An Integrated Production and Maintenance Planning Model with time windows and shortage cost

We present in this paper a problem combining two planning problems studied in the literature: the problem of capacitated lot sizing with shortage cost and the problem of determining optimal maintenance cycle. The aim of our study is to build a new model of joint planning of production and maintenance where preventive maintenance tasks are carried out in time windows to better meet customer demand. We provide an illustrative example that show the effectiveness of integrated model if we compare it to separate model.