Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes

Veinott, Arthur F.

doi:10.1287/opre.13.5.761

Cited by 255 publications

(95 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Inventory control with multiple demand classes has been studied for decades since Veinott (1965), with the aim to distinguish customer values in individual groups and thereafter improve economic consequences in business systems. A large body of literature has studied this problem in different settings.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

Wang¹,

Tang²,

Huo³

2013

Computers & Operations Research

View full text Add to dashboard Cite

, rQ system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the problem complexity, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.

show abstract

Section: A Brief Literature Reviewmentioning

confidence: 99%

“…This inspires the research on inventory control with multiple demand classes. Since Veinott (1965) first introduced a rationing policy to distinguish service levels for different demand classes, there is a growing body of literature in this area.…”

Section: Introductionmentioning

confidence: 99%

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

Wang¹,

Tang²,

Huo³

2013

Computers & Operations Research

View full text Add to dashboard Cite

show abstract

“…The theorems are presented without proofs. (To the best of our knowledge, they were first introduced by Veinott [14]. For a comprehensive discussion of stochastic ordering we refer the reader to [11].)…”

Section: Let X and Y Be Two Random N-vectors We Say That X Is Stochamentioning

confidence: 99%

A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales

Levi¹,

Janakiraman

Nagarajan

2008

Mathematics of OR

View full text Add to dashboard Cite

In this paper, we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst-case performance guarantees.In particular, we introduce dual-balancing policies for lost-sales models that are conceptually similar to dualbalancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost. That is, in each period, we balance two opposing costs: the expected marginal holding costs against the expected marginal lost-sales cost. Specifically, we show that the dual-balancing policies for the lost-sales models provide a worst-case performance guarantee of 2 under relatively general demand structures. In particular, the guarantee holds for independent (not necessarily identically distributed) demands and for models with correlated demands such as the AR(1) model and the multiplicative auto-regressive demand model. The policies and the worst-case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times. Our analysis has several novel elements beyond the balancing ideas for backorder models.Key words: Inventory, Approximation ; Dual-Balancing ; Algorithms; Lost Sales MSC2000 Subject Classification: Primary: 90B05 , ; Secondary: 68W25 , OR/MS subject classification: Primary: inventory/production , approximation/heuristics ; Secondary: production/scheduling , approximation/heuristics 1. Introduction In this paper, we address one of the fundamental problems in stochastic inventory theory, the single-item, single location, periodic-review, stochastic inventory control problem with lost sales, which we refer to as the lost-sales problem. This problem has challenged researchers and practitioners for over five decades as very little is known about the structure of the optimal policy, and there are no known provably good heuristics even for the simplest settings. We build on ideas first proposed by Levi, Pál, Roundy and Shmoys [5]. They proposed what are called dual-balancing policies for a class of inventory models where unsatisfied demand is backlogged rather than lost. These policies have worst-case performance guarantees, that is, for each instance of the problem, the expected cost of the policy is guaranteed to be at most C times the optimal expected cost (for some constant C). In this paper, we discuss the implementation and the worst-case analysis of dual-balancing policies applied to inventory models with lost sales. These models have mathematical characteristics that are very different than the models in which excess demand is backlogged and thus require a fundamentally different and novel worst-case analysis. In particular, we shall describe the first computationally efficient policies for inventory models with lost sales that have a worst-case performance guarantee of 2. The analysis is based on several new ideas that we believe will contribute to future research in this domain.

show abstract

“…Continuous -Review, Backorders Two demand classes Evans (1968) Kaplan ( Dekker et al (1998) N demand classes Veinott (1965) Topkis (1968 Katircioglu and Atkins (1996) Melchiors (2001) Dekker et al Veinott (1965) analyzes an inventory model with several demand classes for a single product. He proposes to use critical inventory levels to ration the on-hand inventory among demand classes.…”

Section: Continuous-review Lost Salesmentioning

confidence: 99%

“…We number the demand classes according to their relative priority, where class 1 has the highest priority. As suggested by Veinott (1965), , for which we require no assumptions about its sign.…”

Section: General Frameworkmentioning

confidence: 99%

A Single-Product Inventory Model for Multiple Demand Classes

2007

View full text Add to dashboard Cite

We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service level requirements. We assume a critical-level control policy, and show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization, under the assumptions of Poisson demand, deterministic replenishment lead-time, and a continuous-review (Q, R) policy with rationing. We propose a computationally-efficient heuristic and develop a bound on its performance.We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and to embed within a multi-echelon setting.

show abstract

Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes

Cited by 255 publications

References 5 publications

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales

A Single-Product Inventory Model for Multiple Demand Classes

Contact Info

Product

Resources

About