministic too.

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Having defined the above variables and parameters, we now discuss the cost terms of the optimization model. First, let us consider the AOH inventory at each stage or stock point in the multi-stage production/ inventory system. In order to do this, we have to introduce the notation of replenishment lead-time. The time span over which the stock point i can be refilled is called the replenishment lead-time at stage i, which is denoted by Li. It is clear that the replenishment leadtime includes the waiting time for inputs and processing time at the stage. So, we have Li ¼ SvðiÞ þ Ti

for i 2 N

(2)

The AOH inventory at each stage should cover and guarantee the demand during a time span, called inventory coverage time, Ui, at a predetermined service level. For demand stages, the inventory coverage time should include the common review period, which is denoted by l. Thus, we have  for i 2 R [ P Li  S i Ui ¼ Li  Si þ l for i 2 E For convenience, we assume that all the customer orders are to be filled immediately, that is, Si = 0 for i 2 E. This assumption could be relaxed easily by setting the service time at the demand stages to be larger than zero. Then, the calculation of Ui is derived to  Li  Si for i 2 R [ P (3) Ui ¼ Li þ l for i 2 E At the beginning of each review period, the onhand inventory level at stock point i should be large enough to cover the average demand, miUi, over the time span Ui. In the mean time, since demand is not constant, we may want to keep more inventories to hedge against demand deviation. With ai as the service factor which denotes the service level at stage i, the base-stock level Bi can be set at pffiffiffiffiffi Bi ¼ mi Ui þ ai s i Ui . At the demand stages, the AOH inventory level can be evaluated as follows (van Ryzin, 2001) pffiffiffiffiffi 1 AOHi ¼ lmi þ ai s i Ui for i 2 E (4a) 2 For upstream (procurement and assembly) stages, the AOH inventory level can be computed as pffiffiffiffiffi (4b) AOHi ¼ ai s i Ui for i 2 R [ P

The WIP inventory level at stage i is simply given by WIPi ¼ mi Ti

for i 2 N

(5)

The cumulative cost of an item finished and stored at stage i, which is denoted by Ci, can be calculated by 8 for i 2 R < ci X Cj for i 2 P [ E Ci ¼ ci þ (6) : j 2 vðiÞ

The cumulative cost of an item being processed at stage i, which is denoted by Wi, can be calculated as follows: 8 for i 2 R < ci X 1 Wi ¼ (7) Cj for i 2 P [ E : 2c i þ j 2 vðiÞ

For stage i, the inventory cost can be written as ðinventory costÞi ¼ hi ðCi AOHi þ Wi WIPi Þ for i 2 N Let H denote the manufacturer’s time interval of interest. All other cost which may be production cost for assembly stages, or procurement cost for procurement stages, or transportation cost for demand stages can be written as ðproduction costjprocurement costjtransportation costÞi ¼ Hci mi

for i 2 N

Thus, the total cost occurred at stage i, namely SCCi, should be SCCi ¼ ðinventory costÞi þ ðproduction costjprocurement costjtransportation costÞi ¼ hi ðCi AOHi þ Wi WIPi Þ þ Hci mi

for i 2 N

The total supply chain cost, namely SCCT, for the entire multi-stage production/inventory system, is the sum of SCCi of all the stages included in the supply chain network. Thus, SCCT can be calculated by X SCCT ¼ ½hi ðCi AOHi þ Wi WIPi Þ þ Hci mi  i2N

for i 2 N

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The objective, therefore, is to minimize the total SCC cost, SCCT, e.g. SCCP Min

X

½hi ðCi AOHi þ Wi WIPi Þ þ Hci mi 

i2N

for i 2 N With Eqs. (1)–(7), we can rewrite the optimization model as follows: ( X pffiffiffiffiffiffiffiffiffiffiffiffiffiffi SCCP Min hi ci ðai s i Ti  Si þ mi Ti Þ i2R

þ

X

20 hi 4 @ c i þ

i2P

X

1 Cj A

j 2 vðiÞ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ai s i SvðiÞ þ Ti  Si 0 1 3 X 1 C j A mi T i 5 þ @ ci þ 2 j 2 vðiÞ 20 1 X X þ hi 4@ci þ Cj A i2E

j 2 vðiÞ

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lmi

þai s i SvðiÞ þ Ti þ l 2 0 1 3 ) X X 1 Cj A mi Ti 5þ Hci mi þ@ ci þ 2 i2N j 2 vðiÞ

subject to X TiOi yiOi  Ti ¼ 0

for i 2 N

(8)

for i 2 N

(9)

