The consideration of opened facilities' operational volumes in designing supply chain network

In this paper, we deal with single-item, multi-period, two-echelon capacitated facility location problems where manufacturing plants and distribution centres (DCs) are decided to be opened or not at the pre-determined potential sites. At each opened facility, our model controls operational level over or under its minimum requirement volume. To do that, we use the big M technique to detect running status. If the opened facility runs at lower minimum requirement volume, penalty cost will occur and add to objective value, which should be as low as possible. This information helps the investors and managers to evaluate performance of their supply chain (SC) network system. The problem is formulated as a mixed integer linear programming (MILP) model with the objective to minimise the total cost including transportation costs, production costs, inventory holding costs, fixed costs for opening facilities, and penalty costs. Based on the specific structure of the developed model, we need one additional constraint set before using Lagrangian relaxation algorithm to solve the problem. Numerical experiments are then conducted to compare the solution of the proposed approach and the optimal solution obtained by the commercial lingo solver.