Time slot management in selective pickup and delivery problem with mixed time windows

The selective pickup and delivery problem addresses real-life issues in logistics and transportation. The aim is to optimally select some pickup locations to collect the required demands and unload commodities at delivery locations. Everyday, much of such logistics processes are outsourced to Third-Party Logistics (3PL) companies. However, decentrally truck scheduling by 3PLs specifically when there are only a limited number of warehouse loading docks and time slots will likely cause the random arrival of carriers at warehouses, capacity violation at loading docks, and consequently increased total costs. This study offers a promising approach to optimize the intricate problem of coordination in transportation logistics. We present an integrated time slot allocation and selective pickup and delivery problem while taking real-world variants and constraints, including mixed time windows and capacity, into consideration. To achieve this, we propose a mixed-integer linear programming formulation for the problem. To solve the model, we utilize some valid inequalities and constraints tightening method to strengthen its linear programming relaxation. In addition, a sensitivity analysis is performed on different problem features to validate the presented model. Computational results illustrate the effectiveness of the presented model and valid inequalities in providing faster and tighter results. With respect to the solution time and the number of nodes, the average of both measures drastically is reduced by approximately 90%, followed by tight lower bounds. Furthermore, the value of the integrated model is investigated on larger-sized instances, which shows the proposed model can achieve significant savings and gains compared to the decomposed subproblems of vehicle routing and time slot allocation.