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.

Automated summary

This paper addresses the problem of combined maintenance and routing optimization for a set of geographically distributed machines in a multi-period environment. It proposes a two-step approach based on column generation, where the first step determines the optimal time until the next preventive maintenance operation and each machine's maintenance frequency, while the second step assigns and schedules maintenance operations for each technician over the planning horizon. The proposed approach balances maintenance cost, routing cost, and failure probabilities.