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Author: Dirk Beyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, convex surplus cost, and lost sales. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s; S) policy is proved.
Author: Dirk Beyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, convex surplus cost, and lost sales. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s; S) policy is proved.
Author: Dirk Beyer
Publisher: Springer Science & Business Media
ISBN: 0387716041
Category : Business & Economics
Languages : en
Pages : 260
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Book Description
This text provides a superbly researched insight into Markovian demand inventory models. The result of ten years of research, this work covers all aspects of demand inventory where they are modeled by Markov processes. Inventory management is concerned with matching supply with demand and is a central problem in Operations Management. The central problem is to find the amount to be produced or purchased in order to maximize the total expected profit, or minimize the total expected cost.
Author: Dirk Beyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s, S) policy is proved.
Author: Dirk Beyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s, S) policy is proved.
Author: Feng Cheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Markov-modulated 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 market conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatisfied demand is fully backlogged. The lost sales situation occurs in many retail establishments such as department stores and supermarkets. We use the analysis of the Markovian demand model with backlogging to analyze the lost sales case; in particular, we establish the optimality of an (s, S)-type policy under fairly general conditions.
Author: Xingyu Bai
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We consider a partially observable inventory system in which the inventory level can only be observed when it reaches zero, the unmet demand is lost, and replenishment orders must be decided so as to minimize the long-run average cost. This problem has an infinite-dimensional state space and is therefore difficult to analyze. We prove the existence of an average-cost optimal policy, using the so-called vanishing discount factor approach. As a main methodological contribution, we provide a way to verify the key condition -- the uniform boundedness of the relative discounted value function -- for the partially observed system. To accomplish that we construct -- for the partially observed system -- a valid policy which in a certain sense "copies" the actions of another policy for the process with a different initial state. To our best knowledge, this paper is the first dealing with inventory models with partially observable inventory levels under the long-run average cost criterion.
Author: Karin Möllering
Publisher: Springer
ISBN: 3658242558
Category : Business & Economics
Languages : en
Pages : 172
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Book Description
The last decades have seen an increasing diversity of customer expectations and growing competitive pressure for a wide variety of industries. Customer segmentation and subsequent inventory rationing provide a way to cope with those customer demands while maintaining a competitive offer. The general idea resembles the yield management practised in the airline or hotel industries: Demand fulfilment for low priority customers might be refused or delayed in order to reserve stock for more important clients. This dissertation thesis from Karin Möllering provides a comprehensive introduction to inventory rationing. It gives an overview of the different approaches studied and identifies state-of-the-art rules. In a second step, the book particularly focuses on an easy-to-implement but highly efficient rationing strategy. For this strategy, a mathematical model is developed that allows for optimization under different objectives. Potential readership includes scholars of inventory control and management science, students interested in these areas as well as practitioners involved in formulating and implementing rationing strategies.
Author: Ganesh Janakiraman
Publisher:
ISBN:
Category :
Languages : en
Pages : 250
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Book Description
Author: Dirk Beyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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 long-run 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.
Author: Suresh Sethi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is concerned with a generalization of classical inventory models (with fixed ordering costs) that exhibit (s, S) policies. In our model, the distribution of demands in successive periods is dependent on a Markov chain. The model includes the case of cyclic or seasonal demand. The model is further extended to incorporate some other realistic features such as no ordering periods and storage and service level constraints. Both finite and infinite horizon nonstationary problems are considered. We show that (s, S) policies are also optimal for the generalized model as well as its extensions.
