Lagrangean Based Heuristic for Integrated Planning Production and Maintenance Problem with Time Windows and Shortage Cost

In this paper, we deal with a problem of integrating production and maintenance. The integrated problem is a combining problem of two problems largely studied in literature: the problem of determining the cycle of preventive maintenance actions, and the main production planning problem known as multi items capacitated lot sizing problem with shortage cost. Preventive maintenance is carried out in time windows to restore the production line to an „as-good-as-new‟ status, and when a production line fails, a minimal repair is carried out to restore it to an „as-bad-asold‟ status. The resulting problem is modelled as a linear mixed-integer program. It takes into account demand shortage and the reliability of the production line. We will solve the problem with a Langrangean heuristic, the computational results show that the heuristic provide a good feasible solution quality in short execution time.