Simultaneous Scheduling of Production and Preventive Maintenance on a Single Machine

In this study, the expected total completion time is minimized in the case of a single machine and random failures. The probability of machine failure is an increasing function of the age and the length of the time interval, and preventive maintenance reduces the machine age to zero. The problem uses a nonlinear integer programming model that is reduced to an unconstrained 0-1 optimization problem. Subsequently, a method for solving the latter model by identifying the preventive maintenance decisions is proposed. A numerical example is provided to illustrate the solution procedure of the proposed method. Finally, a numerical analysis is performed to investigate the effect of changes in the model parameters on the solution. The results show its sensitivity by changing the preventive maintenance plan and the expected value of the total completion time depending on the changed parameters and the value of the change of each parameter. The simplicity and efficiency of the proposed method proves its robustness in solving even middle- and large-size problems.