A fix-and-relax heuristic for the single-item lot-sizing problem with a flow-shop system and energy constraints

Abstract

This study addresses a new single-item lot-sizing problem for flow-shop configurations by integrating the capacity contract selection problem with multiple energy sources. To the best of our knowledge, this problem has never been tackled before. We introduce a mathematical model which defines optimum production plan and energy contract option regarding the objectives and constraints of the production system and energy supplier contract conditions. Since the problem is NP-Hard, a Fix-and-Relax heuristic is introduced to solve the problem. Two different relaxation procedures are applied and the performance of the solution approach is tested on randomly generated instances. It is seen that the obtained results are quite promising. The applied heuristic approach produces solutions with the optimality gap 0.2% in average for the small problem sizes such as (N5_T5,N5_T7). For the larger instances, it allows to reach better results than the results obtained by commercial solvers within a shorter time.