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Design and Operation of an Enterprise-wide Process Network Using Operation Policies. 1. Design Jun-hyung Ryu*,† and Efstratios N. Pistikopoulos‡ Samsung Electronics, San 16 Banwol-Ri, Taean-Eup Hwasung-City, Gyeonggi-Do 445-701, Korea, and Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London SW7 2BY, U.K.
In recent years there has been great industrial and academic interest in the design and operation of enterprise-wide supply chains because of their economic impact under increasingly competitive and narrow profit environments. In this two-paper series, a new modeling framework is presented in order to establish systematic and effective decision support tools for the enterprise-wide supply chains which consist of a large number of industrial production elements such as suppliers, plants, and demands that may be in geographically distinct places. Particularly in part 1, the focus is how to incorporate multiple nodes for the purpose of designing the supply chain. After showing an example to motivate the need of an operating policy in the design of multiple plants, three operating policies, namely, coordination, cooperation, and competition are proposed. Mixed integer linear programming (MILP) models based on these policies are then presented. An illustrative example is presented to demonstrate the potential of the proposed framework. Uncertainty is also one of the most important issues. Therefore in part 2, the effect of uncertainty will be investigated in detail using multiperiod planning models based on the proposed operating policies. 1. Introduction Under current competitive and narrow profit margin environments, the design and operation of enterprisewide supply chains are important research areas having important economic impact in the chemical engineering community because supply chain cost generally involves a significant amount of the total cost. To retain competitiveness, enterprises have to take into account their entire supply chain, from the beginning, which are raw material suppliers, to the end, which are retailers and service providers. The concept of supply chain management has developed almost as a consequence of this competitive pressure to manage enterprises in an integrated and efficient way. The term, “supply chain” is said to emerge in the early 1980s when the potential benefits of integrating business functions such as purchasing, manufacturing, sales, and distribution were discussed.1 Nowadays it is the most frequently and widely used concept in the industry as well as academia. A supply chain for various industries may be defined in many ways, but some general definitions widely used in the open literature are as follows: A supply chain is a network of facilities and distribution options that performs the functions of procurement of materials, transformation of these materials into intermediate and finished products, and the distribution of these finished products to customers.2 Supply chain management is about getting a smooth and efficient flow from raw material to finished goods in your customer’s hands. It is a concept which is * To whom correspondence should be addressed. Tel: 82-31-208-6270. Fax: 82-31-208-6488. E-mail: jun2002q@ naver.com. † Samsung Electronics. ‡ Imperial College.
Figure 1. Schematic representation of an enterprises-wide supply chain.
increasingly replacing traditional fragmented management approaches to buying, storing, and moving goods (Department of Trade and Industry, http:// www.dti.gov.uk). Supply chain management is the process of effectively managing the flow of materials and finished goods from vendors to customers using manufacturing facilities and warehouses as potential intermediate stops.3 The focus of this research is an enterprise-wide supply chain which is the major supply chain of interest in the chemical engineering community as noted by Shah.4 An enterprise-wide supply chain is defined as a supply chain consisting of a number of industrial production elements such as suppliers, plants, and demands in distinct geographical places which are operated by an enterprise. See Figure 1 for its illustration. The design and operation of the enterprise-wide supply chain involves many research issues. The most important issues are multiplicity and uncertainty, which
10.1021/ie049298i CCC: $30.25 © 2005 American Chemical Society Published on Web 02/24/2005
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are the key focus of this two-paper series. Because an enterprise-wide supply chain involves a large number of nodes such as plants, warehouses, distribution centers, and markets which may be in distinct geographical locations, how to incorporate these multiple nodes efficiently in the supply chain is an important issue in deciding the performance of their supply chain and, as a result, the competitiveness of the enterprise. The multiplicity involved in a supply chain can be analyzed into the following two directions: First, a supply chain consists of multiple connections of a supplier and a demand. Two basic nodes in a supply chain are a supplier and a demand. A supplier and a demand are two basic nodes in a supply chain. A supplier gives a product to a demand (and gets a value for it) while a demand gets the product (and gives the value for it). Generally a plant is a supplier and a customer is a demand. But a node in a supply chain may play the role of a supplier and a demand at the same time. For instance, a warehouse plays the role of a demand because it gets products from plants but