Oi 2 SðiÞ

X

CiOi yiOi  ci ¼ 0

Oi 2 SðiÞ

yiOi

8 < 1 ifO is selected i ¼ : 0 otherwise

and

for i 2 N Oi ; Si  0 and integer

X

yiOi ¼ 1

Oi 2 SðiÞ

(10) for i 2 N

SvðiÞ þ Ti  Si  0 for i 2 P

(11) (12)

(13) Ti  Si  0 for i 2 R The objective function includes four parts. The first three parts constitute the overall inventory costs. The

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fourth part includes the other cost (production cost plus procurement cost plus transportation cost) incurred during the manufacturer’s time interval of interest. Constraints (8)–(10) apply to the processing time and production cost corresponding to the selected option at each stage. Constraints (11)–(13) ensure that the service times are integer and the inventory coverage times are nonnegative.

5. Solution algorithms The specific problem identified in this paper can be classified as a combinatorial optimization problem which is characterized by having a finite number of feasible solutions. In principle, finding the optimal solution for a combinatorial optimization problem can be done by enumeration. For example, Dynamic Programming (DP) is an effective, but not necessarily efficient, enumerative solution algorithm for the specific problem in this paper. However, real world problems are often very complicated and the enumeration method is frequently impractical to use because of the large number of feasible solutions. For the specific problem in this paper, when the number of supply chain stages is as large as, say 100, an enumerative algorithm is inefficient given the computational complexity. For his circumstance, heuristic methods could serve as alternative solution algorithms since they search for only a portion of the solution space heuristically and give good quality, but not necessarily optimal, solutions. More specifically, we employ Genetic Algorithm (GA), a heuristic method, to address the specific problem described earlier. GA, first introduced by Holland (1975), is now well-established and widely applied in solving engineering and business problems, including supply chain optimization problems (e.g., Chan and Chung, 2004; Yu et al., 2003). GA is a stochastic search method that imitates the process of natural selection and natural genetics. It starts with a population composed of a set of random solutions called ‘‘chromosomes’’. The population then evolves via successive iterations called ‘‘generations’’.

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Fig. 5. Representation schema of chromosomes.

5.1. Representation scheme For the optimization problem formulated in Section 4, each solution is represented by one chromosome with 2jN j genes—i.e., two genes are considered for each stage, where jN j is the number of stages. The first gene contains the supplier option Oi to which the corresponding stage i is assigned. The second gene contains the selected service time Si for the corresponding stage i. Fig. 5 illustrates the proposed representation scheme. We can see by this representation that only one supplier is selected for each stage and, therefore, constraint (10) is satisfied automatically. Since the optimization problem is a nonlinear integer programming problem with nonnegative solutions, all genes are constrained to nonnegative integers in the GA, satisfying constraint (11) as a result. In addition, the encoding sequence of stages in the chromosome is very important. This is because there are relationships between the two genes or service time decisions of some stages. Hence, only the proper encoding sequence would allow the GA to arrive at an optimal solution. The sequence scheme in this study is as follows. Sequence scheme: The upstream stages should be encoded before their corresponding downstream stages. As an example, consider the supply chain network in Fig. 2. The sequence shown by the labels in the ‘‘circles’’ is a proper sequence for this supply chain. We will explain why the sequence scheme is important and necessary later. 5.2. Feasible solution space The total feasible solution space of the optimization problem in this paper is defined by its constraints. As stated before, constraints (10) and (11) are satisfied through the encoding scheme. Therefore, we only need to consider constraints (8), (9), (12) and (13). The first

