Stackelberg Game Theory Model with Price and Shelf Space Dependent Demand under Revenue Sharing Contract

Abstract

This paper focuses on supply chain coordination under a revenue sharing contract. Demand plays a crucial role in modeling inventory systems, particularly in the retail industry where products need to be brought in and taken out of retail stores within specified timeframes. The question addressed is how to allocate shelf space effectively. Optimal shelf space allocation in retail significantly impacts product sales and profitability. The research demonstrates that by considering factors such as price, allocated shelf space, product brand image, and advertising, a new demand function can be developed. The study explores decentralized, centralized, and coordinated structures using a Stackelberg game model. The findings show that a revenue sharing contract leads to a win-win outcome in the supply chain. Additionally, a numerical example is provided to illustrate the model, and sensitivity analysis is performed on key parameters. The results highlight the significant impact of price elasticity on demand, emphasizing the need to pay close attention to this parameter in real-world applications.IntroductionCoordinating manufacturers and retailers has always been a challenge in decentralized supply chains, as each member seeks individual profit. One practical mechanism for coordination is the revenue-sharing contract, where manufacturers set the wholesale price and retailers pay it. Additionally, retailers share a portion of their profits with manufacturers to incentivize participation in coordinated structures. However, the percentage must be chosen carefully to maximize the profits of both chain members compared to a decentralized structure. In today's competitive world, securing shelf space and determining optimal pricing, particularly in chain stores, has become increasingly intense. Companies can increase their profits by considering various factors that influence customer behavior. This study investigates how manufacturers and retailers in a supply chain leverage advertising and brand image to drive demand while setting prices and allocating shelf space for their products. This new model effectively captures the concept of competition in the market. On the other hand, in today's highly competitive business world, the competition to secure shelf space and determine pricing in department stores has intensified. Pricing and shelf space decisions are influenced by the demand within the supply chain. By considering various factors that impact customer behavior and incorporating them into the model, even though it introduces complexity and challenges in solving the model, the results become more realistic and enhance the model's effectiveness. Customers place great importance on accessing products at the right time and place, making optimal allocation of shelf space in stores and effective shelf space planning crucial steps towards improving and increasing sales in retail stores.Materials and MethodsA two-echelon supply chain, comprising a manufacturer as the leader and a retailer as the follower, is the focus of this study, and Stackelberg game theory is applied to model and analyze this system. The investigated model considers decentralized, centralized, and coordinated structures. Through this research, various factors such as price, allocated shelf space, and the impact of product brand image and advertising are taken into account, leading to the development of a new demand function. The application of the Stackelberg game in the developed model demonstrates how a revenue sharing contract can result in a win-win outcome within the supply chain. Real-world performance analysis of the proposed models is conducted using a dataset from Golrang Holding Supply Chain Network and Ofogh Kourosh Chain Stores Company in Iran.Discussion and ResultsThe proposed problem is modeled under three structures: (1) a decentralized structure where each member of the supply chain (SC) makes independent decisions to optimize its own profit, (2) a centralized structure where a central administrator maximizes the overall SC profit, and (3) a coordinated structure achieved through the design of a revenue-sharing contract. The revenue-sharing contract encourages SC members to transition from the decentralized structure to the centralized one. The results demonstrate that the use of the revenue-sharing contract leads to the sum of retailer and manufacturer profits being equal to the total profit in the centralized structure, with each member achieving higher profit compared to the decentralized structure. Consequently, the revenue-sharing contract facilitates the coordination of the desired supply chain.ConclusionsThis research is based on a real-life case study in the retail industry. The findings of this study are applicable to various retail sectors, including dairy, protein, grocery, cosmetics, fresh fruits, vegetables, and more. Traditionally, price has been viewed as a revenue generation tool. However, it is now recognized that price plays a crucial role not only in generating revenue but also in ensuring customer satisfaction. Therefore, it is important to coordinate and align pricing decisions with factors related to customer management, such as brand image and advertising. The main objective of this research is to design a new model with a multiplicative demand function that considers factors such as price, shelf space, brand image, and advertising. Additionally, the implementation of a revenue-sharing contract has improved system performance. The developed models were solved using Mathematica software, and numerical examples were provided to demonstrate their real-world application and the solution method. The numerical examples revealed that the centralized and coordinated structures experienced price declines compared to the decentralized model, leading to increased profitability in these structures. Furthermore, sensitivity analysis was conducted on key model parameters, highlighting the significance of the price elasticity parameter on demand. This parameter should be given greater consideration in real-world applications. While the study focused on a supply chain structure involving one manufacturer and one retailer, future research can explore supply chains with multiple retailers. It is also possible to combine various supply chain coordination contracts or compare different coordination contracts with each other.

Keywords

• stackelberg game
• shelf space
• revenue sharing contract
• pricing
• supply chain coordination