Modeling and Solving the Cross-Docking Centers Location and Vehicle Scheduling Problem in a Multi-Product Supply Chain with Discrete Pick-up and Delivery

This research studies cross-docking centers location and vehicles routing scheduling problems simultaneously in a three-level supply chain with discrete pick-up and delivery. The proposed problem is formulated as a mixed-integer nonlinear programming model with the aim of reducing total cost includes cross-docking centers construction cost, transportation fixed and variable costs, earliness and tardiness penalty costs. In this supply chain model, vehicles start from a cross-docking center and pick up different products from various suppliers and after classifying and preparing products at cross-docking centers, a different group of vehicles are sent to deliver products to customers. For delivering any kind of product to each customer, a soft time window is considered. Herein, three types of small, medium and large size instances have been generated randomly and solved by using the proposed simulated annealing algorithm. For small problems, the results from simulated annealing algorithm are compared with the solutions obtained by the exact methods.