هماهنگی زنجیره تامین با استفاده از به اشتراک گذاری درآمد قراردادهای وابسته به درآمد

A typical single period revenue sharing contract specifies a priori a fixed fraction for the supply chain revenue to be shared among the supply chain players. Over the years, supply chains, especially in the movie industry, have adopted multi-period revenue sharing contracts that specify one fraction for each contract period. These revenue sharing contracts are of revenue-independent type such that the revenue sharing fractions are independent of the quantum of revenue generated. Motivated by the recent events in Bollywood – one of the popular arms of the Indian movie industry – in this paper we develop and analyze a game theoretic model for revenue-dependent revenue sharing contracts wherein the actual proportion in which the supply chain revenue is shared among the players depends on the quantum of revenue generated. Our aim is to understand why revenue-dependent revenue sharing contracts are (or not) preferred over revenue-independent contracts. We also examine if supply chains can be coordinated over multiple periods using both types of revenue sharing contracts. We build a two-period model characterizing supply chains in the movie industry and highlight the implications of the multi-period contractual setting for the supply chain coordinating revenue sharing contracts. We show that supply chains can be perfectly coordinated using both types of revenue sharing contracts; however, there exist situations in which revenue-dependent contracts outperform revenue-independent contracts. Using revenue-dependent revenue sharing contracts supply chains can be coordinated while providing positive surplus to the supply chain players that is otherwise not possible under certain situations in revenue-independent contracts. We also demonstrate how revenue-dependent contracts enhance supply chain coordination and highlight their significance when the drop in the revenue potential from one period to another is moderate.

Revenue sharing agreements in which retailers pay royalties on product sales to suppliers are widely adopted by supply chains, particularly in the video rental and movie industry. By these agreements, a retailer purchases a product from a supplier for a fixed price and shares a fraction of the revenue with the supplier. The supplier offers the purchase price for the product to the retailer who in turn determines the quantity of the product to be ordered from the supplier before actual demand is realized. Depending on the business situation, the retailer may also determine the retail price for the product when placing the order to the supplier or it may be a price-taker in the market. In this setting, a typical single period revenue sharing agreement specifies a priori a fraction of the supply chain revenue to be retained by the retailer (or to be shared with the supplier). A multi-period version of such revenue sharing agreement is observed particularly in the motion picture industry (see, e.g., [1]). This multi-period contract extends a single period contract by specifying multiple revenue sharing fractions; one fraction associated with each contract period. The proportion in which the supply chain revenue is shared among the players in a typical (single or multi-period) revenue sharing contract is independent of the quantum of revenue realized. Such revenue-independent revenue sharing agreements have been extensively studied in the operations and supply chain management literature (see, e.g., [1], [2] and [3]). However, still missing from the literature are studies focusing on revenue-dependent revenue sharing agreements in which the actual revenue sharing fraction adopted in any period depends on the actual revenue realized. Revenue-dependent revenue sharing contracts do not influence the supply chain profit function, however, they impart a new dimension of contractual uncertainty – in the form of revenue sharing proportion – in the profit functions for the supply chain players, and hence, they potentially influence the supply chain performance. By the contractual specifications, the revenue sharing fractions that ultimately will be adopted are uncertain at the time of designing such contracts. The uncertainty of this kind is an internal phenomenon for the supply chain as appose to demand or revenue uncertainty which is an external phenomenon. A clear understanding of the impact of this internal uncertainty on the supply chain performance is essential from the perspective of contract design. In this paper, we aim to bridge the existing gap in the literature and develop a modeling approach to address coordination related issues in supply chains in the movie industry. By explicitly considering both revenue-dependent and -independent contracts, we also contrast their implications for coordinated supply chains. The motivation for our study comes from the recent events in Bollywood, one of the popular arms of the Indian movie industry (http://www.bollywood.com/). Over the years, multiplex-theater