A multilevel variable neighborhood search heuristic for a practical vehicle routing and driver scheduling problem

This paper addresses an integrated vehicle routing and driver scheduling problem arising at the largest fresh meat producer in Denmark. The problem consists of a one-week planning horizon, heterogeneous vehicles, and drivers with predefined work regulations. These regulations include, among other things, predefined workdays, fixed starting time, maximum weekly working duration, break rule. The objective is to minimize the total delivery cost. The real-life case study is first introduced and modelled as a mixed integer linear program. A multilevel variable neighborhood search heuristic is then proposed for the problem. At the first level, the problem size is reduced through an aggregation procedure. At the second level, the aggregated weekly planning problem is decomposed into daily planning problems, each of which is solved by a variable neighborhood search. At the last level, the solution of the aggregated problem is expanded to that of the original problem. The method is implemented and tested on real-life data consisting of up to 2000 orders per week. Computational results show that the aggregation procedure and the decomposition strategy are very effective in solving this large scale problem, and our solutions are superior to the industrial solutions given the constraints considered in this work.