Supply chain network competition in price and quality with multiple manufacturers and freight service providers

•We model a multitiered supply chain network with competition.•Manufacturers and freight service providers compete in prices and in quality.•Both equilibria and dynamics are investigated qualitatively and numerically.

In this paper, we develop both static and dynamic supply chain network models with multiple manufacturers and freight service providers competing on price and quality. The manufacturers compete with one another in terms of price and quality of the product manufactured, whereas the freight service providers compete on price and quality of the transportation service they provide for multiple modes. Both manufacturers and freight service providers maximize their utilities (profits) while considering the consequences of the competitors’ prices and quality levels. Bounds on prices and quality levels are included that have relevant policy-related implications. The governing equilibrium conditions of the static model are formulated as a variational inequality problem. The underlying dynamics are then described, with the stationary point corresponding to the variational inequality solution. An algorithm which provides a discrete-time adjustment process and tracks the evolution of the quality levels and prices over time is proposed, and convergence results given. Numerical examples illustrate how such a supply chain network framework, which is relevant to products ranging from high value to low value ones, can be applied in practice.