it is also a supplier because it delivers products to customers. Considering the practice that products are delivered from plants to customers via a number of delivery nodes and a supply chain may be also often connected with other supply chains (e.g., raw materials is also the outcome of material producers supply chain), it can be said that a supply chain consists of multiple connections of a supplier and a demand. Second, a supply chain consists of multiple nodes that may do the same role. A demand orders a number of products to an enterprise which has multiple plants to meet them. A demand may require the same product as other demands in different regions and a plant may produce the same product as other plants in different regions. Therefore the total sum of one product ordered by all demands may be met by one plant or more than one product or even by all plants. That is to say, one product may be produced at more than one plant. At the same time, one product may be stored at more than one warehouse (holding costs at each warehouse may be different). Therefore it can be said that a supply chain consists of multiple nodes that may do the same role. Considering above features of multiplicity, there may be a huge number of production paths from a supplier to an end customer depending on which nodes of the supply chain are gone through. Consequently the design problem of an enterprise supply chain can be defined as determining which plant produces which product for which market by how much amount via which transportation. This is a new challenge that surpasses the scope of the previous research in the process industries which focused mainly on maximizing performances of individual processes, neglecting the overall integration of the entire supply chain. In this two-part series of papers, a new modeling framework is presented in order to establish systematic and effective decision support tools for design and operation of the enterprise-wide supply chain. Particularly, this paper is concerned with how to incorporate multiple nodes into a supply chain in efficient and systematic ways highlighting the importance of an operating policy that incorporates multiple nodes of the supply chain in a systematic way. The rest of this paper consists as follows. After the past literature on supply chain management is reviewed with an emphasis on the incorporation of the multiple
nodes, a motivating example is presented to highlight the impact of an operating policy on the design of a supply chain. Three operating policies are suggested for the process industries, and mathematical programming models using these policies are presented. An illustrative example is solved to show the potential of the proposed design methodology with some concluding remarks. 2. Literature Review In this section, previous work concerning supply chain management in chemical engineering community is surveyed. The previous work may be discussed into the following five major research directions. One direction in the literature is the introductory research addressing the issues which should be involved in the management of the supply chain, because the importance of supply chain management has only been recently highlighted. Backx et al.5 described the current manufacturing environment as transient and pointed out that manufacturing plants have to adapt themselves to the transient environment to fully exploit their economic potential. In line with this, they claimed that the operating strategy of the enterprises should be intentionally dynamical. As a strategy, they presented the idea of dissecting the operation of the supply chain into several levels. But the resulting problem becomes very complex and large scale. They hinted the use of decomposition and coordination techniques as a possible way to solve this complex problem. McDonald6 presented the idea of designing enterprises as a whole and not as a localized problem of a specific unit. This work discusses advantages and disadvantages of using global information technologies for operating enterprises. Rosen7 reviewed currently used supply chain analysis methodologies such as optimization, simulation, and heuristics in industries. The author proposed that an ideal direction for the practical supply chain decisionmaking problems would be to combine mathematical programming optimization and simulation tools. Along with above studies in academia, there are a lot of industrial activities. Besides the many individual companies implementing this supply chain management, an institute called the Supply chain council consisting of many companies introduced industrial models named the supply chain operations reference model (SCOR). Diverse industry leaders joined the council such as Dow Chemical, Merck, Texas Instruments, Compaq, and Federal express in order to work together to develop the model from a practical perspective. They defined common supply chain management processes, matched these processes against “best practice” examples, and benchmarked performance data as well as optimal software applications. It aims to find a tool for measuring both supply chain performance and the effectiveness of supply chain re-engineering, as well as testing and planning for future process improvement. There is a group of research activities which are concerned with modeling the supply chain network from the recognition of the above supply chain issues. Most works start from a simple model of a single process and expand to the large scale model of multiple plants in order to construct the realistic supply chain model.
