A new closed–open vehicle routing approach in stochastic environments

ABSTRACT Collection and distribution of finished goods through cross-docking to predetermined customers or retailers are practical and challengeable mathematical modelling, optimization, and logistics problems. Thus, appropriate management of the transportation system can help companies decrease their costs and consequently earn more benefits. There is an abundance of modelling proposals in the literature. In this paper, a multi-cross-docking vehicle routing problem (MCVRP) is combined with close–open mixed vehicle routing problem (COMVRP) in the stochastic environment. It is assumed that the fleet of vehicles is heterogeneous. The objective is to minimize the total cost of serving customers. Since the travel time between retailer nodes is non-deterministic, a hybrid solution methodology is developed, which encompasses robust optimization, as well as firefly and genetic algorithm. Computational results demonstrate that the proposed algorithm can efficiently be used to solve the proposed model.