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A SingleUnit Decomposition Approach to Multiechelon Inventory Systems
"... doi 10.1287/opre.1080.0620 ..."
Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth
, 1996
"... . This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite horizon problems, stationary and nonstationary discounted cost infi ..."
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Cited by 11 (6 self)
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. This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite horizon problems, stationary and nonstationary discounted cost infinite horizon problems, and stationary longrun average cost problems are addressed. Existence of optimal Markov or feedback policies is established. Furthermore, optimality of (s; S)type policies is proved when in addition the ordering cost consists of fixed and proportional cost components and the surplus cost is convex. Key Words. Dynamic inventory model, Markov chain, dynamic programming, finite and infinite horizon, cyclic demand, (s; S) policy. 2 1 Introduction This paper studies stochastic inventory problems with unbounded Markovian demands and more general costs than those considered in the inventory literature. Finite horizon problems, stationary and nonstationary discounted cos...
Optimality of StateDependent (s, S) Policies in Inventory Models with MarkovModulated Demand and Lost Sales
, 1996
"... Markovmodulated processes have been used in stochastic inventory models with setup costs for modeling demand under the influence of uncertain environmental factors, such as fluctuating economic and marketing conditions. The analyses of these models have been carried out in the literature only under ..."
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Cited by 6 (0 self)
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Markovmodulated processes have been used in stochastic inventory models with setup costs for modeling demand under the influence of uncertain environmental factors, such as fluctuating economic and marketing conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatisfied demand is fully backlogged. We study a Markovian demand model in the case when unsatisfied demands are lost. The lost sales situation occurs in many retail establishments such as department stores and supermarkets. The optimality of an (s; S)type policy is established under fairly general conditions. Computational results are also reported. (DYNAMIC INVENTORY MODEL, MARKOV CHAIN, DYNAMIC PROGRAMMING, (s; S) POLICY, LOST SALES) This research was supported in part by NSERC grant A4619 and Canadian Center for Marketing Information Technologies. The authors would like to thank Dirk Beyer, Vinay Kanetkar, Dmitry Krass, the three anonymous referees, and the Are...
Reducing International Risk through Quantity Contracts
, 1998
"... We investigate a tool which small manufacturers engaging in international supply contracts can use to dampen the variations in their income caused by exchange rate #uctuations. The method we study involves contractual speci#cations for a minimum purchase quantity with the buyer. The particular c ..."
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We investigate a tool which small manufacturers engaging in international supply contracts can use to dampen the variations in their income caused by exchange rate #uctuations. The method we study involves contractual speci#cations for a minimum purchase quantity with the buyer. The particular case we consider is that of a smaller manufacturer providing a product to a large overseas corporation, where transactions are conducted in the manufacturer's domestic currency. The large corporation employs a periodic review inventory policy with back orders, incorporating unit, holding and penalty costs which may be statedependent. The state is the current exchange rate, whichvaries in a Markovian manner according to one of three considered models #random walk, mean reverting, and momentum #. Demands for products arrive randomly and may also be state dependent, to a degree determined by the rate of pass through of exchange rate e#ects. We #rst establish that the optimal policy for t...
Inventory management with partially observed nonstationary demand
, 2009
"... Abstract We consider a continuoustime model for inventory management with Markov modulated nonstationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are comp ..."
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Abstract We consider a continuoustime model for inventory management with Markov modulated nonstationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an optimal inventory policy. We also describe a computational procedure to calculate the value function and the optimal policy and present two numerical illustrations.
A Markovian DualSource ProductionInventory Model with Order Bands
, 1998
"... We present a Markovian model of a single #rm engaging in a periodic review inventory policy to procure goods from two alternate suppliers. Each supplier quotes a statedependent minimum order quantity, maximum order quantity, and unit price. The purchasing #rm faces statedependent unit inventory ..."
