A Robust Mathematical Model for Vehicle Routing Problem with Simultaneous Pickup and Delivery and Worker Allocation

Vehicle routing is one of the most important and widespread issues in the field of optimization and decision-making due to its many applications. On the other hand, simultaneous pickup and delivery is one of the most widely used methods in transportation systems. In this state, the routing is done in a way that deliver the needs of all customers with pick up the products of others at the same time. Moreover, in many cases, the goods have a consumption period tardiness in delivery will result in financial penalty. Accordingly, the purpose of this paper is to design a new robust mathematical model for vehicle routing, taking into account the simultaneous pickup and delivery, the time window, and the workers allocation for transportation. In this mathematical model, uncertainty is considered in the important parameters of the model and to deal with this uncertainty, a robust optimization approach is used. The results show that a robust optimization approach improves decision-making and the cooperation of workers leads to a reduction in total transportation costs.