Research on Supply Chain Contract Coordination Simulation Based on Swarm 1

1 This work is partially supported by the National Natural Science Foundation of China (Grant No. 70671010) and the Key Project of Chinese Ministry of Education.(Grant No. 108011)

Xiuguang Bai School of Economics and Management

Beijing University of Posts and Telecommunications

Beijing, China, 100876 baixg960@tom.com

Huaying Shu School of Economics and Management

Beijing University of Posts and Telecommunications

Beijing, China, 100876 shuhy@bupt.edu.cn

Abstract

In order to study the effects of the contract coordination in the supply chain, the Complex Adaptive System (CAS), Agent model-building and supply chain theories were introduced, and the competitive rules and assumption conditions of simulation of the corporations in the supply chain were described. Then competitive environment of the supply chain was constructed on the Swarm simulation platform, and then the three types of contracts’ processes (the optimization of the supply chain, the optimization of the supplier and the retailer) were simulated. The results indicate that an appropriate contract can make all the corporations beneficial and almost maximization, and it can coordinate and promote the whole supply chain continuous and healthy development, which is the goal of contract design. The results have strong practical and instructional significance. 1. Introduction

With the rapid development of technology, economy and capital market, profound changes have taken place in the market competition and the development strategies of enterprises. The competition between single enterprises has gradually evolved to the competition between supply chains of the enterprises. As a result, the enterprises not only need to coordinate their internal resources, but also need to attach great importance to the coordination in supply chains.

The researches on the supply chain can be mainly categorized into two types at present: the theoretical research and the simulation research. The theoretical

researches focus on the contract coordination, stock, risk and so on, using mathematical programming methods to carry on the optimal solution: in contract aspect, Gerard P. Cachon introduced the theory, method and model in detail[1]; Zhuang[2] researched the supply chain coordination mechanism by combining and applying theories of multiple subjects, system science, game theory, operational research and so on; Chen[3] conducted detailed research on the stock order quantity and the ordered merchandise time in advance; Li[4] researched on the uncertainty stock; Yang[5] analyzed the relationship between the uncertainty and the stock firstly and then proposed a multi-stage stock control model. The simulation researches on supply chain mainly use simulation theories such as complex adaptive system, system dynamics and structural equation to simulate the profit allocation or stock and so on. The simulation focuses on the microcosmic aspects at present: Liu[6] studied how to adjust order plan and production plan for the optimization of supply chain and simulated the process with Swarm; Guo[7] constructed the hierarchical structural model and stimulation response model of supply chain, and then simulated with Swarm; Huang[8] modeled and simulated the telecom supply chain using the system dynamics theory. However, simulations from the macroscopical aspects of the supply chain were few. According to this, this paper simulated the whole life cycle of supply chain from the point of cooperation, and found that a better contract can coordinate the supply chain and help it develop healthfully and continuously, and as a result, it can benefit all the participants, which is the development trend.

This paper introduced the complex adaptive system and supply chain theory in the beginning, and then

The 2008 International Conference on Risk Management & Engineering Management

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DOI 10.1109/ICRMEM.2008.15

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constructed the supply chain model and simulated with Swarm, at last analyzed the results of simulation. 2. Complex adaptive system theory

Complex Adaptive System (CAS) was put forward by John Holland in 1994, the 10th anniversary of Santa Fe Institute. CAS is a kind of new thinking and new method to research the complex system. Due to its novel thinking and rich inspiration, the theory has already been applied and proved to be effective in economical, biological, ecological and environmental practices, as well as some social sciences and natural sciences ones. The core of the CAS is regarding the system members as adaptive, active individuals, agent for short, and introducing the macroscopic state change “the emergence”, causing it to produce complexities from the simplicities. The Agent can unceasingly “study” or “accumulation experience” through the interactions with the environment and change its own structure and behaviours according to the experience learned. The entire macroscopic system evolution, including the generation of new levels, the appearances of differentiation and diversity, and the emergence of new Agent which is new, aggregated and larger are all derived gradually on the core of CAS. The causes of the evolution of macroscopic system and the changes of individuals can be all found from the rule of Agent’s behaviour, which can be stimulated under the corresponding external conditions. Then the system drives the Agent’s behaviour rule to emerge the overall characteristic of evolution, and what’s the operational mechanism of the system manifested by the interactions between the system members and the environment, as well as the ones between one member and another, the paper [9] proposed seven characteristics and mechanism of the Agent, in which four represented the agent’s attributes, the rest represented the mechanism when the agent interacted with the environment [9].

