Simultaneous Scheduling of Preventive Maintenance and Production for Single and Parallel Machines

In the last decades, the simultaneous scheduling of production and preventive maintenance has been receiving a considerable attention. Initially, in most researches, maintenance activities were treated as tasks with a fixed period. However, this assumption leads to create a hole in the time horizon. Recently, the variations in maintenance times were addressed, but the starting time is still fixed and known in advance in most of the works. There are few researches that consider the maintenance starting times as decision variables, especially in the non-preemptive case. 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 is represented by a nonlinear integer programming model which is reduced later to an unconstrained 0-1 optimization problem. Subsequently, a method for solving the unconstrained model by identifying the preventive maintenance decisions is proposed. Moreover, the problem for minimizing the expected makespan on the single machine for the same above mentioned maintenance conditions is addressed and two heuristics methods were proposed to solve the problem. Additionally, the problem of parallel machines which are under the same reliability conditions, but they may have different values of maintenance parameters is discussed. An approximation method based on the bin packing‟s first fit algorithm as well as an exact branch and bound method were introduced to solve the problem. Finally, numerical examples were provided to illustrate each solution procedure of the proposed methods and some analysis was performed. The results show the benefits of integrating both decisions of production and maintenance, because some savings in the values of the discussed performance measures were obtained.