Target-oriented robust location–transportation problem with service-level measure

We study a target-oriented, multi-period location–transportation problem where customer demands are uncertain. This problem is to determine the facility locations, production quantities, capacities, and shipment quantities, where the objective is to achieve the desired profit and fill rate to the full extent when it is impossible to reach both. To achieve the goal, we propose a target-oriented framework for the location–transportation problem, where a service-level measure is constructed to guarantee the desired fill rate and a hard constraint on profit is imposed to ensure a decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization approach. To capture the characteristics of a multi-period decision-making process, an affine decision rule is introduced. Our method not only ensures that the transportation decisions of each period can adapt to realized demands wisely, but also prevents the high complexity of the model resulting from uncertainty and adaptation. Specifically, to tackle challenges of problem intractability, we reformulate the robust counterpart of the problem into a conservative approximation in the form of a mixed-integer quadratic program and propose a Benders decomposition approach to produce effective solutions. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.