Now we can model and simulate the real system using multiple Agents after describing the attributes and mechanism of an Agent. The modelling method based on Agent is a “from bottom to top” method, which is different from the traditional “from top to bottom” one. By analysing the behaviour and relationship of many Agents at different levels of the complex compatible system, as well as some abrupt phenomena which are initiated by the multi-agents’ interactions, we can study the evolution process of the whole system, so that grasp the overall system activity.

There’s a great deal of simulation software tools based on Agent overseas at present, such as the Swarm platform of Santa Fe Institute, Repast platform of

Chicago University, Brookings's Ascape and so on. The most famous one is Swarm, which has been adopted by many scholars. There’re two types of Swarm platform, one is based on Object C, and the other is based on Java. In this paper, we simulated the supply chain contract coordination with the Swarm platform based on Java.

3. Supply chain theory

The research on supply chain mainly focuses on contract coordination, stock and risk at present. The contract coordination research is basically conducted on the wholesale price contract, buy back contract, revenue sharing contract, and quantity flexible contract and so on, and the research on stock mainly has definite demand and the stochastic demand EOQ expansion model, while the research on risk has many styles. In this paper, we mainly studied the effects of the contract coordination in the supply chain.

Suppose there are one retailer and one supplier and the retailer must choose an order quantity before the start of a single season that has stochastic demand. Let D>0 be the demand during the selling season. Let F be the distribution function of demand and f its density function: F is differentiable, strictly increasing

and 0 (0) F = . Let )(1)( xFxF −=−

and )(DE=μ : The retail price is p. The supplier’s production cost per unit is cs and the retailer’s marginal cost per unit is cr, cs +cr <p. The retailer’s marginal cost is incurred upon procuring a unit. For each demand the retailer does not satisfy the retailer incurs a goodwill penalty cost gr and the analogous cost for the supplier is gs. For notational convenience, let c = cs + cr and g = gs + gr. As the products unsold at the end of season, the retailer earns v < c per unit, where v is net of any salvage expenses. And the order quantity is q.

Let S(q) be expected value of sales, then )1()()())(1()},{min()( 00 ∫∫ −=+−== qq dyyFqdyyyfqFqDqEqS

Let I(q)be the expected value of products unsold and left in the inventory:

)2()()( )( qSqqI DqE −== − + Let L(q) be the expected value of the unmet

demand: )3()()( )( qSqL qDE −== − + μ

Then the retailer’s profit function is )4()()()()( TqvqSvpq gcg rrrr −−−−+−= μπ

The supplier’s profit function is )5()()( TqqSq gcg ssss +−−= μπ

And the supply chain’s profit function is:

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)6()()()()()()( μππ gqvcqSgvpqqq sr −−−+−=+=Π Thereinto, T is the transfer payment from the retailer to the supplier, and all the contract coordination are discussed by considering the T. From the paper [1], we can get that: if T is the whole price contract, the supply chain can’t be coordinated; if T is the buy back contract, revenue sharing contract and so on, then it will coordinate the supply chain, which can maximize the profit of the supply chain. In this paper, we mainly discussed the supply chain life cycle according to the supply chain coordination that is whether can maximize the supply chain profit. 4. Modelling and simulation 4.1. Model description

