MATHEMATICAL PROGRAMMING FOR THE SELECTION OF THE IDEAL CYCLE LENGTH IN PREVENTIVE MAINTENANCE POLICIES

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Abstract
The preventive maintenance scheduling problem involves sequencing the inspection of M machines within a cyclic policy of length T periods, where each machine must be inspected at least once. In the case addressed here, and during each period t, the maximum capacity for maintenance tasks is limited to one. The machines to be maintained can generate two types of costs: the maintenance cost, incurred in the periods when the machine is inspected, and the operational cost, which arises in the periods when a machine operates without being inspected. Both costs are directly proportional to the number of periods elapsed since the last maintenance of the machine. For this type of problem, it is common to use cycle lengths predetermined by external factors (such as days in a month or weeks in a year). However, this article introduces a mathematical program that calculates the ideal cycle length T and the optimal maintenance frequencies. The results show that in 69,44% of the instances, an ideal T different from predetermined T value is found. The average execution time is 106,96 seconds. Once the ideal cycle length T is obtained, a matheuristic algorithm is then used to sequence the maintenance tasks for each machine. It is observed that in 65,6% of the instances, the average cost of the maintenance policy is lower than when using predetermined T values, achieving an average cost reduction of 2,41%. Key Words: Mathematical programming, preventive maintenance, matheuristic algorithms, activity sequencing.