Mixed Integer Programming Model for open Vehicle Routing Problem with Fleet and driver Scheduling Considering Delivery and Pick-Up Simultaneously

Vehicle Routing Problem (VRP) is a key element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve a set of customers It is required that these vehicles return to the depot after serving customers’ demand. This paper investigates a variant of VRP, in which the vehicles do not need to return to the depot, called open vehicle routing problem (OVRP). The problem incorporates time windows, fleet and driver scheduling, pick-up and delivery in the planning horizon. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling of fleet and driver and routing policies of the vehicles. The objective is to minimize the sum of the costs of all routes over the planning horizon. We model the problem as a linear mixed integer program. We develop a combination of heuristics and exact method for solving the model