There’re supplier Agent and retailer Agent in a supply chain simulation. The complete information sharing is impossible to achieve, therefore in this paper the supplier Agent and retailer Agent are all partial information sharing, and these shared information is attained by exchanging with environmental Agent. Firstly, the supplier Agent provides a contract to the retailer Agent, the retailer Agent may accept the contract or decline. Once a contract is declined, the supplier Agent can either search for new appropriate retailer Agent or revise the contract and then seek another Agent again, until a retailer Agent accepts the contract. The retailer Agent estimates the product demand according to the information provided by environment Agent, and orders the products from the supplier Agent. Then, the two types of Agent carry on price gambling according to the product order quantity, with the purpose to maximize their own profit or to maximize the whole supply chain’s profit through the coordination of the supply chain Agents. The supply chain Agent will record the detailed contract information as the attributes, thereinto supply chain Agent mainly uses coordinated methods such as the wholesale price contract, buy back contract, revenue sharing contract and so on.

In this paper, we mainly studied three types supply chain as the objects: firstly, the supply-chain-max which takes the whole supply chain’s profit maximization as the goal, secondly, the supplier-max which takes the supplier’s profit maximization as the goal, thirdly, the retailer-max which takes the retailer’s profit maximization as the goal, and then we will construct the Agent respectively. For simplicity, we assumed the production cost per unit be the same to every supplier and retailer, but the contracts they signed are different; and each supply chain has its own contract style and members, and all the information is

exchanged through the environment Agent; and the supplier and retailer can choose the supply chain freely, but each retailer can only choose one supplier, and they can change their own contract style and choose another supply chain according to their own profit maximization, we also assumed that the amount of members in all the supply chain are constant. 4.2. Model simulation

According to the rule of the description, we constructed the Agent class, time control table, observer class and so on with Java. After running the code, three standard starting panels of Swarm simulation platform will appear as Figure 1:

Figure a. Control panel Figure b. Parameter of model

Figure c. Observer parameter

Figure 1. Standard starting panel Thereinto figure a is the total control panel which

controls all the processes of the simulation(begin, stop, step, save and exit); figure b is the initial parameter panel, on which “amount” tells the product ordered quantity q; “price” tells the selling price of product; ”num” tells the sum of the suppliers and retailers; “generation” tells the iterative times; figure c is the observer parameter panel, which only has one parameter “display Frequency” that denotes frequency, if display frequency is set bigger, the model operating speed will be accelerated, but some details may possibly be neglected in the simulation.

Run the program with the parameters above, we obtained the following simulation results:

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Figure 2. Product price function

Figure 2 is the product price which changes with the order quantities and the environment, and the change function is supposed to be a sin function.

Figure 3. The members of different styles of

supply chain Figure 3 is the number of the members of the supply

chains of different types. We can see that the supply chain which maximizes the retailer’s profit collapses quickly. This is because we assumed the supplier held stronger power, if the retailers take the maximization of their own profit as goal, then they rarely can sign a contract, hence they will lose money because the lack of products and finally they have to transfer to supply chains of other types; but the suppliers in a supply chain which takes the supplier’s profit maximization as goal may gain largest profits in their own ways for a period of time, because they are in the stronger position, however, the retailers will obtain information from environment Agents gradually and then discover they cannot get their profit maximized in their current supply chain, they will transfer to another supply chain in which they can get profit maximization, this will accelerate the transformation of the supply chain; the supply chain which takes the supply chain’s overall profit maximization as goal will optimize the entire supply chain’s profit, however, the initial imbalance between the strong entity and the weak one or the unfair allocation of profit will cause member's transformation for a period of time, with the allocation of profit getting more and more mature and reasonable, the supply chain’s profit can get more profit than other supply chain can, and finally achieved the win-win situation, therefore it can attract more members to participate in and finally become stable.