two constraints define the solution space of the first gene of each stage, while the latter two constraints define the solution space of the second gene at each stage. The first gene of each stage, as such, is clearly bound on the lower side by one, the minimum number of supplier option index, and on the upper side by the supplier options’ number of the stage, i.e. jSðiÞj for stage i. Once an option is selected at stage i, the predetermined production cost and lead-time of this option are imported as processing lead-time, Ti and production cost, ci of this stage. By doing this, constraints (8) and (9) are verified. The solution space for the second gene is defined by constraints (12) and (13). Constraint (13) indicates that the service time of a procurement stage is no greater than the production lead-time of this stage. That is, for a procurement stage, the second gene is bound by Ti for i 2 R. Constraint (12) indicates that the service time of an assembly stage is no greater than the production lead-time of this stage plus the input service time of this stage. Therefore, for an assembly stage, the second gene is bound by SvðiÞ þ Ti for i 2 P. Now we can explain why we have to define the sequence scheme as indicated before. This sequence scheme of the chromosome can assure the availability of the service times of an assembly stage’s all upstream stages, and therefore assure the calculability of Sv(i) through Eq. (1), i.e. the maximum service time of all the upstream stages. Since the service times of the demand stages are inputs provided by customers to the model, and since we assumed that they are equal to zero, we would always set the second gene of these demand stages to zero in all chromosomes. 5.3. Initialization, evaluation and pre-evaluation heuristic The initialization process is very important in the performance of any GA. In this process, a population

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of chromosomes are generated randomly within the solution space. We can see from the above discussion that all the chromosomes in the initial population are feasible. When the population is formed, all the chromosomes should be evaluated by computing their fitness value one at a time. The evaluation function here is the same as the objective function of the optimization model defined in Section 4. However, before the population can be evaluated, we first employ a simple heuristic algorithm, called pre-evaluation heuristic. This heuristic focuses on the second gene of each chromosome. The detail of the heuristic is as follows. Pre-evaluation heuristic: For each chromosome, at each procurement stage j 2 v(i), we set the second gene Sj to Sv(i) if Sv(i)  Tj, otherwise we set Sj to Tj; at each assembly stage j 2 v(i), we set the second gene Sj to Sv(i) if Sv(i)  Tj + Sv(j), otherwise we set Sj to Tj + Sv(j). This pre-evaluation heuristic, based on service times, can in fact pre-optimize the chromosomes before they are evaluated, and, therefore, improve the performance of the GA. To clarify and without loss of generality, consider again the supply chain in Fig. 2. At this time, a feasible solution X for this supply chain network has already been created randomly. First, we consider the sub-network containing stages 1–5. Here, we can have v(5) = {1, 2, 3, 4}. From the randomly created solution X, we can get S1, S2, S3, S4 and therefore Sv(5) by Eq. (1). Looking at the evaluation function, we can see that S1, S2, S3 and S4 are only related to the first item of the evaluation function and that the value of the first item is not increasing in these four service times. Therefore X can be optimized by resetting S1, S2, S3 and S4 as large as possible but no larger than Sv(5) since this is their maximum value. Further, they also cannot be larger than the processing lead-time of their corresponding stages because of constraint (13). Consequently we can optimize X through resetting each of these service times to the smaller value of Sv(5) and the processing lead-time of its corresponding stage. Next, consider the sub-network containing stages 5–10. At this point, we have v(10) = {5, 6, 7, 8, 9}. Among the five upstream stages of this sub-network, there are four raw material stages. For these stages, our explanation is similar to that for the previous sub-

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network. The only intermediate stage in the upstream stages of this sub-network is stage 5. We can see that S5 is only related to the second item of the objective function. By the same logic, we can optimize X by resetting S5 to Sv(10) if Sv(10)  T5 + Sv(5), or T5 + Sv(5) otherwise, according to constraint (12). Any convergent sub-network in Fig. 2, consequently, belongs to either the first or the second subnetwork discussed above. Hence, we can conclude that the pre-evaluation heuristic optimizes the population that have been created randomly. 5.4. Genetic operations The genetic operations used in the proposed GA are crossover and mutation. Because the crossover operation may produce an infeasible offspring, a simple checking and amending (C&A) algorithm is added after the crossover operation to find out and amend the infeasible offspring. Similarly, the C&A algorithm is used after the mutation operation because it also may create an infeasible offspring. The mutation algorithm used in the proposed GA is a mixed algorithm including boundary mutation. The reason why boundary mutation is introduced is because of the extreme point property of the optimization problem. A detailed discussion follows. 5.4.1. Crossover and C&A algorithm The proposed GA uses a simple crossover operation in which a random crossover point is determined, and the second parts of the two selected chromosomes are exchanged. If the random crossover point is an even number, as shown in Fig. 6a, the integrality of the stages in the two selected chromosomes remains, and the offspring is feasible as is its parents. If the random crossover point is an odd number, as shown in Fig. 6b, the integrality of the selected stage is damaged. That is, only the service times of the selected stage in the two selected parents are exchanged. We can see from the discussion of space range definition that the feasible range of the second gene of a stage is affected by its first gene. More specifically, the first gene of stage i determines the Ti of this stage, and the second gene of this stage cannot be larger than Ti or Sv(i) + Ti. Hence, the solution space of the second gene of the selected stage may change when a crossover like Fig. 6b happens.

