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

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

A Supply Chain Equilibrium Model with General Price-Dependent Demand

The concept of supply chain equilibrium has been widely employed to solve real-life cases. Under this concept, decisions makers move simultaneously and compete in a noncooperative manner to achieve a supply chain network equilibrium. This paper proposes a supply chain network equilibrium model consisting of multiple raw material suppliers, manufacturers and retailers. Unlike previous studies, we assume that the demand for the product at each retail outlet is modeled as general stochastic functions of price that encompass additive-multiplicative demand models used in previous studies. Under general price-dependent demand functions, we derive the optimality conditions of suppliers, manufacturers and retailers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The existence and uniqueness of the solution to the variational inequality are examined. A sensitivity analysis and a series of numerical tests are conducted to illustrate the analytical effects of demand distribution, model parameters, demand level and variability on quantity shipments, prices, and expected profits. Managerial insights are reported to show the impact of different types of demand functions and model parameters on the equilibrium solutions

Analysis of consignment contracts for spare parts inventory systems

Cataloged from PDF version of article.We study a Vendor Managed Inventory (VMI) partnership between a manufacturer and a retailer. More specifically, we consider a consignment contract, under which the manufacturer assumes the ownership of the inventory in retailer’s premises until the goods are sold, the retailer pays an annual fee to the manufacturer and the manufacturer pays the retailer backorder penalties. The main motivation of this research is our experience with a capital equipment manufacturer that manages the spare parts (for its systems) inventory of its customers in their stock rooms. We consider three factors that may potentially improve the supply chain efficiency under such a partnership: i-) reduction in inventory ownership costs (per unit holding cost) ii-) reduction in replenishment lead time and iii-) joint replenishment of multiple retailer installations. We consider two cases. In the first case, there are no setup costs; the retailer (before the contract) and the manufacturer (after the contract) both manage the stock following an (S − 1, S) policy. In the second case, there are setup costs; the retailer manages its inventories independently following an (r, Q) policy before the contract, and the manufacturer manages inventories of multiple retailer installations jointly following a (Q, S) policy. Through an extensive numerical study, we investigate the impact of the physical improvements above and the backorder penalties charged by the retailer on the total cost and the efficiency of the supply chain.Latifoğlu, ÇağrıM.S

Strategic Inventories in a Supply Chain with Vertical Control and Downstream Cournot Competition

Strategic Inventory (SI) has been an area of increased interest in theoretical supply chain literature recently. Most of the work so far however, has only considered a supply chain without downstream competition between retailers. Competition is ubiquitous in most market situations, hence, interactions between SI and retailer competition merits study as a first step in bringing the conversations and insights from this stream of literature to the real world. We present here a two-period and a three-period model of one manufacturer supplying an identical product to two retailers who form a Cournot duopoly. We also study a Commitment contract, where the manufacturer commits to all the selling seasons’ wholesale prices at the beginning of the 1st period. Commitment contracts have been shown previously to eliminate SI carriage over two selling seasons in the absence of retailer competition. We aim to deduce if this type of contract has the same effect in the presence of downstream competition. We determine closed-form Nash Equilibrium decision variable values for each of these models using game-theoretic modeling, a price-dependent linear demand function, and backward induction. We find that, the introduction of downstream Cournot duopoly competition leads to lower profits for both the manufacturer and retailer. This holds, whether the number of selling season is two or three. Consumer Surplus is also uniformly lower under retailer competition, compared to a downstream monopoly supply chain. When we try to deduce the effect of SI carriage under Cournot duopoly competition, by comparing an SC with Cournot duopoly competition and SI allowed between periods, to a similar SC with a Cournot duopoly downstream and a static, repeating, one-shot game in each period, with no SI carried – we find again that manufacturer and retailer profits are both lower when SI carriage is allowed. This holds whether the number of selling seasons is two or three. Consumer Surplus is also lower uniformly over both two and three selling seasons. Under a Commitment contract, over two selling seasons, the manufacturer ends up with an advantage, making a higher profit with downstream retailer competition, than compared to supplying to a monopoly downstream under the same contract. The retailers, while competing as a Cournot duopoly, are not able to use the relative advantage that comes from a Commitment contract to make a higher profit, as they are, when the downstream is a single retailer monopoly. The consumer also is disadvantaged by the introduction of downstream Cournot competition under a Commitment contract. When we compare a manufacturer supplying to a Cournot duopoly downstream of retailers, with, and without a Commitment contract (dynamic ordering), we see that the manufacturer and consumer benefit under a Commitment contract, making higher profits, but the retailer is at a disadvantage. It would be an interesting extension of this work to generalize the results from two and three selling seasons, presented here, to the “n” period case. It would also be benefi-cial to run empirical studies in real-world supply chains to validate if and to what extent the insights developed by this kind of game-theoretic modeling hold in a real-world supply chain setting. Development of contracts that are more effective than a Commitment con-tract in coordinating this supply chain would be another possible area for further research

