Locating and capacity planning for retailers of a new supply chain to compete on the plane

This paper investigates the network design problem of a two‐level supply chain (SC), which is applicable for industries such as automotive, fuel and tyre manufacturing. Models presented in this paper aim at locating retail facilities of an SC and identifying their required capacities in the presence of existing competing retailers of a rival SC. We consider feasible locating space of the retail facilities on the continuous plane with bounded constraints and static competition among the rivals of the markets with deterministic demands. The problem is used for both essential and luxury product cases; hence, we consider elastic and inelastic demands, both. The models discussed in this paper are non‐linear and non‐convex which are difficult to solve. We use interval branch‐and‐bound as optimization algorithm for small size single‐retailer problems, but for large‐scale, multi‐retailer problems we need to have more efficient methods. Therefore, we apply a heuristic algorithm (H1), a simulated annealing (SA) algorithm, an interior point (IP) algorithm, a genetic algorithm (GA) and a pattern search algorithm for solving multi‐retailer problem with elastic and inelastic demands. Computational results obtained from performing different solution approaches for both elastic and inelastic show that mostly IP, PS, and H1 methods outperform the other approaches. The computational results on a real‐life case are also promising. Several extended mathematical models and an example of a typical case with details are presented in the appendices of the paper.