A Markovian approach to modeling a periodic order‐up‐to‐level policy under stochastic discrete demand and lead time with lost sales

Abstract

In this paper, a periodic order‐up‐to‐level policy is developed by using a Markovian approach. Customer demand is modeled by using an empirical distribution. Unmet customer demand is considered as lost sales. The internal storage capacity is limited, and excessive units are stored in external storage space. Replenishment lead time is discrete and stochastic. Because of the characteristics of the demand and lead time, the demand during the lead time and the demand during the protection interval are empirical. The Markovian approach is used to estimate the system measures of performance, including the expected inventory on‐hand, expected lost sales, and expected over‐storage. The successive overrelaxation algorithm is implemented to overcome the dimensional issue of the Markov model. The optimal policy that minimizes the total cost is obtained by using a customized golden section search procedure. The proposed method is applied to a real dataset of consumable products. In addition, the effectiveness of the approach is demonstrated by a comparison with a simulation. The results indicate that the model from our approach can accurately describe the behavior of the periodic order‐up‐to‐level review system.

Inventory Positioning in Supply Chain Network: A Service-Oriented Approach

“…The functions ݂ሺ‫݈|ݔ‬ሻ and ‫ܨ‬ሺ‫݈|ݔ‬ሻ are derived from ݂ሺ݀ሻ, given ݈ [30], [31]. With these estimations, the base stock levels and expected inventories for each internal stage are expressed as,…”