Supply Chain Coordination through a Revenue-Sharing Contract with Two Kinds of Fuzzy Demand

Introduction

Research on supply chain management evolved rapidly in different journals of interest to academics and practitioners. Supply chains are generally complex with numerous activities (logistics, inventory, purchasing and procurement, production planning, intra-and inter-organizational relationships and performance measures) usually spread over multiple functions or organizations and sometimes over lengthy time horizons. Single firm cannot compete as an independent member. The product used by the end customer passes through a number of entities contributed in the value addition of the product before its consumption. Also, the practices like globalization, outsourcing and reduction in supply base have exacerbated the uncertainty and risk exposure as well as more prone to supply chain disruption.

More and more firms want to improve their performance by coordination across the entire supply chain. However, the firms involved in a supply chain sometimes may not belong to the same corporate entities. And then, they prefer to maximize their own profits rather than the profit of the entire supply chain. These decision behaviors based on the individual incentives can cause some inefficiencies. To improve the overall performance of supply chain, the members of supply chain may behave as a part of a unified system and coordinate with each other. Thus “coordination” comes into focus. Supply chain contracts are the tools to coordinate the supply chain. Therefore, there have been many researches on supply chain contracts in order to alleviate the incentive conflict and coordinate firms to improve supply chain performance, which includes the quantity flexibility contracts (Tsay & Lovejoy, 1999), backup agreements (Eppen & Iyer, 1997), buy back or return policies (Emmons & Gilbert, 1998), quantity discount contract (Weng, 1995), and revenue-sharing contracts (Cachon & Lariviere, 2005).

The revenue-sharing contract was first applied in video rental industry. Over recent years, many researchers have attempted to provide the foundations for the role of revenue-sharing contracts in aligning supply chain incentives by characterizing the optimal use of revenue-sharing contract. We will review the literature on revenue-sharing in the next section.

However, it is hard to guarantee that the retailer report the sales truly to the supplier. In fact, the retailer has both incentive and opportunity to underreport the sales to reduce the sharing revenue to the supplier. There are some evidences of opportunistic retailer in different industries where revenue-sharing contracts are used. In the video rental industry, it is reported that some lawsuits where studios sued firms such as Blockbuster and Hollywood Video for underreporting of revenues. In the food industry, Dunkin’ Donuts suspected underreporting of gross sales revenues by a franchisee and took the franchisee to court for breach of contract because the amount of raw materials bought from Dunkin’ Donuts was not consistent with the reported sales. Underreporting of sales is observed when goods are distributed digitally through revenue-sharing contracts, too.

Due to the dishonesty, is it necessary for the supplier to cooperation with the retailer or not? Among literatures about supply chain coordination by revenue-sharing contracts above, market demand is characterized as a determinate or stochastic variable. However, in real world, not only demand changes from one period to another but also high degree of fuzziness is involved in data set. Therefore, it is difficult to estimate its probability distribution due to the lack of historic data. Fuzzy set theory which was originally introduced by Zadeh (1965) provides a framework for handling this type of problem in fuzzy environments. From then on, many researchers such as Zimmermann (1976) and Yager (1977) apply the theory successfully to optimization problems. Recently, Liu (2006) lays a foundation for optimization theory in uncertain environments, in which numerous models are proposed to deal with the optimization problems. This paper characterizes market demand as a fuzzy variable and will talk about what the supplier do when it meets with an opportunistic retailer. And due to the uncertainty of demand, it is characterized a fuzzy variable.