Integrating run-based preventive maintenance into the capacitated lot sizing problem with reliability constraint

A joint model for integrating run-based preventive maintenance (PM) into the capacitated lot sizing problem (CLSP) is proposed, in which the production system is subject to deterioration with usage and PM operations are implemented to restore the system. In this model, both production and PM operations are restricted by the system's maximum capacity, and the system reliability has to be maintained above a threshold value throughout the planning horizon. By linearisation of the reliability constraints, the problem is formulated as a mixed-integer linear programming. An explanatory example is given to illustrate the advantage of the joint model comparing with the interval-based PM policy in terms of system's overall cost. A three-stage heuristic is proposed to solve this integrated model, which includes a Lagrangian-based heuristic for the CLSP. The numerical experiments are conducted to evaluate the performance of the developed heuristics and the computational results show that the heuristics can provide good feasible solutions for the corresponding models. The discussion of the results is finally given in detail.