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# Optimizing freight procurement for transportation-inventory systems under supply and demand uncertainty

## Lingxiao Wu, Yossiri Adulyasak et Jean-François Cordeau

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The procurement of freight services is an important element for the supply chain management of a shipper (i.e., a manufacturer or retailer) that sources transportation services from the third-party logistics market. Motivated by a practical freight procurement problem faced by shippers, we provide a holistic approach to designing freight procurement strategies for transportation-inventory systems that captures the interconnections between freight procurement, transportation, and inventory management. In view of the supply and demand uncertainties, we consider the problem in a multi-stage decision process that complies with the revealing process of the uncertain data. In the first stage, freight service contracts are procured for the entire planning horizon, while the delivery quantities and inventory levels are determined in the subsequent stages. We introduce a mixed-integer linear programming model for the multi-stage problem. To handle a large number of scenarios, we propose a stochastic dual dynamic programming solution approach. The approach is further enhanced through novel feasibility inequalities, optimality inequalities, and a primal-dual lifting method. Extensive computational experiments are conducted and the results demonstrate that our approach scales to instances with up to $$10^9$$ scenarios and that the enhancement strategies significantly improve the performance of the algorithm. We also show that our solution approach outperforms the methods commonly adopted for solving similar problems.

, 35 pages

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G2219.pdf (590 Ko)