Designing an integrated multi-echelon supply chain network with competition

This paper develops a model for competitive supply chain network design which investigates competition between new and existing chains where demand is deterministic and price‐dependent. The network consists of raw material suppliers, manufacturers, retailers, and demand market. The supply chains compete in a non‐cooperative manner and manufacturers produce homogeneous products. The objective is to maximise the future profits of both chains. First, the problem is formulated by mathematical programming and Lagrangian theory is used for adding the constraints to the objective function. Then, the equilibrium conditions are derived and the problem is formulated as a finite‐dimensional variational inequality model. Qualitative properties of the equilibrium pattern are derived to establish existence and uniqueness results under reasonable conditions. The modified projection method is used to solve the variational inequality problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed model and analyse the results under different conditions.