Modelling single-period inventory problem by distributionally robust fuzzy optimization method

摘要

In uncertain single-period inventory problem, the optimal decision often depends heavily on the distribution of uncertain market demand. When only partial demand distribution information is available, it is important for decision makers to order a reliable quantity to immunize against the distribution uncertainty. The main contribution of this paper is to develop a new distributionally robust optimization method for single-period inventory problem, in which the uncertain market demand is characterized by generalized parametric interval-valued (PIV) possibility distribution and its associated uncertainty distribution set. The formulation of our distributionally robust optimization model is based on the proposed uncertainty distribution set, so it can generate a reliable solution to immunize against distribution uncertainty. Under two assumptions on the underlining decision-making environment, the robust counterpart of the original uncertain optimization problem is proposed for single-period inventory problem. To solve the robust single-period inventory model, this paper discusses the computational issue about the infinitely many Lebesgue-Stieltjes (L-S) integral constraints and reformulates the robust counterpart problem as its equivalent deterministic inventory sub-models. According to the structural characteristics of the deterministic inventory sub-models, a domain decomposition method is designed to find the robust optimal solution to our single-period inventory problem. Finally, some computational results are reported about a practical single-period inventory problem to show the primary benefit of using the proposed distributionally robust fuzzy optimization method.