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Fig. 6. Two kinds of crossovers.

In order to maintain feasibility of the offspring, a C&A algorithm is added after a crossover operation like Fig. 6b occurs. The detail of this algorithm is as follows. C&A algorithm: For each offspring, S0i or Si will be checked as to whether it is within its new solution space defined by Oi or O0i. If so, the algorithm will do nothing; otherwise, the algorithm will create a new S0i or Si randomly within its new solution space. 5.4.2. Mutation In every chromosome selected for mutation, a gene is selected randomly. If the selected gene is odd, or is the first gene of the selected stage, the current value of that gene is replaced with a random number selected from its feasible solution space. In this condition, the C&A algorithm described above should be added to keep the offspring feasible because the solution range of the gene after the selected gene, or the second gene of the stage, may change. If the selected gene is even, or is the second gene of the selected stage, the current value of that gene is replaced with the upper bound or the lower bound of its solution space, which is called boundary mutation.

Using boundary mutation can significantly improve the performance of the proposed GA given the following reason. Simpson (1958) studied a non-linear optimization problem of a serial production/inventory system, which can be regarded as a simplified form of the specific problem addressed in this paper. He pointed out that the optimal solution of his problem is largely characterized by an extreme point property, wherein the service time at each stage takes on either the lower or the upper bound of its feasible solution range. Considering the similarity between Simpson’s problem and that of this paper, we choose a boundary mutation when an even gene or Si is selected for mutation. However, our boundary mutation is mended because the problem we address is more complex than Simpson’s. In our problem, when Si is selected for boundary mutation, the whole chromosome may not be affected because of the preevaluation heuristic described in Section 5.3. Therefore, after Si is selected and mutated to S0i , the second genes of stage i’s sibling stages have to be checked and revised. Here, a sibling stage of stage i has the same immediate successor as stage i. For each

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sibling stage of stage i, if the second gene is larger than S0i , it would be set to S0i . 5.5. Selection Once the evaluation function is used for the first time, i.e. after the initial population is created and evaluated, the proposed GA starts the selection and genetic operations. Selection deals with the problem of selecting the valuable chromosomes that will survive and be passed to the next generation. The selection process plays an extremely important role in any GA. In the GA, tournament selection process is employed. First, a predetermined number of chromosomes is selected randomly from the population. Then the best the selected chromosomes is determined—i.e., the chromosome with the lowest fitness value. Finally, the best chromosome will be inserted into the new population. This procedure is repeated until a new population has been created. In the proposed GA, the tournament size, which indicates the lowest selectivity pressure and is largely selected by many experimental applications (Michalewicz, 1996), is set to 2. 5.6. Performance The performance of our proposed GA solution algorithm is favourable and promising. For the example shown in Section 6.1, with a population of 500 and within 100 generations, the proposed GA can normally converge to the best solution. The GA solution is identical to the optimal solution obtained from DP, within five experimental runs, although GA does not guarantee the optimality of the so-called best solution in every single experimental run. Moreover, the average deviation of heuristic solutions from the optimal solution obtained from DP for the five experimental runs is almost negligible. For the example shown in Section 6.1, only 1 or 2 min are required by the proposed GA to arrive at its optimal heuristic solution while DP requires at least 5 min. We can expect, therefore, that, when the number of options and stages in our optimization problem increases to some extent, the proposed GA algorithm would further outperform DP in terms of computational efficiency.

