A profitable pickup and delivery problem with time windows

In most pickup and delivery problems, usually the aim is to minimize either the trip length or duration or the fleet size. Transportation orders or customers are finite sets which should be performed or visited integraly. So, the total earning is supposed to be constant. Conversely, the costs related to trip length or duration or either to the fleet size are consequences of the operations management efficiency. Therefore, typically the objective function is reduced to a cost minimization. On the contrary, this model tends to maximize the global profit. Let’s consider a fleet of vehicles starting at different initial times from different locations and oblige to return to their final depots before fixed maximal times. On their way-back, these vehicles are performing full-truck-load transportation between pickup and delivery points and have to respect time windows for the loading and unloading operations. Realized transportation orders add positive contributions while linking paths generate costs. In summary, the goal for the fleet resides in the selection of transportations orders among available ones while fullfilling the final time requirements and the time restrictions for the un/loading operations.