The Supply Chain Network Model with Freight Service Provider Competition

Abstract

With this chapter we turn to the inclusion of the behavior of freight service providers engaged in competition in supply chain networks. The manufacturing firms are profit-maximizing and provide substitutable (but not identical) products and compete in quantities in a Cournot-Nash manner. The freight service providers, which transport the products to the consumers at the demand markets, are also profit-maximizers, but compete in prices in Bertrand fashion and on quality. The consumers respond to the composition of product and freight service provision through the demand price functions, which are both quantity and quality dependent. We derive the governing equilibrium conditions of the integrated supply chain network game theory model and show that it satisfies a variational inequality problem. We then describe the underlying dynamics and provide some qualitative properties, including stability analysis. The proposed algorithmic scheme tracks, in discrete-time, the dynamic evolution of the product shipments, the quality levels, and the prices until an approximation of a stationary point (within the desired convergence tolerance) is achieved. Numerical examples demonstrate the modeling and computational framework.