A PRODUCTION-DISTRIBUTION MODEL FOR GREEN SUPPLY CHAIN PLANNING

Z.H. Che, H.S. Wang*, and M.C. Chuang

Department of Industrial Engineering & Management

National Taipei University of Technology

1, Sec. 3, Chung-Hsiao E. Rd.

Taipei 106, Taiwan, R.O.C.

hswang@ntut.edu.tw

ABSTRACTThe selection of supply chain partners is an important part in supply chain

production-distribution planning, nowadays environment preservation has gained more and more attention, so each member of supply chain should first consider the suppliers who would supply “green components/products” when they choose components/products suppliers. This study will discuss the production-distribution problem of green supply chain system and intent to construct a suitable optimum mathematical programming model to solve this problem. This model would contain European Union Directive of WEEE and RoHS, so that it could select the partners whose products are designed under environment-protection concept when plan the supply chain structure. This research also proposes a solution model based on particle swarm algorithm (PSO), and compares the result with the solutions gained by linear programming to prove the applicability of the solution model proposed in this research. Finally this research uses the Visual Basic 6.0 to develop the decision information system, so that the decision makers could use this system to make the green supply chain plan in no time.

Keyword: green supply chain, WEEE, RoHS, particle swarm algorithm

1. INTRODUCTIONEnvironmental protection has never been taken into consideration in traditional supply chain management. Green (environmentally-friendly) productivity has gradually emerged as a topic of concern with the increasing demands for green products in the recent decade. Deans (1999) demonstrated that environmental protection has been promoted in American industry and the consideration of environmental protection became a significant constant in purchase policy and the supplier selection process. Directives of WEEE and RoHS published by European Union in 2003 will have impact on electronic products and related industries because products which are incompatible with the directives will be prohibited to come into European Union for sale. Many leading electron and motor manufacturers have realized the importance of the directives and have proposed many strategies in response. The rising green supply chain management is actually one of the strategies in response.Supplier selection is an important link in the purchase process. Regarding quality, if the supplier provides products of poor quality to the lower level manufacturers, the products produced by the lower level manufacturers will be relatively poor as well. In

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terms of cost, the purchase cost accounts for 60% of the total cost. Hence, considerations of full scale factors shall be taken in selecting the supplier to find out the optimized one by multi-aspect evaluation. With the rising of the environmental protection awareness, the materials needed by products to be sold in European countries must comply with the directives of WEEE and RoHS. Hence, this study will take the directives of WEEE and RoHS as appraisal factors in supply chain partner selection. The two directives, together with cost, quality, delivery time, and production capacity will serve as the basic conditions for supply chain partner selection. This study is mainly aimed at in-depth discussion of hierarchical supply chain network system, expecting to construct the most appropriate supply chain system and production distribution decision-making model. As the supply chain system partner appraisal is a very important procedure, this study proposes a systematic method to construct the partner appraisal model. Effectively satisfying the customers’ demands, we plan out the most appropriate supply chain system and production decision to assist the decision-making personnel to get rapidly and effectively the decision-making schemes appraisal results.