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Tsiakis et al.8 presented a supply chain design model for the steady-state continuous processes. Their supply chain model was constructed based on determining the connection between multiple markets and multiple plants. According to their formulation, a market is connected to a single plant but there may be a case when it is more profitable and desirable to connect a market to more than one plant. Uncertainty was taken into account by considering multiple scenarios. However the number of scenarios in their application is limited, so the actual performance of their model in representing the actual supply chain remains unanswered. McDonald and Karimi9,10 presented models for planning and scheduling of parallel semicontinuous processes. Their model is expanded for the supply chain and used in their succeeding works of Gupta and Maranas11 and Gupta, Maranas, and McDonald.12 Zhou et al.13 used a multiobjective programming method to incorporate multiple conflicting objectives such as economic, material, social, and environmental sustainability within a supply chain. Wilkinson14 and Dimitriadis15 were concerned with how to solve the scheduling problem of the large scale process network. They tried to aggregate a large number of small time periods into relatively assembled time periods and transformed the original large scale problem into problems with the reasonably solvable size. The results of the aggregated problems are then disaggregated to fit into the detailed specification. The third is concerned with investigating newly generated issues involved in supply chains. Applequist et al.16 introduced financial investment techniques in order to handle the financial risks associated with the design and planning of supply chains. They tried to evaluate the expected values under variances, but the simplified criteria in their model to avoid computational complexities did not fully solve the problem. Parageiougiu et al.17 explored strategies for launching a new pharmaceutical product considering capacity expansions of manufacturing processes. They presented an optimization model for a pharmaceutical company covering from the experimental level to the future process network planning. Gjedrum et al.18 studied the compromise of profits between the producer and the demand in a supply chain using the game-theoretic equilibrium, which is based on constraints guaranteeing minimum profit levels. Most problems formulated as a result of modeling become complex, and the sizes of problems are huge. Therefore some researchers were interested in how to solve this complex problem and implement it in the actual applications. The fourth approaches the supply chain management from the perspective of software manipulation. Because a supply chain involves various kinds of nodes, it is practically a very important issue to integrate the different operating systems of nodes. Das et al.19 presented some works on integrating the scheduling and control issues of the process industries. But more research is expected to come in this direction for the implementation of the realistic supply chain management. The fifth approaches the supply chain management using the concept of control. Many researchers conceived of the actual supply chain as a dynamic system subject to uncertainty and tried to use control methodologies for the sake of emulating the mechanism of the supply
Table 1. Market Demand for a Motivating Example product quantity (tons)
A
B
C
D
E
250
150
180
160
120
Table 2. The Fourth Operating Policy for a Motivating Example plant P1 P2 P3
product
product quantity (tons)
A, B, C 150, 100, 60 D, B, C 160, 50, 60 E, A, C 120, 100, 60 sum of investment cost ($)
investment cost ($) 140 580 83 197 124 169 347 946
chain dynamics. The control methodologies are simple control laws (Perea et al.20) and basic model predictive control concepts (Bose and Pekny;21 Flores .22). As can be seen in the discussions of the previous works, there is an increased interest on the supply chain and their design issues. However many works are only concerned with constructing a mathematical model as a simple expansion of single models or simulating the dynamics of the supply chain. Therefore it becomes clear that there is a need for a modeling framework which focuses on incorporation of multiple nodes of supply chain in a systematic way which will be the main objective of this paper. Next, a motivating example is presented to motivate the importance of an operating policy incorporating multiple plants in the design problem of multisite plants. 2.1. Motivating Example. Consider an enterprise which has three batch plants located in geographically distant places for one big market of which demands are shown in Table 1. All three plants have the same capacity and may make all products. The aim of this example is to investigate how an operating policy can contribute to design an enterprise consisting of multiple plants. For designing a single plant, some researchers such as Kocis and Grossmann23 proposed a mathematical model minimizing the production cost of the plant to meet demands. (See, for example, the model by Kocis and Grossmann.23) To design multiple plants, determination of how to operate multiple plants should be considered, i.e., an operating policy that guides which plant makes which product by how much should be incorporated into the model. Four alternative operating policies are considered in this paper. The first operating policy aims to make some products made at some plants and others at other plants arbitrarily. For instance, the whole demand of product A is satisfied by plant 1, product D by plant 2, and product E by plant 3 (see Table 2). If this operating policy is incorporated in the model of Kocis and Grossmann,23 the result shown in Table 2 gives an investment cost of $347 946. Because more than one products will be made, it is necessary to change a process configuration for a product into that for a different product, which consumes a considerable cost and time. It is thereby reasonable to try to reduce the number of products per plant in order to minimize the cost. Therefore the second policy aims to minimize the number of products per plant by producing the whole quantity of a product at one plant. This policy may reduce potential setup times and costs which may be required if a plant makes a number of products. If this operating policy is incorpo-
Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 2177 Table 3. The First Operating Policy for a Motivating Example plant P1 P2 P3
product
product quantity (tons)
A, E 250, 120 B, D 150, 160 C 180 sum of investment cost ($)
investment cost ($) 164 153 75 723 85 544 325 420
Table 4. The Second Operating Policy for a Motivating Example plant P1 P2 P3
product
product quantity (tons)
A, B, C, D, E 100, 50, 60, 50, 40 A, B, C, D, E 100, 50, 60, 50, 40 A, B, C, D, E 50, 50, 60, 60, 40 sum of investment cost ($)
investment cost ($) 125 705 125 705 106 461 357 871
Table 5. The Third Operating Policy for a Motivating Example plant P1 P2 P3
product
product quantity (tons)
A, B, C 150, 50, 100 D, E 60, 60 A, B, C, D, E 100, 100, 80, 100, 60 sum of investment cost ($)
investment cost ($) 144 881 47 528 146 763 339 172
rated in the model of Kocis and Grossmann,23 each plant makes two products at most. The investment cost is $325 420 (see Table 3). On the other hand, let us suppose a policy opposite to the second. The third operating policy aims to maximize the number of products made at each plant. Consequently, all five products are made at all three plants. The investment cost by this policy where each of three plants produces similar amounts of products is $357 871 (see Table 4). Even if some of plants become unavailable due to breakdowns, an enterprise with this policy in reality may produce all products faster than an enterprise by the first policy which require abrupt setup times and costs. The final alternative policy is a combination of the second and the third. Plant 1 and plant 2 are grouped as one imaginary plant and the grouped plant and plant 3 then produce all five products according to the third policy. The products for the grouped plant are divided between plant 1 and plant 2 according to the second policy. The investment cost by this policy (see Table 5) corresponds to $339 172. From the above results, it can be seen that the investment cost of multiplants is changed by their operating policy. This proves that the choice of an operating policy is economically critical in the optimal design of the multiplants. Furthermore when there is more than one market, the importance of the operating policy increases significantly because connections between plants and markets should be decided in addition to the connection between plants and products. Consequently, the operating policy should decide which plant makes which products for which market in what quantity. In the next section, a new modeling framework is presented for design of enterprise-wide process networks. Three operating policies, coordination, cooperation, and competition, are proposed and mathematically posed as novel mixed integer linear programming (MILP) models. 2.2. An Operating Policy of an Enterprise-wide Process Network. The motivating example demonstrates that an operating policy that decides which plant
Figure 2. A diagram of a coordination policy.
makes which product and in what quantity is necessary to design an large scale integrated system, which is an enterprise-wide process network (EPN). Regarding the decision making in the integrated system, supply chain, Backx et al.5 suggested that individual elements of the supply chain can be designed for the purpose of local or global objectives. In this section, their idea will be materialized by proposing three operating policies. Each policy enables an EPN to be optimally designed by placing prior importance on the individual elements of EPN. First of all, before the design of an EPN is addressed, the entities of EPN are identified as suppliers, plants, and markets: suppliers provide plants with raw materials. (In this study, the suppliers are assumed to provide plants with enough raw materials for production.) Plants use the raw materials to make products for the markets which order the products. The operating policy distributes demands and raw materials between multiple plants. Three operating policies are suggested in the following subsections. 2.2.1. A Cooperation Policy. The second policy groups the markets and connects them to individual plants. All demands of a market are satisfied at one plant, and it is therefore known as an one-market oneplant policy or a cooperation policy. The plant produces all products needed to satisfy the demands of the grouped market. This is a market-oriented production policy because the market can select the plant for the demand. The various markets can be grouped according to the similarity of demands or geographic factors for reasons such as delivery costs. A short distance between a market and a plant can be advantageous for products with high delivery costs or a short period of circulation. On the other hand, the production cost with this policy may be higher than the cost with a coordination policy because there may be many setups for different products. Figure 2 and Figure 3 show diagrams of coordination and cooperation policies in an EPN with three plants and three markets. 2.2.2. A Coordination Policy. The first policy groups the products by type regardless of the markets. It links each product with a single plant and is known as an one product-one plant policy. It imposes the whole demand for a product from all markets on one plant. This operating policy is termed a coordination policy. Because this policy enables the plants to select the products by optimization, it is a production-oriented policy. Irregular increase in demands can be effectively accommodated by increasing the production of the
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Figure 3. A diagram of a cooperation policy.
