Coordinating pricing and inventory decisions in a multi-level supply chain: A game-theoretic approach

Abstract

This paper concerns coordination of enterprise decisions such as suppliers and components selection, pricing and inventory in a multi-level supply chain composed of multiple suppliers, a single manufacturer and multiple retailers. The problem is modeled as a three-level dynamic non-cooperative game. Analytical and computational methods are developed to determine the Nash equilibrium of the game. Finally, a numerical study in computer industry is conducted to understand the influence of the market scale parameter and the components selection strategy on the optimal decisions and profits of the supply chain as well as its constituent members. Several research findings have been obtained.components selection decisions to maximize his net profit. The retailers' problem will focus on the replenishment cycles and retail prices for the products.We describe CSCSPI problem as a three-level dynamic non-cooperative game with respect to the overall supply chain. The suppliers formulate the bottom-level non-cooperative simultaneous sub-game and at the same time as a whole play the middle-level non-cooperative simultaneous sub-game with the manufacturer. The suppliers and the manufacturer also being a group formulate the top-level non-cooperative simultaneous whole game with the retailers. Once the whole game settles an equilibrium solution, none of the any chain members is able to improve its payoff (i.e. profits) by acting unilaterally without degrading the performance of other players. We propose both analytical and computational methods to obtain the Nash equilibrium of this game.The game model and the proposed solution algorithm constitute a powerful decision support for solving the CSCSPI problem. Its use is demonstrated and tested through a numerical example. The impacts of the market scale parameter and components selection on the decisions and profits of all the chain members are also investigated.This paper is structured as follows. The next section presents a brief review of the literature related to pricing and inventory coordination, product family design, Game Theory for supply chain coordination. In Section 3, we give the problem description and some notations. We formulate the mathematical model of the CSCSPI problem in Section 4. Section 5 proposes the analytical and computational methods used to solve the CSCSPI problem in Section 4. In Section 6, a numerical study and the influence of market scale parameter and the components selection strategy have been presented. Finally, this paper concludes in Section 7 with some limitations and suggestions for further work. Literature reviewPricing, inventory decisions, and product family design and platform products development, have been extensively studied in supply chain coordination. Although the three areas are closely interrelated with each other, they are rarely been studied in an integrated, systematic manner. Recently, Game Theory (GT) has also been applied to analyze supply chain coordination problem. This section will briefly review a few representative work...

An Integrated Pricing and Inventory Model for Deteriorating Products in a two stage supply chain under Replacement and Shortage

“…Yu et al [1] determined the joint optimal price-inventory decisions in a fuzzy pricedependent newsvendor framework. Huang et al [2] modeled the coordination of suppliers and components selection, pricing and replenishment decisions in a three-level supply chain as a dynamic non-cooperative game model. Ghoreishi et al [3] dealt with an economic production quantity inventory model for noninstantaneous deteriorating items under in ationary conditions, permissible delay in payments, customer returns, and price-and time-dependent demand.…”

Analysis of Production - Inventory Decisions in a Decentralized Supply Chain

“…Some recently published papers consider coordination problem with marketing-pricing decisions in a two echelon supply chain. SeyedEsfahani et al (2011) investigate this problem by applying four game-theoretic models including cooperative, Nash, Stackelberg-retailer and Stackelberg-manufacturer games; Huang et al (2011) study coordinating pricing, inventory decisions, and supplier selection in a supply chain; Sarlak and Nookabadi (2012) study a three-level supply chain to synchronize the timing of retailers' orders with the supplier's order cycle by timing discount contract; Pezeshki et al (2012) consider a type of revenue sharing reservation contract with penalty in a supply chain for coordinating price and capacity building decisions; Kunter (2012) applies cost and revenue sharing mechanism to coordinate the channel.…”

Bi-level programming for supplier selection under quantity discount policy

“…Each contributor, in this network, tries to control a set of decision variables and makes decisions based on its needs and interests. Therefore, some studies have studied the SC components cooperation based on pricing, inventory and production planning, supplier selection, product designation, capacity allocation, and so on [2]. This paper considers a network with a single vendor and multiple suppliers to feed the nal customer.…”