Inventory Management Based on Target-Oriented Robust Optimization

We propose a target-oriented robust optimization approach to solve a multiproduct, multiperiod inventory management problem subject to ordering capacity constraints. We assume the demand for each product in each period is characterized by an uncertainty set that depends only on a reference value and the bounds of the demand. Our goal is to find an ordering policy that maximizes the sizes of all the uncertainty sets such that all demand realizations from the sets will result in a total cost lower than a prespecified cost target. We prove that a static decision rule is optimal for an approximate formulation of the problem, which significantly reduces the computation burden. By tuning the cost target, the resultant policy can achieve a balance between the expected cost and the associated cost variance. Numerical experiments suggest that although only limited demand information is used, the proposed approach performs comparably to traditional methods based on dynamic programming and stochastic programming. More importantly, our approach significantly outperforms the traditional methods if the latter assume inaccurate demand distributions. We demonstrate the applicability of our approach through two case studies from different industries.