An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion

@article{Federgruen1986AnIM,
  title={An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion},
  author={Awi Federgruen and Paul H. Zipkin},
  journal={Math. Oper. Res.},
  year={1986},
  volume={11},
  pages={208-215}
}
This paper considers a single-item, periodic-review inventory model with uncertain demands. We assume a finite production capacity in each period. With stationary data, a convex one-period cost function and a continuous demand distribution, we show under a few additional unrestrictive assumptions that a modified basic-stock policy is optimal under the discounted cost criterion, both for finite and infinite planning horizons. In addition we characterize the optimal base-stock levels in several… 
View via Publisher
www0.gsb.columbia.edu
353 Citations
Highly Influential Citations
18
Background Citations
126
Methods Citations
25
Results Citations
6

353 Citations

Stochastic Inventory Models with Limited Production Capacity and Periodically Varying Parameters

It is proved that modified base-stock policies are optimal for the finite-horizon planning model and for both the infinite-Horizon discounted and undiscounted cost criterion and it is shown that the optimal base- stock levels can be calculated via a simple but efficient value-iteration method.

A Capacitated Production-Inventory Model with Periodic Demand

For a single product, single-stage capacitated production-inventory model with stochastic, periodic (cyclic) demand, the optimal policy is found and some of its properties are characterized and several insights into the model are provided.

Optimal policy for inventory systems with capacity commitment and fixed ordering costs

Optimal Production and Inventory Policy for Multiple Products Under Resource Constraints

We show that a modified base-stock policy is optimal for multiproduct, infinite-horizon production-inventory systems, where demand for the products is random and the products share a finite resource…

A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand

Computing the Optimal Policy for Capacitated Inventory Models

We consider an infinite-horizon inventory model with finite production capacity and stochastic demands. Federgruen and Zipkin [2][3] showed that a base-stock policy is optimal; however, they did not…

The capacitated multi-echelon inventory system with serial structure. 1. The 'push ahead'-effect

It is shown that under the average cost criterion the optimal order strategy may be characterized by a so-called 'push ahead'-effect and it is found that a modified base-stock policy approximates the optimal policy quite well.

Base stock policies for production/inventory problems with uncertain capacity levels

Production planning with stochastic seasonal demandand capacitated production

We consider a production/inventory problem with stochastic seasonal demand. A scarce resource limits production in each time period, and setup time is negligible. Linear and stationary costs are…

Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost

...

References

SHOWING 1-10 OF 23 REFERENCES

DETERMINISTIC PRODUCTION PLANNING WITH CONCAVE COSTS AND CAPACITY CONSTRAINTS.

A multi-period single commodity production planning problem is studied in which known requirements have to be satisfied. The model differs from earlier well-known studies involving concave cost…

Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints

We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product…

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…

Technical Note - A One-Product Production/Inventory Problem under Continuous Review Policy

It is shown that the problem may be modeled as an M/D/1 queueing system with the optimal policy being a two-critical-number policy and in computational tests that were performed, optimal policies were computed in less than 1/8 second of CPU time.

A production-inventory control model with a mixture of back-orders and lost sales

We consider a production-inventory control model of finite capacity, in which backordering up to a certain level is allowed. We assume that there exist two possible production rates. The control is…

The Compensation Method Applied to a One-Product Production/Inventory Problem

This paper considers a one-product, one-machine production/inventory problem, related to a server backlog process for an M/M/1 system in which the server departs when the system empties, and returns when the backlog exceeds a specified threshold.

The Status of Mathematical Inventory Theory

This paper surveys the current status of mathematical inventory theory. The review is limited to studies which seek optimal policies for dynamic inventory models. Models with certain and uncertain…

An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints

We consider the situation of a single item having a deterministic, time-varying demand pattern. Production lot sizes, so as to minimize the total of setup and carrying costs, are to be determined…

Deterministic Production Planning: Algorithms and Complexity

A class of production planning problems is considered in which known demands have to be satisfied over a finite horizon at minimum total costs. For each period, production and storage cost functions…

Optimal control of batch service queues

A batch service queue is considered where each batch size and its time of service is subject to control and policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are shown.