Green vehicle routing problem with queues

Abstract Organizations spend considerable amount of time and money in distributing goods from production centres to customers who are geographically distributed. When vehicles are engaged to make long trips, along with serving the customers it may halt at facility centres like toll booths, warehouses, refuelling stations etc., for some service. The cost and time associated with these halts will have an impact on the overall cost of the route. But, when organizations plan a route with minimum cost, the costs associated with halts in the facility centres are generally not accounted. When these facility centres are limited in number, vehicles should wait for their turn to get the service which has an impact on the overall cost of the tour. This paper intends to address the issues that are associated with the waiting time at the refuelling station. Green Vehicle Routing Problem with Queues (GVRP-Q) is introduced in this paper. GVRP-Q aims to serve a set of customers, but includes halts in between for refuelling in the refuelling stations. Each refuelling station is modelled as M/M/1 queue model, where vehicle is allowed to wait in the queue. The impact of this wait time on the overall cost of the route is studied in this paper. GVRP-Q is solved using an enhanced Chemical Reaction Optimization (e-CRO) where the performance of CRO is enhanced by a bacterial transformation. Experiments are conducted on bench mark data sets and the results predict the influence of the wait time on the overall route cost.