Matheuristics for scheduling of maintenance service with linear operation cost and step function maintenance cost

Abstract

We study a problem of scheduling machine maintenance activities in discretized periods, under the constraint that a maximum of one activity can be scheduled for each period. The scheduled maintenance activities will be repeated in a cyclic policy with a given cycle length.The problem is to find a scheduling policy specifying which activity is executed in each period in order to minimize the total cost.Two kinds of costs are assumed: operation and maintenance costs. Both of them depend on the number of periods since the last machine maintenance service. The operation cost occurs during the periods in which a machine is not maintained and increases linearly. The maintenance cost takes place in the periods in which a machine is maintained and is defined as a step function. The steps in the maintenance cost function could be justified by the fact of considering the machine element's substitution when this machine is run for too long without being maintained. This cost structure reduces the gap between the academic problem and the industrial reality.In this paper, the scheduling problem with linear operation cost and step function maintenance cost is defined and formalized. In addition, different matheuristic algorithms are proposed for its resolution. Lower bounds for the objective function are proposed and the computational results show an average deviation from the optimal solution lower than or equal to 3.19%.