Integrated strategy of Vehicle Routing and Maintenance

This paper deals with the Vehicle Routing Problem (VRP) considering specific situations of transcontinental transportation where heavy vehicles travel over long distances between cities in a difficult environment favoring a non-negligible probability of failure of critical components. Hence, these transportation vehicles are subject to random breakdowns and repairs of random duration, which can obviously delay deliveries. A preventive maintenance (PM) policy is proposed which suggests performing PM actions (generally preventive replacement of the critical component) when reaching selected customers (cities). The purpose of this work is to determine simultaneously the optimal delivery sequence and the optimal sequence of PM actions (i.e. the customers cities at which PM should be performed) in order to minimize the expected total cost per time unit, considering penalties on late arrival and maintenance costs. A mathematical model is developed expressing the total expected cost rate taking into account the vehicle's reliability, maintenance actions costs and durations (PM and minimal repair), transportation cost, and penalties corresponding to late arrivals. For cases of numerous customers to be served, a genetic algorithm is proposed to obtain a nearly optimal integrated vehicle routing and maintenance strategy for any given settings of the problem. A numerical example is presented and the obtained results are discussed.