INVENTORY AND SUPPLY CHAIN MODELS WITH FORECAST UPDATES
1.6. Competitive Supply Chains
Competitive study is another body of research that investigates the efficiency of supply chain management. In this book, Chapter 8 is concerned with the pricing issue and the value-of-information issue based on game theory.
The behaviors of the decision makers are locally rational and are often in- efficient from a global point of view. The attention of some researchers has turned to mechanisms for improving the efficiencies of the entire supply chain.
Contractual arrangements and information sharing fall mainly into this area.
It is understood that no single agent has control over the entire supply chain.
Therefore, no agent has the power to optimize the entire supply chain. It is also reasonable to assume that each agent will attempt to optimize his own preference, knowing that all of the other agents will do the same.
The methodological tool employed in this field is game theory. The modeling of a game can be either static or dynamic, with or without complete information, in settings of supply chain management. With game theory, the behavior of players can be determined when they seek to maximize their own welfare. The key issues include whether there exists a Nash equilibrium, the uniqueness of the equilibrium, and whether the optimal policies belong to the set of Nash equilibria. The most interesting part is finding whether competitive and optimal behavior coincide, assessing which party would benefit, and examining cases where the supply chain coordination is a matter of interest.
In a single-period setting, Lippman and McCardle [48] extend the standard newsboy problem to a competitive setting, where the random demand is split between two or more firms. Suppliers compete with others to maximize their own profits. The authors examine the effect of competition on industry in- ventory and the relation between equilibrium inventory levels and the splitting rule.
A number of papers provide more detailed models of supply chain inven- tory management with information updates and collaborative decision making
within two independent parties. Recent examples include Tsay [66], Cachon andZipkin [12], Barnes-Schuster, Bassok, and Anupindi [5], andDonohue [18].
Of these four, the last one is the most relevant to our model, as described below.
For those papers considering supply-contract issues in inventory management with prior demand information, see Tsay [66] for a detailed review. Tsay [66] investigates quantity-flexibility contracts in a multiparty supply chain: the buyer purchases no less than a certain percentage below the forecast, whereas the supplier delivers up to a certain percentage above. He focuses on the im- plications of quantity-flexibility contracts for the behavior and performance of both parties and for the supply chain as a whole.
Cachon and Zipkin [12] analyze channel competition and cooperation in a supply chain with one supplier and one retailer. In a one-period setting, the Nash equilibrium of the game, between the supplier and the retailer, is derived through choosing their individual order quantity to their own objectives. The optimal solution is derived if the objective is to minimize total supply chain costs. They emphasize the contracting issues in realizing the value of cooperation. They also provide a Stackelberg model in the same setting, which is different from ours mainly in that we consider a two-stage problem with information updating within a period.
Barnes-Schuster, Bassok, and Anupindi [5] provide a two-period correlated- demand model for analysis of the role of options in a buyer-supplier system. In the first period, while the buyer decides profit-maximizing order quantities for both periods, as well as the options that would be exercised partially or totally in the second period, the supplier makes decisions on the profit-maximizing production quantity. In the second period, the buyer chooses to exercise quantity options based on the observed demand in a previous period. The authors give a numerical evaluation of the value of options and coordination as a function of demand correlation and the service level offered.
Donohue [18] investigates a supply-contract problem in which a manufac- turer and a buyer are involved in a two-stage problem. She designs a centralized system where the manufacturer decides the production quantities in both peri- ods and faces the demand in the market directly, which means only one player in the channel. With this centralized system as a benchmark, the decentralized system includes the two players in the two-stage problem. The contract pricing scheme is fixed—that is, {wi^W2'> b) where Wi is the wholesale price in stage i and b is the return price for excess product at the end of the season. For the issue of supply-contract pricing, Emmons and Gilbert [20], Monahan [52], Lee and Rosenblatt [45], and Rosenblatt and Lee [56] investigate supply contracts with quantity-discount schemes. In innovative works from a marketing perspective,
Jeuland and Shugan [38] and Weng [69, 70] consider the impact of pricing in channel coordination.
Chapter 8 focuses on a problem that can be stated as follows: the production lead time of the manufacturer requires a buyer to make purchase decisions with- out accurate demand information. The buyer is aware that improved demand information will be available at a later time. A purchase contract that allows the buyer to modify its initial order quantity before a specific date with both fixed and variable penalties provides volume flexibility to the buyer and brings additional income to the manufacturer (supplier). To the buyer, the problem is how to make initial orders and how to react to the demand information obtained in the later stage to minimize total cost. To the supplier, the problem is how to design the contract to maximize profit.
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