Multi-period distribution networks with purchase commitment contracts

Retailers which deliver products directly to their customer locations often rely on Logistics Service Intermediaries (LSI) for order management, warehousing, transportation and distribution services. Usually, the LSI acts as a shipper and subcontracts the transportation to carriers for long-haul and last-mile delivery services. All agents interact and are connected through cross-docking facilities. As the demand from customers may vary significantly over time, the shipper’s requirements for transportation evolve accordingly at the tactical level. This creates opportunities for the shipper to take advantage of medium-term contracts with the carriers at prices lower than those offered by the spot market. The study focuses on the tactical design, through dynamic contracts, of a suitable network of cross-docking facilities and related transportation capacities (belonging to different carriers) to reduce the shipper’s operational costs. In this article, we propose an MILP formulation for the multi-period planning problem with minimum purchase commitment contracts faced by the shipper. We propose exact and heuristic decomposition methods for the the model, respectively, based on combinatorial Benders cuts and on relax-and-repair approaches. The performance of these algorithms is experimentally compared to that of commercial solvers (branch-and-cut and classical Benders). The numerical results show that our methods perform comparatively well for the solution of large size instances and brings economic benefits to the shipper.