demanded products without setup cost. However, delivery cost between a market and a plant may be expensive if this policy decides a plant which is far from the market. Figure 2 shows the diagram of a coordination policy in an EPN with three plants and three markets. 2.2.3. A Competition Policy. The last policy allows each plant to make any product for any market. The demand of a market can be satisfied, either fully or in part, by any plant, so long as it maximizes the profit. This is termed a competition policy. A competition policy is different from the policies mentioned above in that the division of a demand enables flexible production. For example, the demand of a market can be met by more than two plants. It is possible for the model using a competition policy to give the same result as one using a coordination or a cooperation policy. In the next section, for the three EPN design problems considered above, three operating policies will be presented using mathematical programming techniques. The design of the EPN determines the capacities of the plants and suppliers and production routes from suppliers via plants to markets.
produces i for market d, then 1; else 0 ys,l ) binary variable; if source s is required at plant l, then 1; else 0 yl,d ) binary variable; if plant l delivers to marketD, then 1; else 0 yl,i ) binary variable; if plant l makes product i, then 1; else 0 The assumptions are as follows: All parameters, such as sale price or demand, are deterministic and known in advance. A demand for a product is assumed to be fulfilled completely, therefore the product sale income is given by the product of the sale price multiplied by the demand. A capacity of a plant is expressed as a linear combination of productions of individual products. The unit transfer cost between a market, a plant, and a supplier is known in advance. Suppliers can provide each plant with enough raw material for the plant to satisfy the demand. The capacity of the plant is assumed to be large enough to cover the sum of demands of a product. For the third assumption, if plant l can produce A, B, and C, the capacity of plant l, Pl, is assumed to be
RlAXlA + RlBXlB + RlCXlC e Pl
where Rli is the known coefficient of the product for plant l and Xl,i is the production quantity of a product i by the plant l. The model is formulated as a following mixed integer linear programming (MILP) problem. The objective function is the maximization of the profit
max profit ) total sale - production cost source cost - delivery cost (2) On the basis of the first assumption, maximizing profit is equivalent to minimizing cost. The authors would like to highlight that the main objective of supply chains is to maximize the profit. The sale, production and source cost are expressed as
total sale )
3. Model Formulation The model will be based on the following nomenclature: Indices i ) product 1, ..., N l ) plant 1, ..., L s ) source supplier 1, ..., S d ) market demand 1, ..., D Parameters Xl,iL ) lower bound of quantity of product i at plant l Xl,iU ) upper bound of quantity of product i at plant l Xl,i,dL ) lower bound of quantity of product i at plant l for market d Xl,i,dU ) upper bound of quantity of product i at plant l for market d spd,i ) per unit sale price of product i at market d scs,l ) per unit source cost coefficient for source s to plant l dcl,d,i ) per unit deliver cost coefficient for product i from plant l to market d Rl,i ) capacity coefficient of product i for total capacity of plant l ksl ) conversion factor of raw material s at plant l pcl,i ) per production cost of product i at plant l Dmd,i ) demand of product i at market d NOMl,i ) number of available markets for plant l and product i NOPd,i ) number of available plants for market d and product i Variables Xl,i ) production quantity of product i at plant l (ton) Xd,i ) demand of product i at market d (ton) Xl,d,i ) production quantity at plant l of product i for market d (ton) raws,l ) required raw material for source s at plant l (ton) yl,d,i ) binary variable; if plant l
