An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions.

► The paper proposes two strong mixed integer programming models for capacitated lot sizing problems. ► Equivalency of these two models is theoretically proved. ► The paper also develops a hybrid exact methods and heuristics framework. ► The framework is very efficient at solving lot sizing problems.