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6. Numerical results To demonstrate how the proposed mathematical model can be used as a decision support for investigating the impact of product platform commonality on optimal SCC, we present and discuss a specific case application involving a family of notebooks. 6.1. Notebook computers This particular case is concerned with the optimal configuration of the supply chains shown in Figs. 2, 3a and 3b. For the three supply chain networks, all components in the generic BOM are bought from external vendors except for the intermediate subassembly and the end-products. For most components, several alternative suppliers are available for choice during the configuration process. Table 1 lists the parameters of the alternative options at each stage. The first two columns give the index and name of each stage corresponding to that in Fig. 2. The option column indicates a number of options each with its own processing time and cost. An option with a short processing time usually has a high processing cost. Thus, at each stage, the options are ranked in the decreasing order of processing time or the increasing order of production cost. We also assume that the product manager sets the service level at 98% at each stage. Furthermore, the manufacturer operates 360 days in a year, and the annual holding cost rate is 40%. The common review period for the three demand stages (stages 15, 16 and 17) is equal to 1 day. The daily demands at these three demand stages are given in Table 2. The correlation coefficients between different market demands are set to zero, i.e. r1516 ¼ r1517 ¼ r1617 ¼ 0. 6.2. Configuration results Using the mathematical model and solution algorithm presented already, we obtain the optimal configurations reported in Table 3. Table 3 lists the configuration results of the three kinds of supply chain networks: GSC, ISCA and ISCB. The ‘‘supplier option selection’’ column lists the option selection results of the three supply chain

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Table 1 Alternative suppliers and their lead-times and production costs Index Stage name

Option Processing Production time cost

1

Parts w/8 week LT

1 2 3 4

40 20 10 0

$ $ $ $

2

Parts w/4 week LT

1 2 3

20 10 0

$ 200.00 $ 202.50 $ 205.03

3

Parts w/2 week LT

1 2

10 0

$ 155.00 $ 156.93

4 5

Parts on consignment 1 Circuit board assembly 1 2

0 20 5

$ 200.00 $ 120.00 $ 150.00

6

LCD display

1 2

60 5

$ 300.00 $ 350.00

7

1

30

$ 200.00

8

Miscellaneous components Metal housing

1 2

70 30

$ 225.00 $ 240.00

9

Battery

1 2

60 20

$ 40.00 $ 45.00

Subassembly

1 2

5 2

$ 120.00 $ 132.00

10

130.00 133.25 134.91 136.59

CD-RW drive

1 2

40 5

$ 30.00 $ 35.00

12

DVD drive

1 2

40 5

$ 15.00 $ 16.50

13 14

Notebook A assembly Notebook B assembly US demand— Notebook A

1 1

1 1

$ 30.00 $ 30.00

1

5

$ 12.00

2

1

$ 20.00

1

15

$ 15.00

2

2

$ 30.00

1

5

$ 12.00

2

1

$ 20.00

16

17

Europe demand— Notebook A US demand— Notebook B

US demand—Notebook A Europe demand—Notebook A US demand—Notebook B

s 120 50 80

Table 3 Configuration results of the three kinds of supply chain networks Supplier option selection

Service time

GSC ISCA ISCB GSC ISCA ISCB 1 2 3 4 5 6 7 8 9 10 11 12 13 14

networks. Numbers in this column indicate the selected supplier options at each stage for each network. From this column, we can see that there are three discrepancies at stages 1, 2 and 3, which have been marked by a dashed ellipse for attention. At stage 1, option 1 and option 3 are configured for the ISCA

m 200 75 125

network and the ISCB network respectively while option 1 is selected for the GSC network; at stage 2, option 3 and option 2 are configured for ISCA and ISCB respectively while option 2 is selected for the GSC network; and at stage 3, option 2 is configured for the ISCA network while option 1 is selected for the ISCB network and the GSC network. These results

Index Stage name

11

15

Table 2 Demand parameters

15 16 17

Parts w/8 week LT Parts w/4 week LT Parts w/2 week LT Parts on consignment Circuit board assembly LCD display Miscellaneous components Metal housing Battery Subassembly CD-RW drive (Notebook A) DVD drive (Notebook B) Notebook A assembly Notebook B assembly US demand— Notebook A Europe demand— Notebook A US demand— Notebook B

