A simultaneous facility location, vehicle routing and dynamic pricing in a distribution network

Abstract

Abstract This paper incorporates location, pricing and routing decisions by the goal of maximizing profit in a distribution network. In this problem, multiple consecutive time periods are considered in the decision of depot locations at the beginning of the planning horizon, pricing, and routing during each period. According to the varying willingness to pay (w.t.p) of the consumers across different regions and time periods, dynamic regional pricing techniques were incorporated into this problem. In this study, a non-linear mixed integer model is proposed for solving the problem. This model is then converted into a mixed integer quadratic constrained problem that can be solved with the CPLEX solver. Due to the inability of the exact algorithm to solve certain medium and all large instances, and in order to improve the obtained upper bounds for medium test problems, lagrangian relaxation (LR) was introduced. Two pure and hybrid heuristic algorithms are proposed for tackling this problem. The heuristic algorithm includes price optimization and location-routing steps. In the hybrid heuristics, these steps are embedded in the particle swarm optimization (PSO) and self-learning PSO (SLPSO) algorithms framework. Computational experiments illustrate the efficiency of the proposed algorithms. Sensitivity analysis indicates the necessity of switching from the pure heuristic to the hybrid version for scarce capacity settings.