Multi-item capacitated lot-sizing problem in a flow-shop system with energy consideration

This paper discusses a multi-item capacitated lot-sizing and scheduling problem in a flow-shop system with energy consideration. A mixed integer linear programming is formulated. The planning horizon is defined by a set of periods where each one is characterized by a length, an electricity price, a maximal allowed power and an external demand. Since the capacitated lot-sizing problems are NP-hard, a fix-and-relax heuristic is developed. To evaluate the effectiveness of the proposed heuristic, computational experiments are presented and numerical results are discussed and analyzed. The obtained results are promising.