1

1

3

10

0

10

2

3

2

10

0

10

1

2

1

10

0

10

1

1

1

0

0

0

1

1

1

0

0

30

1 1

1 1

1 1

0 0

0 0

30 30

1 1 1 1

1 1 1 1

1 1 1

0 0 5 5

0 0 5 5

30 30 35

1

5

1 1

1

1

6 1

35 6

6

36

2

2

0

0

2

2

0

0

2

2

0

0

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show that suppliers with lower option indices have been assigned in the GSC network. As mentioned earlier, for each stage, the supplier options are ranked in the decreasing order of processing time or the increasing order of production cost. Hence, the index of an option can indicate the option’s manufacturing capability. The results of supplier option selection in Table 3 show that product platform commonality allows the manufacturer to source from raw material vendors with lower capabilities. The ‘‘Service Time’’ column of Table 3 lists the service time configuration results of the three supply chain networks. Numbers in the column indicate the selected service times for each network’s stages. Unlike the supplier option selection results, the service time results are not so intuitive as to indicate some clear implications. Recall from our discussion in Section 3.3 that the service time decision is actually a decision about optimal AOH inventory placement. Hence, we can translate the service time configuration results of Table 3 into Fig. 7, which shows the AOH inventory levels of each stage of the three supply chain networks. From Fig. 7, we can see how the AOH inventory level changes under the impact of product platform commonality. Let us compare the two lines: GSC and ISCA + ISCB. The procurement stages can be divided into two groups. One is the platform component stages which are shared by ISCA and ISCB, i.e. stages 1–4 and 6– 9, and the other group includes component stages which are unique in ISCA or ISCB, i.e. stages 11 and 12. For the platform component stages, the AOH inventory levels in the GSC network are not always

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lower than those in the ISCA + ISCB network as expected from a risk-pooling effect. For example, at stage 7, the AOH inventory level in the GSC network is higher than that in the ISCA + ISCB network. However, for the stages from end-product assembly to customer demands, i.e. stages 13–17, the AOH inventory levels in the GSC network are always no higher than those of the ISCA + ISCB network. This outcome shows that under the impact of product platform commonality, the AOH inventories are reallocated along the supply chain towards the upstream stages. As for unique component stages, the AOH inventory levels are higher than those in the ISCA + ISCB network. This is identical with the results which Baker et al. (1986) have got through analytical analysis. Apart from the above stages, there exist several assembly stages of the manufacturer in the supply chain, i.e. stages 5 and 10. As we can see from Fig. 7, at these stages, the AOH inventory levels in the GSC network are higher than those in the ISCA + ISCB network. The explanation should be the same as that for procurement stages presented above. In terms of the various cost components for the resulting supply chain configurations in Table 4, we can see that the AOH inventory cost of ISCA + ISCB ($ 2,891,897) is significantly decreased to the AOH inventory cost of the GSC network ($ 2,561,832) by 11.41% due to the effect of product platform commonality. As for the total SCC cost, we find that product platform commonality contributes to the noticeable reduction of $ 426,768 in the total SCC cost from the ISCA + ISCB network ($ 270,443,275) to the

Fig. 7. AOH inventory levels of each supply chain network.

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Table 4 Configuration costs

AOH inventory cost WIP inventory cost Production cost Total SCC cost Time to market a b

ISCA

ISCB

ISCA + ISCB

GSC

Reduction (%)

$ 1912891 $ 8334430 $ 176189040 $ 186436361 78

$ 979006 $ 3719458 $ 79308450 $ 84006915 77

$ 2891897 $ 12053888 $ 255497490 $ 270443275

$ 2561832 $ 12619675 $ 254835000 $ 270016507 78a/77b

11.41 4.69 0.26 0.16

For Notebook A. For Notebook B.

GSC ($ 270,016,507) network. We see also that WIP inventory cost of GSC increases by 4.69% and the production cost of the GSC network decreases by 0.26% because the lower capability options at stages 1–3 are selected in the GSC network. When the lower capability options are selected, the processing times of the corresponding stages increase while the production costs of the corresponding stages decrease. As a result, the WIP inventory cost, which is closely related with the processing time of each stage, increases and the overall production cost, which is closely related with production cost of each stage, decreases. Product platform commonality, therefore, appears to have a significant effect on AOH inventory cost reduction and a noticeable effect on total SCC cost reduction. Finally, we can see from Table 4 that the times to markets of each product variant in the GSC network are the same as those in the ISCB and ISCB networks. This implies that product platform commonality does not delay the time to market.

