IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PARTA: SYSTEMS AND HUMANS, VOL. 36, NO. 1, JANUARY 2006 53 Supply-Chain Coordination With Combined Contract for a Short-Life-Cycle Product Bin Liu, Student Member, IEEE, Jian Chen, Senior Member, IEEE, Sifeng Liu, Member,IEEE, and Rong Zhang Abstract—A contract is a mechanism to realize the performance improvement of a supply-chain system or to achieve the perfect coordination of a supply-chain channel. This paper deals with the coordination issue of a selling channel for a short-life-cycle prod- uct. First, a new type of contract combining the return policy with markdown money according to the practice under which some companies sell their products with different marketing policies in different selling periods is designed. This case is illustrated using a stochastic dynamic-programming model. Then, the necessary condition to achieve channel coordination with this combined contract is derived; and given the scheme to allocate the coordi- nation profit, the generalized method to find the optimal contract parameters is developed. Lastly, with analysis and simulations, it can be concluded that the supply-chain coordination with the single contract in literatures for two-period selling depends on the demand distribution and the cost structure of a system, but the combined contract that was designed depends only on the cost structure of a system. It can further be concluded that the com- bined contract can ensure channel coordination and arbitrarily allocate coordination profit, and that the combined contract is generalized with several classical contracts as its special examples. Furthermore, the supplier will become the active initiator of the combined contract under the high-risk setting because the com- bined contract can strengthen his status in the channel system and improve his performance. Index Terms—Combined contract, dynamic-programming model, short life cycle, simulation, supply-chain coordination. I. I NTRODUCTION A S A NEWLY fashioned management thought, supply- chain management emerged from serious competition in the global market. Though published only recently, it has been the ascendant in the globalization environment. More and more companies are convinced that “the competition between companies will be replaced by one between supply chains in the future” [1]. They all know that their products will only have an advantage over the competition when they actively seek trustworthy copartners, and build long-term and steady Manuscript received November 29, 2004. This paper was supported in part by National Science Foundation of China (NSFC) under Grant 70473037 and Grant 70321001, in part by the Doctor of Philosophy (Ph.D.) Fund of the Ministry of Education of China under Grant 20020287001, and in part by the Innovation Fund for Ph.D. candidates of Nanjing University of Aeronautics and Astronautics (NUAA) under Grant 4003-019010. This paper was recom- mended by Associate Editor M. Zhou. B. Liu, S. Liu, and R. Zhang are with the College of Economics and Management, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing 210016, China (e-mail: liubhnau@163.com; sfliu@nuaa.edu.cn; greensnow162@sina.com). J. Chen is with the School of Economics and Management, Tsinghua University, Beijing 100084, China (e-mail: Chenj@em.tsinghua.edu.cn). Digital Object Identifier 10.1109/TSMCA.2006.859172 strategic relations with them. If all companies or agents of the supply chain unite under the coordination of the global system and take actions to meet the global-system objectives, they can maximize both their profits and the social benefits under the constrained condition even though some uncertain factors exist. However, it is difficult to put this ideal action into practice in the decentralized supply-chain system. As rational “economic persons,” companies wish to balance self-interest and reduce risks by cooperating with other companies; at the same time, they must give up actions that are beneficial for themselves but are hazardous to others. Therefore, the credits and cooperation between companies cannot depend solely on moralities, but must be normalized by a feasible mechanism, which will directly affect the decision actions of companies and decide the allocation and coordination of profits and risks. This mechanism is called the contract [2]. By contracting, the companies on the supply chain can unite their decisions within the framework of the whole-system benefit. Thus, it is worthwhile and significant to study supply-chain contracts. There are mainly two methods to ensure the performance improvement or to achieve the perfect coordination of a supply- chain system: one is the contract, and the other is information updating or information technique. With the contract, we can adjust the contract parameters (such as the wholesale price, ordering quantity, lead time, and so on) to encourage suppliers and buyers and to arbitrarily allocate the coordination profit. Through information updating, we can reduce the uncertainty in management practice. This paper mainly discusses the former. We can divide contracts of the supply chain into two kinds: the pricing contract and the ordering-quantity con- tract. Among the pricing contracts, there are quantity dis- counts, return policy, markdown money, revenue sharing, and so on. Among the ordering-quantity contracts, there are the minimum purchase commitments, the quantity-flexible con- tract, backup agreement, and so on. The return policy and markdown money are correlative to the contract that we de- signed in this paper. On the return policy, Pasternack [3] considered the pricing problem for a short-life-cycle prod- uct and ensured channel coordination with optimal pricing and return-policy models. It was shown that the credit return with the full-price model could achieve channel coordination in the one-supplier-and-one-retailer system, but is suboptimal in the multiretailer system; however, the full return with the credit-price model could ensure the channel coordination of the multiretailer. Kodama [4] studied the single-period in- ventory model with partial returns and additional orders in the arrival of the selling season, and it was shown that this policy could increase the retailer’s expected profit. Tsay [5] 1083-4427/$20.00 © 2006 IEEE