A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit. An effective variable neighbourhood search (VNS) heuristic for this problem is proposed. The neighbourhoods are based on reversing segments of routes (sub-routes) and exchanging segments between routes. Computational results on sixteen standard benchmark problem instances show that the proposed VNS is comparable in terms of solution quality to the best performing published heuristics.