Target-oriented Robust Location-transportation Problem with Service-level Measure

Abstract

We study a target-oriented, multi-period location-transportation problem where customer demands are uncertain and transportation decisions are adaptative. This problem is meant to determine the facility locations, production quantities, capacities, and shipment quantities, with the objective of achieving the desired profit and fill rate to the full extend when reaching both is impossible. To realize that objective, we propose a target-oriented framework for location transportation problem, where service-level measure is constructed to guarantee desired fill rate, and a hard constraint on profit is imposed to ensure decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization framework. Additionally, to incorporate the characteristics of a multi-period decision-making process, an affine decision rule is introduced, which 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 due to the uncertainty and adaptation. That is to say, to tackle the intractability, we reformulate the robust counterpart into a conservative approximation which is a mixed-integer quadratic programming, and then effective solutions can be produced with Benders Decomposition algorithm. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.

Keywords: location-transportation problem, distributionally robust optimization, target-oriented, service-level measure, affine decision rule, benders decomposition

JEL Classification: R41