Lagrangian relax and fix heuristics for integrated production planning and warehouse layout problem

We present a real world production warehousing case, where the company always faces the challenges to find available space for their products and to manage the items in the warehouse. We develop a decomposition algorithm to solve a mixed integer programming formulation of warehouse layout with capacitated lot sizing problem. The problem with real data is a large scale instance that is beyond the capability of optimization solvers. We propose a Lagrangian relax and fix heuristics to solve the problem efficiently. Computational results demonstrate the effectiveness of the proposed method by comparing the performance of the proposed method and branch and bound method.