(1)
∑d ∑i spd,iDmd,i
production cost ) source cost )
∑l ∑i pcl,iXl,i
∑s ∑l scs,lRaws,l
(3) (4) (5)
The total production quantity of a plant should be less than the capacity of the plant, as follows N
Rl,iXl,i e Pl ∑ i)1
(6)
When a plant makes a product i, the production quantity is given by the following inequality relation N
∑i
N
Rl,iXl,iL
e
N
∑i Rl,iXl,i e ∑i Rl,iXl,iU
(7)
The upper and lower bounds of the capacity are set when product i is manufactured
yl,iXl,iL e Xl,i e yl,iXl,iU
(8)
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If a plant makes a product, the required quantity of raw material should be transferred to the plant. The amount of raw material required is calculated from the demand and a conversion factor
Raws,l g Xl,iyl,i/ks,l for (s, l ) ys,l ) 1
The production quantity is given by D
Xl,i )
(9)
The constraints set by an operating policy will be described in relation to each policy. The constraints for a coordination policy are as follows. All demands of a product are satisfied by one plant; thus one plant is chosen for the product
(10)
(16)
If a product is desired by a market and all demands of the market are satisfied by a certain plant, then the plant should make the product. This logical constraint regarding the relationship between the market, plant, and product can be seen in eq 17
yd,i + yl,d e 1 + yl,i
L
∑l yl,i ) 1
∑d Dmd,i yl,d
(17)
Finally, the design problem of an EPN according to an cooperation policy (COOP) as presented below
Therefore the delivery cost is
delivery cost )
∑l ∑d ∑i dcl,d,i Dmd,i yl,i
(11)
max
spd,i Dmd,i - ∑ pcl,i Xl,i - ∑ scs,l Raws,l ∑ d,i l,i s,l
∑ Dmd,i yl,d
and the production quantity of a plant is represented as Subject to
D
Xl,i g
∑d
Dmd,i yl,i
(12) N
Rl,i Xl,i e Pl ∑ i)1
Finally, the design problem of an EPN according to the coordination policy (CORP) is presented below
max
∑ d,i
spd,i Dmd,i -
∑ l,i
(18)
l,i,d
pcl,i Xl,i -
∑ s,l
N
scs,l Raws,l -
∑ dcl,d,i Dmd,i yl,i
(13)
l,i,d
∑i
N
Rl,i Xl,iL e
∑i
N
Rl,i Xl,i e
∑i Rl,i Xl,iU
Xl,i yl,i/ks,l e Raws,l yd,i + yl,d e 1 + yl,i
Subject to
D
∑d Dmd,i yl,d e Xl,i
N
Rl,i Xl,i e Pl ∑ i)1 N
N
∑i Rl,i Xl,i
L
L
∑l yl,d ) 1
N
∑i Rl,i Xl,i e ∑i Rl,i Xl,i
U
e
yl,i Xl,iL e Xl,i e yl,i Xl,iU
The constraints for a competition policy are as follows. The delivery cost is defined as
Xl,i yl,i/ks,l e Raws,l D
delivery cost )
∑d Dmd,i yl,i e Xl,i L
The constraints for a cooperation policy are as follows: One plant is chosen for a market L
(14)
∑l ∑d ∑i dcl,d,i Dmd,i yl,d
D
Xl,i g
∑d Xl,d,i
yl,d,i Xl,d,iL e Xl,d,i e yl,d,i Xl,d,iU
(20) (21)
D
The delivery cost is the sum of demand and its delivery coefficient
delivery cost )
(19)
A product made at a plant l can be transferred to any market which is expressed by (20) to (23)
∑l yl,i ) 1
∑l yl,d ) 1
∑l ∑d ∑i dcl,d,i Xl,d,i
∑d yl,d,i e NOMl,i
(22)
L
(15)
∑l yl,d,i e NOPd,i
(23)
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Figure 4. Optimal process networks according to three suggested policies: (a) coordination; (b) cooperation; (c) competition policy.
