Supply chain planning with order/setup costs and capacity constraints a new Lagrangian relaxation approach

In our previous work, we developed a heuristic approach that combines Lagrangian relaxation (LR) with local improvement for supply chain planning modeled as a multi-item multi-level capacitated lot sizing problem. In this paper, we explore some structural properties of the problem and improve the approach by reducing the number of Lagrange multipliers. As the previous one, our new LR approach only relaxes the technical constraints that each 0-1 setup variable must take value 1 if its corresponding continuous variable is positive. By taking the advantages of the reduced number of the multipliers, the new approach can obtain solutions of the same high quality with a reduced computation time.