A Supply Chain Network Game Theoretic Framework for Time-Based Competition with Transportation Costs and Product Differentiation

Abstract

In this paper, we developed a supply chain network game theory model with differentiated products and transportation costs in the case of time-based oligopolistic competition. The firms are profit-maximizers and have, as their strategic variables, the product shipments and the delivery times to the consumers at the demand markets with the delivery times including both the production times and the transportation times. The demand price functions are functions of the demands for the products at the different demand markets as well as their delivery times. The governing Nash equilibrium conditions are formulated as alternative variational inequalities. An algorithm is proposed, which yields closed form expressions, at each iteration, for the product shipments, the delivery times, as well as the associated Lagrange multipliers. Supply chain network numerical examples are given to illustrate the modeling and the computational approach.

Keywords: supply chains, oligopolies, networks, game theory, Nash equilibrium, product differentiation, transportation costs, time-based competition, build-to-order, made-on-demand, variational inequalities