2. LITERATURE REVIEWThe green supply chain, in broad sense, refers to the requirements of supplier, products and environmental protection management, namely, the incorporation of environmental protection principles in supplier management mechanism. It aims to empower the products with concepts of environmental protection to raise market competitiveness. Whereas, the currently known green supply chain refers to the supply chain effects of green products promoted by European Union when we enter into 21st century. The developed nations of European Union, who have realized the intertwined interests in supply chain, actively made legislations for some environmental protection issues by bypassing moral persuasion. And they have planed out the schedule for implementing WEEE and RoHS, expecting to bring the world manufacture industry into a new more environmentally-friendly era by relying on the huge commercial market of European Union. Sarkis (2003) proposed a strategy decision to make structure to assist the management in making decisions. In this article, the green supply chain management elements and the way of these elements serving as the basic conditions for the decision making structure were stressed and discussed. And the decision-making structure mainly includes 5 strategies: product life cycle strategy, operational life cycle, environmental effects on the organizational implementation strategy, the organizational efficiency demands and the green supply chain scheme.With the rising of environmental protection awareness, governments begin to force many companies to improve their environmental practices. In response to the concerns of the green topics, in the past ten more years, many companies have started to implement a series of environmental planning, which mainly falls into three types: Type 1, the main purpose of the company management was to reduce the air pollution, solid wastes, the waste water and energy consumption of the factories (Hunt and Auster,1990) ; Type 2, after entering into 1980s, companies started to promote the use of clean technologies in the manufacturing process (Porter and van der Linde,1995); Type 3, since 1990, companies started to change operational procedures and to promote environmental inspection structure to modify products and services. At present, we are entering into the fourth stage where many companies start to set up green plans aimimg at organizing their supply chains from the perspective of environmental efficiency (Noci, 1995; Hass, 1996).

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Noci (1997) proposed three major steps for green supplier appraisal: 1) confirming the company feasible green strategy, 2) defining the method of operational measurement to appraise supplier‘s environmental protection practices, 3) choosing the most effective method to implement supplier‘s selection to make the supplier conform to the company‘s environmental protection strategy. Humphreys et al. (2003) argued that only principles of quality and flexibility were considered in the traditional process of supplier selection. However, with the ever-increasing environmental pressure, many major companies began to consider environmental topics and evaluate the environmental performance of their suppliers. Hence, a decision making supporting tool was proposed to help the company to integrating environmental protection principles with the supplier selection process. Thanks to the lobbying and negotiations of enterprises and governments, WEEE Directive was divided into the current WEEE Directive and RoHS Directive (the restriction of the use of certain hazardous substances in electrical and electronic equipment) in 2000. One directive stresses recycling, reuse and renewal while the other emphasizes on the restriction of the use of hazardous substances. In response to the requirements of WEEE Directive, the members of European Union have set up an electrical and electronic equipment recycling mechanism and have taken related measures to ensure the minimum goal of recycling from private users annually 4 kilos of WEEE per capita. With respect to RoHS Directive, European Union Council and European Union Conference have agreed to prohibit the use of lead, cadmium, mercury, hexavalent chromium, polybrominated biphenyl (PBB) and polybrominated diphenyl ether (PBDE) flame retardants in electrical and electronic equipments since July, 2006. In fact, in order to sale products to European Union, other related new directives and policies such as EuP (Energy Using Products), REACH (Registration, Evaluation and Authorization of Chemicals) and IPP(Integrated Product Policy) shall be taken into consideration in production. And products design data shall be renewed to call into bringing out the positive contributions of green products.

3. PROBLEM DESCRIPTION AND MATHEMATICAL FOUNDATIONDue to the skyrocketing of the environmental protection awareness, suppliers are forced to manufacture greener products. Hence, manufacturers are in need of a decision-making model to appraise which supplier is in line with directives and conforming to the conditions of minimum total costs and best quality. Therefore, this study is aimed at selecting partners in a supply chain system and distributing production. The supply chain partner selection constants include: maximum production capacity, minimum operational production capacity, transportation time, production cost, and product recycling rate. The model of this study is constructed under the following assumptions: (1) Assumption of known demand quantities at all demands ends. (2) In the purchase of spare parts, limitations of maximum production capacity and

minimum operational production capacity exist. Only if the order number shall never exceed the maximum production capacity and must reach the minimum operational production capacity, the supply chain partner is willing to accept the order.

(3) The stock of first stage is 0. (4) Transportation cost will never change with the transportation load but being

calculated by unit transportation cost.

The constants used for the mathematical model are illustrated as follows: Supply chain stage No., .

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Partner of stage 、partner of stage ; .Total number of stages.Total number of partners.Minimum operational production capacity of partner of　stage .

Maximum operational production capacity of partner of　stage .

The quantity transported from of partner of stage to partner of stage .

T score of unit manufacturing cost of partner of　stage .

