Determining the fill rate for a periodic review inventory policy with capacitated replenishments, lost sales and zero lead time

Abstract

In this paper we consider a periodic review order-up-to inventory system with capacitated replenishments, lost sales and zero lead time. We consider discrete demand. It is shown that the initial stock levels of the different review periods form a Markov chain and we determine the transition matrix. Furthermore we study for what probability mass functions of the review period demand the Markov chain has a unique stationary distribution. Finally we present a method to determine the fill rate.Keywords: Inventory; Periodic review; Fill rate; Capacitated replenishment; Lost sales IntroductionIn several publications the fill rate is discussed for periodic review inventory systems with uncapacitated replenishment. [5], in this paper the lead time is assumed to be negligible. In a part of [2], capacity is also considered, but in the context of multistage systems with process limitations. In [6] and [7] finite horizon fill rates are considered and compared with the infinite horizon fill rate.We consider a single-item inventory system that applies a periodic review order-up-to inventory policy with lost sales and zero lead time. Because of the lost sales assumption and the zero lead time assumption, the inventory position (number of products on hand minus number of products backlogged plus number of products on order) equals the stock level (number of products on hand). In such inventory policy the stock level is reviewed periodically and every review an order is placed to raise the stock level to a fixed level, the order-up-to level s (a positive integer). We assume the demand during one review period (period between two reviews) to be discrete with a given probability mass function. We

Allocation Policies to Fulfil Heterogeneous Service Requirements under Resource Pooling

“…The investigation on the optimal length of PRP from both suppliers' and buyers' perspectives still requires further attention, over and above that which has been historically recommended (e.g., Thomas, 2005;Dubois, Allaert, & Witlox, 2013) and the results of our exposition. Other future research direction can be including multiple products in the allocation policies where the aggregated service level of all products is considered to measure the performance of the supplier.…”