2018/03/18 by Satya S. Malladi, Malladi, Satya S., Alan L. Erera +4
Business, Management and Accounting · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Supply Chain and Inventory Management #math.OC
paper · pdf · doi:10.48550/arxiv.1803.06742
openalex publication_date 2018/03/18 · arxiv created 2022/02/12 · arxiv updated 2022/02/15 · openalex created_date 2022/08/07 · openalex updated_date 2026/07/28
We consider a periodic review inventory control problem having an underlying modulation process that affects demand and that is partially observed by the uncensored demand process and a novel additional observation data (AOD) process. We present an attainability condition, AC, that guarantees the existence of an optimal myopic base stock policy if the reorder cost K=0 and the existence of an optimal (s, S) policy if K>0, where both policies depend on the belief function of the modulation process. Assuming AC holds, we show that (i) when K=0, the value of the optimal base stock level is constant within regions of the belief space and that each region can be described by two linear inequalities and (ii) when K>0, the values of s and S and upper and lower bounds on these values are constant within regions of the belief space and that these regions can be described by a finite set of linear inequalities. A heuristic and bounds for the K=0 case are presented when AC does not hold. Special cases of this inventory control problem include problems considered in the Markov-modulated demand and Bayesian updating literatures.