T score of unit manufacturing time of partner of　stage .

T score of unit transportation cost of partner of stage to partner of stage .T score of batch transportation time of partner j of stage i.

TMD Customer order quantities.T score of average product quality of partner of　stage .

Appraisal scores of partner of　stage .

T score of customers’ purchase or not of partner of stage .

T score of green customers’ market share of partner of stage .3ijGR T score of passing ISO14000 verification of partner of stage for.

T score of having environmental protection policies of partner of stage .

T score of having environmental protection plans of partner of stage . 6ijGR T score of having recycling product design of partner of stage .

T score of having renewable product design of partner of stage .

T score of product recycling percentage of partner of stage .

T score of having reverse logistics system of partner of stage for.

T score of solid wastes of partner of　stage .

T score of energy consumption of partner of　stage .

T score of air pollution of partner of　stage .

T score of waste water of partner of　stage .

T score of led content of electrical and electronic equipments of partner of　stage .T score of mercury content of electrical and electronic equipments of partner of stage .T score of hexavalent chromium content of electrical and electronic equipments of partner of stage .T score of polybrominated biphenyl (PBB) content of electrical and electronic equipments of partner of stage .T score of polybrominated diphenyl ether (PBDE) content of electrical and electronic equipments of partner of stage .T score of cadmium content of electrical and electronic equipments of of partner of stage .T score of solid wastes treatment costs of partner of stage .

T score of chemical wastes treatment costs of partner of stage .

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T score of air pollution treatment costs of partner of stage .

T score of water pollution treatment costs of partner of stage .

T score of energy consumption costs of partner of stage .

Unit manufacturing cost of partner of stage .

Average unit manufacturing cost of stage .

Standard deviation of unit manufacturing cost of stage .

Average product quality of partner of stage .

Average of average product quality of of partner of stage .

Standard deviation of average product quality of stage .

This variable determines whether stage ‘s supplier will be selected or not.

Customers‘ purchase of partner of stage .

Green customers‘ market share of Partner of stage .

Passing ISO14000 verification of partner of stage .

Having environmental protection policies of partner of stage .

Having environmental protection plans of partner of stage .

Having recycling product design of partner of stage .

Having renewable product design of partner of stage .

Product recycling percentage of partner of stage .

Having reverse logistics system of partner of stage .

Led content of electrical and electronic equipments of partner of stage .

Mercury content of electrical and electronic equipments of partner of stage .Hexavalent chromium content of electrical and electronic equipments of partner of stage .Polybrominated biphenyl (PBB) content of electrical and electronic equipments of partner of stage .Polybrominated diphenyl ether (PBDE) content of electrical and electronic equipments of partner of stage .Cadmium content of electrical and electronic equipments of partner of stage .

The mathematical model of this study is illustrated as follow:Object function: minimize the total cost after T transformation technology.

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In which, (1)

Subject to: Satisfying the limitation of partner‘s production capacity.

(2)

Satisfying the limitation of partner‘s production capacity.

for i=2,3；j=1,2,…,J (3)

Making the whole supply chain process satisfy customers‘ demands

(4)

Ensure the balance of input and output of all the partners.

(5)

Transportation quantity shall be more than 0. and integer for all i,j,k (6)

Namely, the product recycling rate of stage ‘s supplier must be less than 4.

for all i,j (7)

Means stage ’s supplier ’s electrical and electronic equipments’ led, mercury, cadmium and hexavalent chromium, PBB, PBDE contents shall be less than 1000ppm.

for all i,j (8)

Means stage ’s supplier ’s electrical and electronic equipments’ cadmium contents shall be less than 100ppm.

for all i,j (9)

This variable determines whether stage ‘s supplier will be selected or not. (10)

5. PROPOSED METHODOLOGYThe solution finding process in this article is illustrated in Fig. 1 with each step being elaborated as follows.

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Fig. 1. Solution finding process.

