An Integrated Model of the Capacitated Vehicle Routing Problem and the Vehicle Scheduling Problem at the Multi-door Depot

To be an efficient Supply Chain (SC), the coordination and integration of the activities in the SC are mandatory. Routing vehicles is an optimization problem in the SC. When the routed vehicles return to the depot and the doors at the depot are busy, the returned vehicles have to wait to unload the accumulated shipments. Moreover, properly scheduling these vehicles to those doors at the depot to minimize the waiting time is considered to be an optimization problem in the SC. Therefore, in this study, routing vehicles to collect the shipments from suppliers and scheduling vehicles to doors at the depot, based on first come first serve basis, are simultaneously solved. Hence, the objective of this integrated vehicle routing and scheduling problem (VR&SP) is to minimize the total cost which contains the following components; vehicle travelling cost between suppliers, loading cost at the suppliers, vehicle waiting cost, unloading cost at the depot and vehicle operations cost. A Mixed Integer Quadratic Programming (MIQP) model is developed to solve the integrated VR&SP. The Branch and Bound algorithm is employed to obtain the exact optimal solution to this MIQP using LINGO optimization software. The compatibility of the developed MIQP model is verified by the randomly generated small-scale instances. Therefore, it can be concluded that, this model solves the vehicle routing to suppliers and vehicle scheduling to doors at the depot simultaneously. Since VR&SP is a NP-hard problem, heuristics or meta-heuristic methods are recommended to solve the large-scale instances of VR&SP.