Figure 4. Average accumulation repayment of

each kind of supply chain Figure 4 shows the average accumulative return of

each type of supply chain. The supply chain which takes the retailer profit maximization as goal can accumulate relatively high return in a short time, however, as the suppliers hold stronger power in the supply chain and gradually get more information from the environment Agent, they will transfer to other supply chains (change the contract), which would cause the retailers can’t buy appropriate products and have to transfer to other supply chains; Suppliers in the supply chain which takes the supplier’s profit maximization as goal will get more accumulative return because they are in the stronger position, however, as the retailers get more information from the environment Agent, they will gradually find supply chains which can get them more profits than the original one and then transfer to the supply chains which are more profitable, consequently, the suppliers will lose money due to product overstocking and be obliged to transfer; the supply chain which takes whole supply chain’s profit maximization as goal, can get both the suppliers and retailers best accumulative return if the contract is reasonability designed, therefore it can attract more members to get involved and its accumulative return can increase continuously, appearing a tendency.

Figure 5. The average net repayment of each

type of supply chain Figure 5 shows the average net return of each type

of supply chain. The supply chain which takes the retailer’s or the suppliers’ profit maximization as goal can only obtain positive net profit in a short time, but most of the time, the net profit is negative. This is mainly because that with the exchange of information with the environment Agent, majority retailers and

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suppliers will transfer to other supply chains which can get more profit, though they can achieve the profit maximization in a short time in the beginning; the supply chain which takes the whole supply chain’s profit maximization as goal can simultaneously consider the supplier’s and retailer’s profit, thus it can realize the supply chain coordination and achieve the win-win situation, therefore obtains the sound net return. 5. Conclusion

This paper simulated three types of supply chain with the Swarm platform and found that the supply chain contract had large impact on the supply chain coordination. A good contract can benefit all the members in the supply chain, and ensure the supply chain develop healthily and steadily, while some speculative contracts will not only destroy the entire supply chain’s profit, but also cause the supply chain collapse, and oblige the entities to revise the contract to transfer to the supply chain which benefit all members, and this is the trend at present which has great impact on constructing strategic partner relationships. Besides, we changed the order quantities of the products and the amounts of suppliers and retailers and got that: with different order quantities and strong-weak statuses, the incentive effects under the same profit allocation solution will be different, even if the whole supply chain is in optimal situation. Therefore the contracts which are used in the different industries and with different order quantities should not be identical. This paper proved the effects and influence of contract coordination from the simulation angle, hoping the finding can provide some suggestion to the cooperation enterprises.

6. Acknowledgment

The authors are grateful for the supports of the National Natural Science Foundation of China (Grant No. 70671010) and the Key Project of Chinese Ministry of Education (Grant No. 108011).

7. References [1] GP. Cachon, Supply Chain Coordination with Contracts,

to appear in the Handbooks in Operations Research and Management Science: Supply Chain Management, edited by Steve Graves and Ton de Kok and published by North-Holland, 2002, pp.7-20.

[2] P. Zhuang, Study on the Coordination Mechanism for Supply Chain, Transactions of Nanjing University of Aeronautics & Astronautics, Nanjing, 2004.

[3] J. Chen, The Coordination Strategy Analysis of Supply Chain, Hunan University, Hunan, 2006.

[4] L. Li, Research on Supply Chain Inventory, southwest Jiaotong University, Chengdu, 2000.

[5] Q. Yang, Study on supply chain inventory control strategy, Jiangsu University, Zhenjiang, 2005.

[6] X. Liu, Study on Distributed Multi-Agent Simulation Model for Supply Chain Coordination, Dalin University of technology, Dalin, 2005.

[7] Y. Guo, Research on Complexity and Adaptability model of SC System, Qingdao University, Qingdao, 2005.

[8] Y. Huang, System dynamics model of the telecom operation industry supply chain, Beijing University of Posts and Telecommunications, Beijing, 2004.

[9] G. Xu, System Science. Shanghai Scientific and Technological Education Publishing House, Shanghai, 2000.

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