Step 1: Green partner appraisal process configurationThis step is to figure out the appraisal principles of consideration in the green partner appraisal process. The defining principles include quality, ISO14000 verification, cost, time, production capacity and product recycling rate.

Step 2: Collection of partner data Related data such as: each supplier’s production cost, transportation cost,

transportation time, production capacity limitation and so on. Step 3: Data T transformatiom This step is to adopt T transformation technology to integrate different appraisal

principles such as cost and quality. The T transformation approaches of production cost and quality is presented as follows.

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for all i,j (11)

for all i,j (12)

The standard value after T transformation is termed as T score. The average value of T score is 50 with standard deviation of 10. They will be integrated into the object functions and restriction equations of the mathematical planning models to find out the optimized solution of supply chain combinations of partners.

Step 4: Partner selection This step is to adopt the particle swarm algorithm to find out the optimized supply

chain combinations of partners and production distribution quantity by taking consideration of appraisal principles of production cost, transportation time, the green principle.

Sub-step 4.1: Randomly producing a few groups of particles from the known product market demands and the particles shall be able to pass all the restriction equations. If not, re-producing randomly new groups of particles until being satisfied.

Sub-step 4.2: The particles acquired this time are the individual optimized values. Sub-step 4.3: Calculating the fitness functions of all the particles (Eq.(1)) for

comparison; as for finding out the minimized target function, the particle with the minimum fitness function value is the optimized one in the particle cluster. Remembering the cluster optimized value and comparing it with the following generations.

Sub-step 4.4: Using the equations proposed by Shi and Eberhart (1998) (Eq.(13)~(14)) to renew the location and speed. After renewal, re-inputting the particles into the restriction equation for test, if failing to satisfy (Eq.(2) ~(9)) , re-producing randomly speed until all the renewed particles satisfying the restriction equations before entering into the calculation of next generation.

(13)

(14)

In which, is the velocity of particle i in generation k, is the velocity of

particle i in generation k+1, w is the inertia weight, and are the acceleration constants, is the value of the particle individual optimized location, is the cluster optimized location memory value, is the location of particle i in generation k+1, is the random number between 0~1.

Sub-step 4.5: After the second generation, the individual optimized value shall be compared with the cluster optimized value. And, the cluster optimized value shall be compared with the cluster optimized value which has been memorized by the previous generations.

Sub-step 4.6: Repeating the preceding steps 4.3~4.5 until reaching the requested generations.

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Step 5: Getting the most appropriate partner combinations and production distribution quantity.

6. CASE STUDYThis study uses a 2-3-3-2 supply chain structure to illustrate the concept of the whole system. As shown in Fig. 2, partners of various stages have different unit manufacturing cost, unit transportation cost, minimum production capacity, and maximum production capacity. This structure takes consideration of only one single product, which is manufactured by the supply chain structure and distributed to different partners to reach the goal of minimum cost and meet the final requirements by different quantity combinations. Parts of data after T transformation are shown in Table 1.

Fig. 2. 2-3-3-2 supply chain network structure.

Table 1 Part of results after T transformation.Supplier

1 42.06 61.06 40.38 41.5 54.75 45.56 38.09 46.69 38.932 49.62 51.01 63.02 53.64 31.02 60.37 63.17 40.06 46.843 60.97 51.01 40.38 41.5 54.74 45.56 44.36 46.69 38.934 68.53 40.95 40.38 65.79 54.74 38.15 38.09 40.06 46.845 30.71 61.06 51.7 41.5 54.74 60.37 63.17 66.57 62.65

In designing the experiment, we implement different experimental combinations by using groups of particles parameters: generation 40 and generation 50, particle number of 50 and 60, inertia weight of 0.4 and 0.5, and maximum velocity of 6 and 10. It can be known from the experiment results that the minimum fitness function value is 50540.14. All the experimental results are shown in Table 2. By comparing the results, we can find that combination (i) in Table 2 costs minimum time and get the convergence and the optimized parameters combination is generation 50, number of particles of 50, inertia weight of 0.4 and maximum velocity of 6. Fig. 3 shows the evolution process of combination (i). Fig. 4 demonstrates the optimized partner

