Integrated model of production planning and imperfect preventive maintenance policy for single machine system

This paper investigates the integrated problem of imperfect preventive maintenance and tactical production planning for a single machine system, in which a set of products must be produced in lots throughout a specified finite planning horizon. The machine is assumed to be subject to random failure, and periodic preventive maintenance (PM) and periodic system overhaul are executed to reduce the risk of failure. The PM is assumed to be imperfect and system overhaul is perfect, and minimal repair is conducted at machine failure. The objective is to determine both the lengths of PM cycle and system overhaul cycle to minimise the expected sum of PM costs, repair costs, system overhaul costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the planning horizon. The problem is formulated as an integer linear programme problem and is solved by comparing the results of several multi‐product capacitated lot‐sizing problems. An illustrative example is also given to show the steps to obtain an optimal solution and show the cost benefit of integrated production and maintenance strategy.