# Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model

@article{Federgruen1984ComputationalII, title={Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model}, author={Awi Federgruen and Paul H. Zipkin}, journal={Oper. Res.}, year={1984}, volume={32}, pages={818-836} }

Clark and Scarf Clark, A., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Mgmt. Sci.6 475-490. characterize optimal policies in a two-echelon, two-location inventory model. We extend their result to the infinite-horizon case for both discounted and average costs. The computations required are far easier than for the finite horizon problem. Further simplification is achieved for normal demands. We also consider the more interesting case of multiple locations at the lower…

## 323 Citations

### Computationally simple and unified approach to finite- and infinite-horizon Clark–Scarf inventory model

- Business
- 2010

In this article, it is shown that an easily computed and simply structured policy for making work-order decisions is optimal in the Clark–Scarf inventory model. That is a model of a make-to-stock…

### Computationally Simple and Unified Approach to Finite and In finite Horizon Clark-Scarf Inventory Model

- