A distributionally robust optimization model for inventory-transportation integrated optimization problem of petroleum products under uncertainty

In the downstream supply chain of petroleum products, the logistics planning optimization is a crucial issue that not only involves the inventory management of oil depots to stabilize market supply, but also needs to take transportation into account and develop a reasonable resource allocation plan associated with replenishment costs. However, the fluctuation of market sales makes oil product outbound volumes full of uncertainty, which also increases the challenge and difficulty of planning optimization. Therefore, this paper investigates the inventory-transportation integrated optimization problem of petroleum products, proposes a novel distributionally robust optimization (DRO) modeling method aiming at a solution scheme addressing the uncertainty in real business. Firstly, considering the uncertainty of random variable distribution, an ambiguity set is confirmed based on the maximum mean discrepancy (MMD) metric. Subsequently, a MMD-DRO model is combined and transformed into an equivalent and solvable mixed-integer linear programming model. Futhermore, with regard to the deficiency of solvers in handling large-scale regional problems, a logic-based Benders decomposition (LBBD) algorithm is designed and enhanced by heuristic strategies. Finally, with the cases from PetroChina, the efficacy and applicability of the proposed approach are validated, and demonstrated the superior performance of the improved LBBD algorithm.