Cost analysis of an (S−1,S) inventory system with two demand classes and rationing

Isotupa, K. P. Sapna

doi:10.1007/s10479-013-1407-3

Cited by 19 publications

(15 citation statements)

References 13 publications

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“…[WBSW15,p. 733] (2) Randomized differentiated admission control is incorporated in many models and is discussed indepth by Isotupa ([Iso06], [Iso07], [Iso11], [IS13], [Iso15]) in a sequence of papers. Isotupa investigates inventory systems with (r, Q)-and base stock policy for two classes of customers.…”

Section: Discussion Of the Modelling Assumptions (1)mentioning

confidence: 99%

Stability of queueing-inventory systems with different priorities

Otten¹,

Daduna²

2022

Preprint

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We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well.

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Section: Discussion Of the Modelling Assumptions (1)mentioning

confidence: 99%

Stability of queueing-inventory systems with different priorities

Otten¹,

Daduna²

2022

Preprint

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“…Their model assumes that the service level of low-priority customers is measured by a response time guarantee, while the service level of the high-priority customers is measured by the fill rate. For the lost sales models within the continuous review (S − 1, S) framework, Dekker et al (2002), Kranenburg and van Houtum (2007), and Isotupa (2015) all study a critical level policy for multiple demand classes with Poisson demand processes.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimizing stock levels for service-differentiated demand classes with inventory rationing and demand lead times

Vicil¹

2020

Flex Serv Manuf J

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In this paper, we study a service parts inventory management system for a single product at a parts distribution center serving two priority-demand classes: critical and non-critical. Distribution center keeps a common inventory pool to serve the two demand classes, and provides differentiated levels of service by means of inventory rationing. We assume a continuous review one-for-one ordering policy with backorders and Poisson demand arrivals. Only one demand class provides advance demand information whose orders are due after a deterministic demand lead time, whereas the orders of the other demand class need to be satisfied immediately. The problem has been studied before, but remained a challenging problem. The quality of the existing heuristic for estimating the critical class service levels can diminish significantly in some settings and the search routine for the service level optimization model relies on a brute force approach. Our contribution to the literature is twofold. For the given class of inventory replenishment and allocation policies, first we determine the form of the optimal solution to the service level optimization model, and then we derive an exact optimization routine to determine the optimal policy parameters provided the steady-state distribution is available. The computation of steady-state probabilities is needed only once. Second, we propose an alternative approach to estimate steady-state probabilities. By analyzing the limiting behavior of transition probabilities during infinitesimal time intervals, we are able to characterize the relationships between the steady-state probabilities, which satisfy nicely formed balance equations under the so-called Independence Assumption. In the numerical study section, we show that our approach provides superior performance in estimating service levels than the existing heuristic for all the examples considered. We also compare the performance of using the critical class service levels computed according to our method against the service levels computed by the existing heuristic, and show that our method can provide inventory savings up to 16.67%.

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“…In one section of their study, they consider pure lost sales model within the framework of (S − 1, S) policy with rationing. Isotupa (2015) studies a continuous review, lost sales (S − 1, S) inventory system for two prioritydemand classes with Poisson demand processes. The model is restricted to the independently and identically distributed exponential order lead times.…”

Section: Literature Reviewmentioning

confidence: 99%

Inventory rationing on a one-for-one inventory model for two priority customer classes with backorders and lost sales

Vicil¹

2020

IISE Transactions

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In this study, we are primarily motivated by the research problem of recognizing heterogeneous customer behavior towards waiting for order fulfillment under the threshold rationing policy (also known as the critical level policy), and aim to find its effect on system stock levels and performance measures. We assume a continuous review one-for-one ordering policy with generally distributed lead times. In the first model, we consider the case in which low-priority customer class exhibits zero patience for waiting if the demand is not satisfied immediately (a lost sale), while the demand of high-priority customer class can be backordered. This is the first study in the literature to consider this model. We provide an exact analysis for the derivation of the steady-state probability distribution and the average infinite horizon cost per unit time. We then develop an efficient procedure to minimize the average expected cost rate by deriving bounds on the optimal cost, which reduces the enumeration space considerably. In the numerical study, we show the relative savings achieved by implementing the proposed threshold rationing policy over some of the traditional industry practices. In the second model, we study the opposite case in which the high-priority customer class exhibits zero patience for waiting. The existing study in the literature uses simulation to demonstrate that the performance of the critical level policy is robust with respect to the form and variability of the lead time distribution provided the mean lead times are identical. Then it proposes using the Continuous-Time Markov Chain (CTMC) equivalent of the model as an approximation. In this study, we establish a theoretical basis for the rationale of using the CTMC approach as an approximation. We show that under certain assumptions the steady-state probabilities of the system with generally distributed lead times are identical to the steady-state probabilities of the CTMC system with the same mean. This result enables us to link the dynamics of the studied model to the CTMC model, which then allows us to provide a theoretical explanation to the empirically observed phenomenon that why the steady-state probabilities and performance measures are near-insensitive to the form and variability of the lead time distribution as long as mean lead times are identical.

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Cost analysis of an (S−1,S) inventory system with two demand classes and rationing

Cited by 19 publications

References 13 publications

Stability of queueing-inventory systems with different priorities

Stability of queueing-inventory systems with different priorities

Optimizing stock levels for service-differentiated demand classes with inventory rationing and demand lead times

Inventory rationing on a one-for-one inventory model for two priority customer classes with backorders and lost sales

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