owners in Bollywood have dictated the terms of trade with the movie-producers in determining the number of screenings of a movie and also in negotiating the parameters of revenue sharing agreements. Moreover, the terms and conditions of the contractual agreements between theater owners and producers have been varying according to status and star-cast of a movie. For instance, if a popular actor's movie is being released, then theater owners budge while sharing the revenues. But if a lesser known actor's movie is being released, they dictate the terms and demand a larger revenue share. In recent years, the producers have been demanding a flat (or fixed) fraction of all movie revenues, i.e., a single period revenue-independent revenue sharing contract, irrespective of star-cast, budget, and box-office collection, etc. On the contrary, the theater owners have been insisting on sharing profits based on the “performance” of the movie at the box-office, i.e., a revenue-dependent revenue sharing contract. The conflict between the players in adopting either revenue-dependent or -independent revenue sharing contracts resulted in the producers going on an indefinite strike starting April 4, 2009, that has caused an estimated loss of USD 40–60 million to the industry. On June 12, 2009, the strike ended when both parties agreed to 50, 57.5, 62.5 and 70% revenue share for the multiplexes for the first, second, third and fourth week, respectively, for all movies [4]. In other words, the players have adopted a multi-period revenue-independent revenue sharing contract. Motivated by these events in Bollywood, in this paper we develop and analyze game theoretic models for both revenue-dependent and -independent revenue sharing contracts for supply chains characterizing the movie industry. Our aim is to understand why revenue-dependent revenue sharing contracts are (or not) preferred over revenue-independent revenue sharing contracts. We examine if supply chains in the movie industry can be coordinated over multiple periods using both types of revenue sharing contracts. We build a two-period model to highlight the implications of the multi-period contractual setting for the supply chain coordinating revenue sharing contracts. Our analysis provides some interesting results that are not so typical in the supply chain coordination literature. We show that supply chains can be perfectly coordinated over multiple periods using both revenue-dependent and -independent revenue sharing contracts, however, there exist situations in which revenue-dependent revenue sharing contracts outperform revenue-independent revenue sharing contracts that yield zero surplus to the supplier. (In this paper, profit is also referred to as surplus.) Nevertheless, revenue-dependent revenue sharing contracts provide positive surplus to all players in the supply chain that is otherwise not possible under certain situations in revenue-independent revenue sharing contracts. Unlike revenue-independent revenue sharing contracts, revenue-dependent revenue sharing contracts are able to separate the high revenue generating state from the low revenue generating state, and the supply chain can maximize its surplus by aligning the players' decisions in the decentralized setting under each of the unequal revenue generating states that also provides admissible profit sharing among the players. Accordingly, we contribute to the existing literature by showing that revenue-dependent revenue sharing contracts are able to achieve surplus distribution that is not possible under revenue-independent revenue sharing contracts. We also show that revenue-dependent revenue sharing contracts are preferred over revenue-independent revenue sharing contracts while coordinating the supply chain with positive profit shares for the players when the drop in the revenue potential from one period to another is moderate. In this regard, our model and the results are applicable for supply chains in other industries such as public libraries offering seasonal products like weekly/biweekly magazines, car rentals offering new models, seasonal fashion goods, etc. The remainder of the paper is organized as follows. In the next section, we review the supply chain coordination related literature focusing on revenue sharing contracts and place our study appropriately. In Section 3, we build a two-period model for revenue-dependent revenue sharing contracts for supply chains in the movie industry. In Section 4, we analyze our model for the centralized and decentralized setting under both revenue-dependent and -independent revenue sharing contracts. In Section 5, we analyze our results from the perspective of supply chain coordination under both types of revenue sharing contracts. In Section 6, we compare and contrast supply chain coordinating revenue-sharing contracts, and analyze the implications of the two types of contracts. In Section 7, we discuss our main findings and conclude the paper by providing some guidelines for future research. All proofs are relegated to Appendix.

