A Lagrangean relaxation approach for capacitated lot sizing problem with setup times

In this research, we consider a production planning problem that determines the production timings and quantities for multiple products over a finite number of periods without violating capacity constraints. This problem is commonly referred to as the capacitated lot sizing (CLS) problem. We develop a model that explicitly considers setup times for products and different types of production capacities such as regular time and overtime. We develop a heuristic based on Lagrangian relaxation to solve this CLS problem. Computational results show that our algorithm gives reliable results while comparing solution values to lower bounds.