Vendor-Buyer Coordination in Supply Chains

Collaboration between firms in order to coordinate supply chain operations can lead to both strategic and operational benefits. Many advanced forms of collaboration arrangements between firms exist with the aim to coordinate supply chain decisions and to reap these benefits. This dissertation contributes to the understanding of the conditions that are necessary for collaboration in such arrangements and the benefits that can be realized of such collaboration arrangements. This dissertation focuses on the vendor-buyer dyad in the supply chain. We identify and categorize collaboration arrangements that exist in practice, based on a review of the literature and combine this with formal analytical models in the literature. An important factor in the benefits of collaboration is the benefit of reduced costs of transport, by realization of economies of scale in the context of capacity-constrained trucks. As a contribution to the understanding of the dependence of transport costs on the volume transported, we demonstrate how transport tariffs for orders of less-than-a-truckload in size on a single link can be deduced from a basic model. The success of a collaboration arrangement depends on agreement about the distribution of decision authority and collaboration-benefits. We study a collaboration arrangement in which the vendor takes responsibility for managing the buyer's inventory and makes it economically attractive to the buyer by offering a financial incentive, dependent on the maximum level the buyer permits to be stocked. This dissertation demonstrates that this incentive alignment leads to considerable cost savings and near-optimal supply chain decisions

Essays in Measuring, Controlling, and Coordinating Supply Chain Inventory and Transportation Operations

Supply chain collaboration programs, such as continuous replenishment program (CRP), is among the most popular supply chain management practices. CRP is an arrangement between two partners in a supply chain to share information on a regular basis for lowering logistics costs while maintaining or increasing service levels. CRP shifts the replenishment responsibility to the upstream partner to avoid the bullwhip effect across the supply chain. This dissertation aims to quantify, measure, and expand the benefits of CRP for the purpose of reducing logistics cost and improving customer service. The developed models in this dissertation are all applied in different case studies supported by a group of major healthcare partners. The first research contribution, discussed in chapter 2, is a comprehensive data-driven cost approximation model that quantifies the benefits of CRP for both partners under three cost components of inventory holding, transportation and ordering processing without imposing assumptions that normally do not hold in practice. The second contribution, discussed in chapter 3, is development of a verifiable efficiency measurement system to ensure the benefits of CRP for all partners. Multi-functional efficiency metrics are designed to capture the trade-off in gaining efficiency between multiple functions of logistics (i.e. inventory efficiency, transportation efficiency, and order processing efficiency). In addition, a statistical process control (SPC) system is developed to monitor the metrics over time. We discuss suitable SPC systems for various time series behaviors of the metrics. The third contribution of the dissertation, discussed in chapter 4, is development of a multi-objective decision analysis (MODA) model for multi-stop truckload (MSTL) planning. MSTL is becoming increasing popular among shippers while is experiencing significant resistance from carriers. MSTL is capable of reducing the shipping cost of shippers substantially but it can also disrupt carriers’ operations. A MODA model is developed for this problem to incorporate the key decision criteria of both sides for identifying the most desirable multi-stop routes from the perspective both decision makers