Capacitated and multiple cross-docked vehicle routing problem with pickup, delivery, and time windows

The vehicle routing problem (VRP) in cross-docked distribution networks is an important research topic in the supply chain management literature. This paper formulates a mixed integer linear programming model of a special type of capacitated and multiple cross-docked VRP with pickup, delivery, and time windows. The problem is to design a set of routes for vehicle fleets servicing pickup and delivery nodes with defined demands and time windows to achieve the minimum transportation and fixed costs. We propose a hybrid of the genetic algorithm and particle swarm optimization (HGP) to solve the formulated NP-hard problem. Small-size problems are solved by HGP and then compared with the exact method using CPLEX to validate the effectiveness of the proposed hybrid algorithm. Extensive experiments have been conducted for medium and large-size problems and the results show the proposed HGP provides better solutions in the allocated time compared to CPLEX.