The design problem according to a competition policy (COMP) is presented below
max
spd,i Dmd,i - ∑ pcl,i Xl,i - ∑ scs,l Raws,l ∑ d,i l,i s,l ∑ dcl,d,i Xl,d,i (24) l,i,d
3.1. Case Study. By use of the MILP formulation given above, the following example is solved. Consider an enterprise with three plants, 1, 2, and 3, all at different locations. In addition, there are three markets, Lo, Pa, Be, and three material suppliers, rA, rB, and rC. The plants can produce A, B, and C from the three materials. The products are made according to the following first-order reactions
Subject to
rA f A k ) k1 N
rB f B k ) k2
Rl,i Xl,i e Pl ∑ i)1 N
N
rC f C k ) k3 N
∑i Rl,i Xl,iL e ∑i Rl,i Xl,i e ∑i Rl,i Xl,iU Xl,i yl,i/ks,l e Raws,l D
∑d Xl,d,i e Xl,i yl,d,i Xl,d,iL e Xl,d,i e yl,d,i Xl,d,iU D
∑d yl,d,i e NOMl,i L
∑l yl,d,i e NOPd,i The above three models are summarized in Table 6. Table 6. Summary of Three Models in Terms of Participating Euqations coordination model
cooperation model
competition model
eqs 10-13
eqs 14-18
eqs 19, 21-24
The problem data are given in Tables 7-9. The model is solved using GAMS/CPLEX on an Ultrasparc workstation. Table 16 and Figure 4 show the maximum profits and the optimal product transfer routes using three operating policies. 3.1.1. Setup Cost. Processes cannot make all quantities of products at one time. For the batch process, a number of batches should be operated. When multiple products are processes, a different batch sometimes needs a new setup which requires time and cost. The example is solved without considering the setup cost. In practice, the setup cost is an important factor in a multiproduct plant. For example, two options are available in the production of two products A and B by two plants, plant 1 and plant 2, either both plants make both products or the production is divided between the plants such that plant 1 makes A and plant 2 makes B. The difference between the former and the latter is not only in the production cost but also in the setup cost; the latter has no setup. In this paper, consider a single campaign process where all batches of one product are produced before moving to the next.
Table 7. Data for Example 1, Plants production cost ($)
upper bound (tons)
lower bound (tons)
conversion factor
raw material cost ($/ton)
plant
capacity (tons)
A
B
C
A
B
C
A
B
C
rA
rB
rC
rA
rB
rC
1 2 3
1500 1900 2000
16 20 14
19 15 10
12 17 19
2000 2000 2000
2000 2000 2000
2000 2000 2000
100 100 100
100 100 100
100 100 100
0.55 0.45 0.5
0.7 0.65 0.6
0.45 0.55 0.65
9 10 12
9 8 7
8 11 9
Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 2181 Table 8. Data for Example 1, Delivery Cost
Table 12. An Optimal Design According to a Competition Policy
product ($ /ton) plant
market
1
Lo Pa Be Lo Pa Be Lo Pa Be
2 3
A
B
10 11 13 20 19 18 14 18 15
product (tons)
C
15 14 16 19 18 19 11 15 13
14 15 17 15 15 15 12 14 13
plant 1 total plant 2 total plant 3
Table 9. Data for Example 1, Market sale price ($/ton)
product demand (ton)
A
B
C
A
B
C
Lo Pa Be
132 139 126
133 138 126
133 142 127
600 400 500
400 400 600
600 600 400
Table 10. An Optimal Design According to a Coordination Policy product (ton)
total plant 2 total plant 3
market
A
Lo Pa Be
600 400 500 1500
B
C
500 600 400 1500 400 400 600 1400
total
Table 11. An Optimal Design According to a Cooperation Policy product (tons) plant 1 total plant 2 total plant 3 total
market
A
B
C
Lo Pa Be
400
400
600
400 600
400 400
600 600
Lo Pa Be
600 Lo Pa Be
Lo Pa Be
600 400 500 1500
B
C 600 600 1200
Lo Pa Be
275
Lo Pa Be
275 400 125 600 1125
400 400
Table 13. Raw Material Supply According to a Coordination Policy required raw material (tons) plant
rA
plant 1 plant 2 plant 3 sum of required raw material (tons)
2727.27
rB
rC 2333
2909 2909
2727.27
2333
Table 14. Raw Material Supply According to a Cooperation Policy
Lo Pa Be Lo Pa Be
A
total
market
plant 1
market
400
required raw material (tons) plant
rA
rB
rC
plant 1 plant 2 plant 3 sum of required raw material (tons)
727.27 1333.33 1000 3060.6
571.43 615.39 1000 2186.82
1333.33 1090.91 615.39 3040.63
Table 15. Raw Material Supply According to a Competition Policy required raw material (tons) plant
rA
rB
plant 1 plant 2 plant 3 sum of required raw material (tons)
2727.27 2727.27
rC 2666
423 1875 2298
615.38 3281.38
600 Table 16. Profits Based on Three Suggested Policies
