Robust Ordering Strategy For Multi-Period Inventory Control Problem Under Uncertain Demand

The data of real-world optimization problems more often than not is uncertain due to prediction errors, measurement errors, implementation errors and other reasons. In hope that a small data uncertainties will not affect significantly the feasibility and optimality properties of a solution, people usually use norminal data to handle optimization problems with uncertain data and get the corresponding nominal optimal solution. However, in real life, we see that even a pretty small perturbations of the data may heavily affect the quality of the nominal solution and make the nominal optimal solution completely meaningless. Therefore, there exists a real need of a technique capable of detecting cases when data uncertainty can heavily affect the quality of the nominal solution, and in these cases to generate a realible solution, one which is immunized against uncertainty. Robust optimization which is a novel methodology for handling optimization problems with uncertain data can solve the above problem.In this paper, we employ robust optimization method to solve multi-period capacitated inventory control problem under uncertain demand. Firstly, We describe uncertain demand by using factor-based demand model. Secondly, we formulate robust inventory models and derive robust ordering strategy under static replenishment policy and linear replenishment policy. Finally, we make numerical experiments. Further, we discuss the effects of inventory capacity on ordering strategy and compare the performance of linear replenishment policy with static replenishment policy.This paper is an extension over the related work of Ben-Tal et al.[1], our contributions can be summarized as follows:First of all, we assume that inventory capacity is finite and discuss the effects of inventory capacity on ording strategy. While Ben-Tal et al.[1] assume that inventory capacity is infinite, they ignore the effects of inventory capacity on ording strategy. Secondly, we describe uncertain demand by using factor-based demand model. When the factor support set is the same as the factor means support set, our model becomes the adjustable robust counterpart model of Ben-Tal et al.[1]. Finally, we extend the model of Ben-Tal et al.[1] to a multiproduct setting...