Incorporating location, inventory and price decisions into a supply chain distribution network design problem

The goal of this paper is to study a profit-maximization location-inventory problem in a multi-commodity supply chain distribution network with price-sensitive demands. The problem determines location, allocation, price and order-size decisions in order to maximize the total profit of serving the customers. The problem is formulated as a mixed-integer nonlinear programming model and solved using a Lagrangian relaxation algorithm for the two cases of uncapacitated and capacitated distribution centers. The computational results show that the quasi-optimality tolerance is reasonable and the computational time is very small for solving large-sized instances of the problem.