Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s, S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted

Computing the optimal replenishment policy for inventory systems with random discount opportunities

Operations Research495790-795OPRE

Advances in Inventory Management: Dynamic Models

In this study, we develop and analyze models incorporating some of the dynamic aspects of inventory systems. In particular, we focus on two major themes to be analyzed separately: nonstationarity in demand rate and unfixed purchasing prices. In the first part of the study, we consider an inventory system with a nonstationary demand rate. In particular, we consider critical service parts subject to obsolescence. Inventory management of such items is notoriously difficult due to their slow moving character and the high risks involved when they are not available or no more needed. In practice, there is a need for policies tailored for service parts taking these aspects into account and easy to implement. We propose an obsolescence based control policy and investigate its performance and impact on costs. We find that ignoring obsolescence in the control policy increases costs significantly and early adaptation of base stock levels can lead to important savings. In the second part of the study, we consider an inventory system where the supplier offers price discounts at random points in time. We extend the literature by assuming a more general backordering structure. That is, when the system is out of stock, an arriving customer either decides to be backlogged with a certain probability or leaves the system and becomes a lost sale. We derive equations to calculate optimal policy parameters and demonstrate that allowing backorders in face of random deal offerings can result in considerable savings