A mixed-integer linear formulation for a capacitated facility location problem in supply chain network design

Abstract

In this research, we deal with a multi-item, multi-period, two-echelon capacitated facility location problem. With every period in horizon planning, manufacturing plants and distribution centres are decided to open or not at predetermined potential sites. The developed model is formulated as a mixed integer linear programming (MILP) model with the objective of minimising the total cost, including transportation cost, inventory holding cost, and fixed costs for opening facilities. We employ a Lagrangian relaxation algorithm for solving the developed model. Before decomposition into sub-problems, the initial structure of developed model is modified, three additional constraint sets add to two sub-problems, and these are the key differences of our algorithm. For validation testing, some numerical experiments are used for solving, and the solutions obtained from the Lagrangian relaxation algorithm are respectively compared with the solutions obtained by the LINGO solver. With good achievements of this research, our proposed model can be applied and the proposed approach is an advantage for getting the specific solutions.