Optimality of (s, S) Policies in Inventory Models with Markovian Demand

@article{Sethi1997OptimalityO,
  title={Optimality of (s, S) Policies in Inventory Models with Markovian Demand},
  author={Suresh P. Sethi and Feng Cheng},
  journal={Oper. Res.},
  year={1997},
  volume={45},
  pages={931-939}
}
This paper is concerned with a generalization of classical inventory models (with xed 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 nite and innnite horizon nonstationary problems are considered… 
View via Publisher
166 Citations
Highly Influential Citations
9
Background Citations
81
Methods Citations
26
Results Citations
5

166 Citations

Citation Type

Citation Type

Note on the optimality of (s, S) policies for inventory systems with two demand classes
Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth
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…
Stochastic Multiproduct Inventory Models with Limited Storage
This paper studies multiproduct inventory models with stochastic demands and a warehousing constraint. Finite horizon as well as stationary and nonstationary discounted-cost infinite-horizon problems…
ON A PERIODIC REVIEW INVENTORY MODEL WITH UNCERTAIN DEMAND IN A RANDOM ENVIRONMENT Hirotaka Matsumoto and
This paper is on the analysis of a single product, periodic review inventory model, where the distributions of demands vary with the state of the environment variable. The state of the environment is…
Average Cost Inventory Models: An Analysis Using Schal's Vanishing Discount Results
Schal (1993) proves that, under certain assumptions, optimal policies for Markov Decision Processes (MDPs) under the infinite horizon discounted cost criterion converge to the optimal policy under…
Joint pricing and inventory control with a Markovian demand model
Average Cost Optimality in Inventory Models with Markovian Demands
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…
Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs
We develop a new, unified approach to treating continuous-time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted…
Optimal policy for inventory systems with capacity commitment and fixed ordering costs
A periodic-review inventory model in a fluctuating environment
We study a single-item periodic-review inventory model in a fluctuating environment with a fixed lead time of λ periods. The state of the environment at the beginning of each period is described by a…
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 23 REFERENCES
Optimality of (s, S) Policies in Inventory Models with Markovian Demand
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…
Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem
The optimal ordering policy for a n-period dynamic inventory problem in which the ordering cost is linear plus a fixed reorder cost and the other one-period costs are convex is characterized by a…
A periodic review inventory model with Markovian supply availability
Inventory Control in a Fluctuating Demand Environment
TLDR
An inventory model, where the demand rate varies with an underlying state-of-the-world variable that can represent economic fluctuations, or stages in the product life-cycle, for example, is presented.
On the Opimality of $( {s,S} )$ Inventory Policies: New Conditions and a New Proof
Scarf [6] has shown that the $( {s,S} )$ policy is optimal for a class of discrete review dynamic nonstationary inventory models. In this paper a new proof of this result is found under new…
Optimal Inventory Policy.
WE ipropose to outline a method for deriving optimal rules of inventory policy for finished goods. The problem of inventories exists not only for business enterprises but also for nonprofit agencies…
Dynamic Programming and Stochastic Control
What do you do to start reading dynamic programming and stochastic control? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has…
The Optimality of (S,s) Policies in the Dynamic Inventory Problem with Emergency and Non-Stationary Stochastic Demands
Optimal Inventory Policy for the Arrow-Harris-Marschak Dynamic Model
  • In
  • 1958
Optimal Replenishment Policies for the Dynamic Inventory Problem
  • 1992
...
1
2
3
...