In recent years, supply chains in various industries, particularly in the movie industry, have adopted revenue sharing agreements in which retailers share revenues with suppliers in proportion of the fraction decided ex-ante. By these contracts, the proportion in which the supply chain revenue is shared among the players is typically independent of the quantum of revenue generated. While in the movie industry the players sign such multi-period revenue-independent revenue sharing agreements in which the retailer's revenue share increases in time, the revenue sharing fractions are independent of the quantum of revenue generated in any period. Not limited to such time-dependent revenue sharing contracts, in this paper we examine revenue-dependent revenue sharing contracts in which a set of revenue sharing fractions are chosen in accordance with possible revenue realizations in each period, and the actual proportions in which supply chain revenues are shared among the players in each period depends on the actual revenue generated. The motivation for our study comes from the recent events in Bollywood. While the movie producers demanded a single period revenue-independent revenue sharing contract, multiplex-theater owners insisted on revenue-dependent revenue sharing contracts. The conflict between the players in adopting either revenue-dependent or -independent revenue sharing contracts resulted in the producers going on an indefinite strike in 2009. Our objective in this paper is to examine why revenue-dependent revenue sharing contracts are (or not) preferred over revenue-independent contracts. We also examine if a typical supply chain in the movie industry can be coordinated over multiple periods using both types of revenue sharing contracts. In this regard, we build a two-period model characterizing the supply chain in the movie industry. Revenue-dependent contracts do not influence the supply chain profit function. However, they impart a new dimension of contractual uncertainty – in the form of revenue sharing proportion – in the profit functions for the supply chain players, and hence, they potentially influence the supply chain performance. Therefore, in this paper our aim is to understand the implications of revenue-dependent contracts on the players' performance. We build and analyze a two-period game theoretic model and provide some interesting results that are not so typical in the supply chain coordination literature. For instance, our results show that the supply chain can be perfectly coordinated using both revenue-dependent and -independent revenue sharing contracts, however, there exist situations in which revenue-dependent contracts outperform revenue-independent contracts that yield zero surplus to the supplier. Nevertheless, using revenue-dependent contracts, the supply chain can be perfectly coordinated while providing positive surplus to the supply chain players that is otherwise not possible under certain situations in revenue-independent contracts. By considering state dependent revenue sharing fractions, the supply chain players can separate the high revenue generating state from the low revenue generating state in their coordination efforts, and thereby, the supply chain is able to maximize its surplus by aligning the players' decisions in the decentralized setting under each of the unequal revenue generating states. We believe this is the most significant contribution of our work presented in this paper. We also show that revenue-dependent contracts enhance supply chain coordination such that in comparison with revenue-independent contracts they yield larger range for the revenue retention factor with admissible profit sharing. Further, the benefits of enhanced coordination by adopting revenue-dependent contracts as against revenue-independent contracts are derived for the moderate values of the revenue retention factor. Thereby, from the managerial perspective it is beneficial to adopt revenue-dependent contracts in coordinating the supply chain with positive profit shares for the players when the drop in the revenue potential from one period to another is moderate. The model and the results presented in this paper may be interpreted as a building block in the development of richer and more comprehensive framework for revenue-dependent contracts. We conclude this paper with some guidelines in this regard. First, the choice of the revenue sharing fractions in revenue-dependent contracts can be endogenous to the model. The existing studies including our own study presented here assume that the revenue sharing fractions are exogenously given. The endogeneity of the revenue sharing fractions may provide an additional degree of freedom to the supply chain players in resolving conflicts and coordinating the supply chain especially when the revenue retention factor is small. Moreover, this possible modification in traditional revenue sharing contracts can help researchers in modeling negotiating powers of the supply chain players. Second, it will be interesting to study revenue-dependent revenue sharing contracts in the presence of competing movies adopted for exhibition simultaneously. Third, in the case of multi-period contractual settings, insights in simultaneously determining revenue sharing proportions and length of each time period are essential in view of the current practice of sliding revenue sharing fractions from one period to other. Fourth, it would be interesting to examine the implications of varying risk-taking attitudes of the supply chain players for contract design. In view of the emergence of movie studios undertaking both production and distribution activities under their purview, it is important to analyze the supply chain settings wherein the supply chain players derive cost reduction by combining the roles of the diverse supply chain players. We believe that many such extensions will be helpful in developing results that go beyond qualitative insights and provide aids for decision support.