500 500
600 600
400 400
coordination policy
cooperation policy
competition policy
401 620
383 550
410 973
profit ($)
The production cost of a plant is changed when the setup cost is included
product cost ) pure production cost + setup cost (25) The setup cost is expressed as follows
setup cost ) no. of production changes × setup cost coefficient (26) With these constraints and the data in Table 17, the example is solved including the setup cost. A further example with four plants, five products, and eight markets is solved both with and without setup cost. The result is shown in Table 18. The setup cost of the second
Table 17. Setup Cost setup cost ($)
plant 1
plant 2
plant 3
80000
80000
80000
example is the same as the setup cost of the first. In these examples, both a coordination and a competition policy give the same profit and product configuration. Therefore it can be said that reducing the number of products per plant is beneficial to the total profitability. 4. Discussion In this paper, three EPN design models using operating policies which are respectively a coordination, a cooperation, and a competition policy, are proposed
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Table 18. Resolved Profit Considering Setup Cost profit ($) example example 1 example 1 with setup cost example 2 example 2 with setup cost
coordination
cooperation
competition
401 620 281 621
383 550 182 872
410 973 281 621
1 986 500 1 644 856
1 785 300 1 185 317
2 186 800 1 644 856
using MILP formulation. Two examples are solved for the illustration of the proposed design methodology. A few remarks are made about the assumptions and constraints that are used in the models. First, the designs according to the coordination and the cooperation policy are based on the assumption that the capacity of the plant is much larger than a demand of a market. Although the assumption can be generally acceptable, there can be some cases that a demand of a product can be delivered from more than two plants, in which case the problem can be only constructed in a design according to a competition policy. Therefore among the three policies, it is not appropriate to decide which policy is global optimal under any problems. The optimal design of specific case can be decided after examining the results according to the three policies. As a next stage of research, it may be possible to make one framework which includes all the three policies and chooses a best policy depending on the marketing conditions. Second, the production condition in the proposed model is expressed as linear, but a more complex nonlinear equation can be used in the model. Third, suppliers, plants, and markets are considered as the elements of an EPN in the proposed EPN model. The warehouse can be also included in the design of an process network. However, the warehouse can be taken as another kind of a market which does not produce products but holds the products for the final retail market. In the end, an EPN can be constructed with markets of two levels. The relation from a warehouse to a retail market or a customer can be also connected according to the proposed operating policies. Fourth, the parameters of the above examples are assumed to be deterministic. However, the parameter can be variable. For example, the demand, which is assumed to be fixed in the proposed design model, is considered as having different discrete values in multiperiod planning of chemical processes which is investigated in the next subsection. Furthermore, the external conditions of production such as demand, sale price, and source cost and the internal conditions such as conversion factor and equipment availability can be uncertain, and the existence of uncertainty can affect the performance of an EPN. Accordingly, considering the uncertainty in the design of an EPN is well motivated and will be studied in the next period of this project. Literature Cited (1) Harland, C. M., Supply Chain Management Relationships, Chains and Networks, Br. J. Manage. 1995, 7, 45. (2) Ganeshan, R.; Harrison, T. P. An Introduction to Supply Chain Manangement; 1995.
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Received for review August 4, 2004 Revised manuscript received December 28, 2004 Accepted January 19, 2005 IE049298I
