On the multi-period combined maintenance and routing optimisation problem

This paper focuses on the combined maintenance and routing optimisation problem in a multi-period environment that consists of scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and corrective operations. This study uses a two-step approach based on column generation. The first step consists of a maintenance model that determines the optimal time until the next preventive maintenance operation, and each machine’s maintenance frequency while minimising the total expected maintenance costs. The second step involves a routing model that assigns and schedules maintenance operations for each technician over the planning horizon while minimising the routing and maintenance costs. We formulate the second step problem as a periodic vehicle routing problem and to solve it, we propose a column generation approach. The master problem is a set partitioning formulation that indicates which machines must be visited in the planning horizon. This decomposition has two auxiliary problems: the first one is an elementary shortest-path problem to find a feasible path for each period and the second one finds a set of visiting periods for each machine. Our approach balances the maintenance cost, routing cost, and failure probabilities.