6. Supply Chain Network Competition with Multiple Freight Options

This chapter extends the results in Chap. 5 to include multiple freight options for the manufacturers to ship their products from their manufacturing plants to consumers at the demand markets. We first develop a static supply chain network model of Cournot-Nash competition with product differentiation, multiple freight options, and quality competition. Each manufacturing firm seeks to maximize its own profit by determining its product shipments and product quality. We utilize variational inequality theory for the formulation of the governing Cournot-Nash equilibrium. We then construct the projected dynamical systems model, which provides a continuous-time evolution of the product shipments of the firms and the product quality levels, and whose set of stationary points coincides with the set of solutions to the variational inequality problem. We establish stability analysis results using a monotonicity approach and construct a discrete-time version of the continuous-time adjustment processes, which yields an algorithm, with closed form expressions at each iteration. The algorithm is then utilized to compute the solutions to several numerical examples. A sensitivity analysis on changes in the demand price functions is also conducted.