6.3. Sensitivity analysis under different holding cost rates The holding cost rate is an important strategy parameter used by product managers to estimate the risk of holding inventories on-hand and in the pipeline. Through this holding cost rate, production cost and inventory cost can be balanced. If the holding cost were to be set high, the inventory cost of the supply chain would be large relative to the production cost, and, as such, the manufacturer would not prefer to hold inventories. Figs. 8 and 9 display the AOH inventory cost and total SCC cost for the GSC and ISCA + ISCB networks as a function of the holding cost rate. In these two figures, we can see how product platform commonality impacts AOH inventory cost and total SCC cost under different holding cost rates. Also, we can see that as the holding cost rate increases, product platform commonality contributes more to the reduction in AOH inventory cost and total SCC cost.

Fig. 8. AOH inventory cost as a function of the holding cost rate.

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285

Fig. 9. Total SCC cost as a function of holding cost rate.

Table 5 Supplier option configuration results of each kind of supply chain network under different holding cost rates Index Stage name

SL 20%

30%

50%

60%

70%

80%

GSC ISCA ISCB GSC ISCA ISCB GSC ISCA ISCB GSC ISCA ISCB GSC ISCA ISCB GSC ISCA ISCB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Parts w/8 week LT Parts w/4 week LT Parts w/2 week LT Parts on consignment Circuit board assembly LCD display Miscellaneous components Metal housing Battery Subassembly CD-RW drive (Notebook A) DVD drive (Notebook B) Notebook A assembly Notebook B assembly US demand— Notebook A Europe demand— Notebook A US demand— Notebook B

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1 1 1

1 1 1

1 1 1 1

1 1 1 1

1 1 1

1 1 1 1

1 1 1 1

1 1 1

1 1 1 1

1 1 1 1

2 1 1

2 1 2 1

2 1 2 1

2 1 1

2 1 2 1

2 1 2 1

2 1 2

1

1

1

1

1

1

1

1

1

1

1 1

1

1

1 1

1

1

1 1

1

1

1 1

1

1

1 1

1

1

1 1

1 1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

1

1

2

2

2

2

2

2

2

2

2

2

1

1

2

1

2

2

2

2

2

2

2

2

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Fig. 10. AOH inventory levels of each supply chain network under different holding cost rates.

Table 5 presents the supplier option configuration results of the three supply chain networks, under holding cost rates 20%, 30%, 50%, 60%, 70% and 80%. In each column, the discrepancies between the three supply chain networks are marked by a dashed

ellipse just as in Table 3. Looking at Table 5, we can find that for the holding cost rate of 30% and 70%, at stage 17, (an end-product delivery stage), and stage 10 (the generic product assembly stage), an option with higher index (i.e. higher capability with lower

G.Q. Huang et al. / Journal of Operations Management 23 (2005) 267–290 Table 6 Time to market of each supply chain network under different holding cost rates SL

ISCA ISCB GSC a b

20%

30%

50%

60%

70%

80%

91 81 91a/81b

78 81 78a/77b

78 77 78a/77b

78 67 78a/77b

65 67 65a/64b

65 64 65a/64b

For Notebook A. For Notebook B.

production cost and longer processing lead-time) is selected in the GSC network than that in the ISCB network, while the option selected in ISCA is the same as that in the GSC network. As discussed earlier, the service time configuration results are not intuitive to understand for individual stages, and are actually decisions affecting optimal AOH inventory placement. Therefore, we will not present the service time configuration results here. Instead, we translate the service time configuration results under different holding cost rates into Fig. 10, which shows the AOH inventory levels of each supply chain network under different holding cost rates. From this figure, we see similar results as have been observed from Fig. 6. Table 6 presents the time to market of each supply chain network under different holding cost rate. 6.4. Managerial implications Based on the computational results and analyses presented above, we can advance a general proposition that product platform commonality does have significant impacts on both the performance and the configuration decisions of the respective supply chains. There are several managerial implications that can be derived from this general proposition. First, we observe that the AOH inventory cost is reduced significantly while the total SCC cost is reduced to a noticeable extent in the GSC network. Moreover, this impact becomes larger when the holding cost rate increases. This finding indicates that product platform commonality would generally reduce supply chain costs. Second, we find that suppliers with lower option indices are often assigned at procurement stages in the GSC network. This finding implies that product

