A mixed-integer programming model for integrated production and maintenance

This paper deals with the production planning and preventive maintenance scheduling on a single machine multi-product capacitated lot-sizing problem (CLSP). The machine is assumed to be subject to random failures. Preventive maintenances at the beginning of each production period to reduce the risk of failure and minimal repairs at failure is considered. The aim is to minimize the sum of the total production and maintenance costs related to inventory, backorder, production, set-up, preventive maintenance (PM), and minimal repair (MR) under demand satisfaction and machine capacities constraints over the entire horizon. Using the Weibull model, we present a mixed-integer linear programming (MIP) model to solve the problem.