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combinations and production distribution quantity: partner 1 manufacturing 25 units, distributing 7 units to partner 3, 6 units to partner 4; partner 3 manufacturing 46 units and distributing 34 units to partner 7, 12 units to partner 8; partner 4 manufacturing 24 units, distributing 12 units to partner 7, 12units to partner 8; partner 7 manufacturing 46 units, distributing 10 units to partner 9, 36 units to partner 10; partner 8 manufacturing 24 units, distributing 12 units to partner 9, 12 units to partner 10.

Table 2 Results of Fitness and calculation time for all

combinations.Generation

number40 50

Particle number

50 60 50 60

V_maxInertia weight

60.4 (a)50545.11A,2.5B (e)50540.14,2.9 (i)50540.14,2.2 (m)50543.78,2.70.5 (b)50540.14,2.3 (f)50540.14,3.2 (j)50540.14,2.7 (n)50540.14,3.3

100.4 (c)50542.62,2.3 (g)50542.69,2.7 (k)50540.14,3.2 (o)50540.14,3.20.5 (d)50542.2,3 (h)50540.143.5 (l)50540.14,3.6 (p)50540.14,3.2

A: Fitness B: calculation time (sec)

50300

50400

50500

50600

50700

50800

50900

51000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Generation

Fig. 3 Evolution process of combination (i).

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Fig. 4 Results of combination (i).

In order to verify the feasibility of the particle swarm algorithm proposed in this study, this study compares the optimized solution with the solution got from the linear planning. The object function value obtained from linear planning is 50540.14, taking only1 second. This study adopts the equations (15) and (16) by Wang and Che (2007) to calculate APDF and APDT, and employs T test to test the object function values and computation time. The results are shown in Table 3.

(15)

(16)

As seen from Table 3, the optimized fitness by using this method is as good as the one obtained from linear planning. However, it takes more time than LP. APDF value is 0, APDT value is 1.9063. The average solution finding time varies less than 2 seconds. Although, the solution-finding model is not as fast as the linear programming model in terms of velocity, when the supply chain network structure is more complex with more factors being considered (for example, production loss), the simple LP cannot complete the supply chain planning. Therefore, the particle swarm algorithm solution finding model has its feasibility in certain circumstances.

Table 3 Comparison of LP and the proposed method. Combination

(a) (b) (c) (d) (e) (f) (g) (h)APDF 0.0001 0 0 0 0 0 0.0001 0APDT 1.5 1.3 1.3 2 1.9 2.2 1.7 2.5

(i) (j) (k) (l) (m) (n) (o) (p)APDF 0 0 0 0 0.0001 0 0 0APDT 1.2 1.7 2.2 2.6 1.7 2.3 2.2 2.2

Average of APDF:0Average of APDT:1.9063Results of the proposed approach Mean of fitness (M1):50541.18Std. of fitness (S1):1.6006

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Mean of computational time (M2):2.9063Std. of computational time (S2):0.4374t-Test for P-Value t-StatisticH0:μM1= F(LP) 0.5442 0.6205H0:μM2= T(LP) 0.0007 4.2283F(LP):Fitness obtained from LPT(LP):Computational time for LP

7. CONCLUSIONSThe main purpose of this article is to provide a particle swarm solution-finding model for decision-makers to find out green partners quickly. The decision-making model cannot only determine the most appropriate partner combinations as well as determining the optimized production distribution quantity to minimize the total cost. This study adopts the T transformation technology and particle swarm algorithm. The T transformation technology is mainly to integrate different features. The particle swarm algorithm is to find out the optimized partner combinations and production transportation quantities. According to the comparison results, the solution-finding model proposed in this study is the same as the one obtained from LP. However, it takes more time to get the solution. This study will discuss the feasibility of the proposed particle swarm algorithm solution finding model under more complex supply chain network structure and conditions of considering losses.

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