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We present a Markovian model of a single #rm engaging in a periodic review inventory policy to procure goods from two alternate suppliers. Each supplier quotes a statedependent minimum order quantity, maximum order quantity, and unit price. The purchasing #rm faces statedependent unit inventory holding costs, as well as backorder #penalty costs if they are unable to immediately satisfy their customer demand. We show that a modi#ed basestock policy is optimal in the situation where the suppliers have lead times which di#er by one time unit. This policy is de#ned by a vector of pairs of numbers # one for each lead time # indexed by the states of the Markovchain. In each state the #rm will place orders as close to these two indices as possible, while satisfying the stipulated minimum and maximum order sizes. In addition, we demonstrate that use of In#nitesimal Perturbation Analysis, or IPA, to compute the optimal vector of inventory levels is valid for arbitrary lead times, ...
Inventory Management: Information, Coordination and Rationality
"... The success of a product in today’s global marketplace depends on capabilities of firms in the product’s supply chain. Among these capabilities, effective inventory management is a capability necessary to lead in the global marketplace. The chapter provides a discussion of four fundamentals of effe ..."
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The success of a product in today’s global marketplace depends on capabilities of firms in the product’s supply chain. Among these capabilities, effective inventory management is a capability necessary to lead in the global marketplace. The chapter provides a discussion of four fundamentals of effective inventory management. First, it requires managers to know how best to use available information. Second, managers need to quantify the value of information. Third, they need to coordinate decentralized inventory operations. Finally, effective inventory management requires decision tools that can be embraced by their users. The chapter’s emphasis is on the use of information, and the role of new information technologies in inventory management. Previous research on inventory management played an important role in the advancement and development of new technologies and processes. Today more research is needed because new technologies (such as RFID RadioFrequency Identification) and new management methods (such as collaborative forecasting and planning) are emerging and evolving faster than ever before. Inventory management and research will continue to play a central role in the success of a product and the firms in its supply chain. The chapter brings together separate but inherently related streams of research in inventory management. By doing so, we highlight potential research opportunities that lie on the boundaries.
DYNAMIC PRICING AND REPLENISHMENT IN A PRODUCTIONINVENTORY SYSTEM WITH MARKOVMODULATED DEMAND
, 2004
"... System with MarkovModulated Demand ..."
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The Classical Papers of Iglehart (1963) and Veinott and Wagner (1965) Revisited
 Journal of Optimization and Applications
, 1999
"... This paper revisits the classical papers of Iglehart (1963) and Veinott and Wagner (1965) devoted to stochastic inventory problems with the criterion of longrun average cost minimization. We indicate some of the assumptions that are implicitly used without verification in their stationary distribut ..."
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This paper revisits the classical papers of Iglehart (1963) and Veinott and Wagner (1965) devoted to stochastic inventory problems with the criterion of longrun average cost minimization. We indicate some of the assumptions that are implicitly used without verification in their stationary distribution approach to the problems, and provide the missing (nontrivial) verification. In addition to completing their analysis, we examine the relationship between the stationary distribution approach and the dynamic programming approach to the averagecost stochastic inventory problems. This research was supported in part by a Feodor Lynengrant provided by the A. von Humboldt Foundation and NSERC Grant A4619. Thanks are due to Youhua (Frank) Chen, HansJoachim Girlich, Arie Harel and Dmitry Krass for helpful comments. y Technical Staff Member, HewlettPackard Laboratories, Palo Alto, California. z Professor, School of Management,The University of Texas at Dallas, Richardson, Texas. 1 1 ...
Optimal Pricing and Production Policies of a MaketoStock
, 2007
"... We study the effects of different pricing strategies available to a productioninventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are invest ..."
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We study the effects of different pricing strategies available to a productioninventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: Static pricing, where only one price is used at all times, environmentdependent pricing, where price changes with the environment, and dynamic pricing, where price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This paper presents some structural properties of optimal replenishment policies, and a numerical study which compares the performances of these three pricing strategies. 1