287

platform commonality would allow the product manager to choose an external raw material vendor with lower capability (i.e. with lower production cost and longer processing lead-time). On the other hand, at the generic product assembly stage and demand stages, higher capability (i.e. with higher production cost and shorter processing lead-time) options are often chosen in the GSC network. This finding implies that under the impact of product platform commonality, the manufacturer’s supply chain would become more agile with regard to the course of production from product assembly to customer orders. Third, the AOH inventory levels at unique component and assembly stages are found to increase constantly, while the AOH inventory levels at stages from end-product assembly to customer demand always decrease in the GSC network. This finding implies that product platform commonality would lead to an increase of inventories of unique components and semi-finished products and a reduction of inventories of finished products. Fourth, another interesting finding about the AOH inventory is that, at common component stages, the AOH inventory levels do not always decrease under the impact of product platform commonality. This finding leads us to conclude that the risk-pooling effect would not always dominate the inventory levels for platform products. In fact, platform component commonality reduces the overall inventory cost by reallocating inventories to upstream stages towards raw materials because the holding costs for raw materials are much lower than those of finished products. Finally, time-to-market for the GSC network does not seem to vary much from that of each of the ISC networks. This implies that product platform commonality would not increase time-to-market.

7. Conclusions and future work In this paper, we have made several contributions to the research literature with respect to integrated optimal configuration of supply chains and platform products. Foremost, we have identified the optimal configuration of platform products, manufacturing processes and supply sourcing in the flexible supply chain as an important area for rigorous and systematic research. More importantly, through a specific

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scenario, we have demonstrated an approach to the development of decision supports for investigating the mutual impacts between the decisions of supply chain configuration and platform product development. As another contribution, we have formulated a mathematical decision model for optimizing the sourcing, manufacturing process and end-product delivery configuration, and AOH inventory placement decision in the supply chain considering commonality among variants in a product family. After proposing the mathematical model, we proposed and developed the use of Genetic Algorithm to solve our optimization problem. From the computational results we observed that the GA performs well in terms of the quality of the best solution as it is consistent with the optimal solution obtained from Dynamic Programming (DP), while GA outperforms DP in terms of computational efficiency. The model and the GA-based heuristic procedure may be used by managers as a decision support tool, as well as for conducting sensitivity analysis. In this paper we also furthered understanding and knowledge about the mutual impacts of the configuration decisions through a series of sensitivity analyses using the proposed model and algorithm. We have derived a number of interesting general observations and managerial implications from the specific case application and simulations. An immediate extension of this paper would be to incorporate more manufacturing process and supply chain parameters and variables that are sensitive to product platform commonality. More sensitivity analyses could then be conducted using these additional parameters and variables. In this paper, we deliberately focused our attention on a limited number of decision variables. The resulting model, however, does not exclude the consideration or the future inclusion of other aspects such as backorder cost, quantity discount, pricing policies, marketing strategies, setup and changeover costs, etc. More ambitiously, stationary demands can be replaced by non-stationary demands. Likewise, some constraints can be modified or relaxed. For example, the unlimited capacity assumption can be replaced by a capacity constraint at each stage. The solution heuristic of the model would then have to be modified according to these revised constraints. If the configuration were extended to product design, then platform development and customization costs should also be considered in the model. However, it should be

noted that the added complexity may not necessarily gain additional insights and any addition should be closely related to the purpose of the model and the analysis. In addition, the case application examined only one performance indicator—supply chain cost. Multiple criteria are ideally and practically desirable. Other performance indicators such as total supply chain profit, total supply chain cycle time, etc. may be more appropriate for certain applications. Also, in the case application, the decision model was built for the manufacturer while alternative supply sources were treated as the domains of the supplier selection decision variable. The decision model would require extension if suppliers themselves are considered as ‘‘manufacturers’’ who use the same or similar decision models. Once suppliers are treated as individual business entities, they would have their own individual business objectives. Such extended model considering suppliers’ suppliers would allow us to investigate different supply chain coordination and integration strategies such as full integration, partial coordination, common objective, competition, leadfollower, shared information, etc. Finally, other platform strategies such as modularity may be considered in the model. This extended model would become an integrated decision support for integrated optimal configuration of platform products and flexible supply chains. The problem formulation and especially the solution algorithms would have to be significantly revised. With this extended model, the impact of decision parameters and variables related to modularity on the supply chain performance could then be examined. Acknowledgement The authors acknowledge the CRCG of the University of Hong Kong and NSFC (Grant No.: 70371023) for partial financial support for this research. They thank the reviewers for their critical but constructive comments. References Baker, K.R., 1985. Safety stocks and commonality. Journal of Operations Management 6 (1), 13–22.

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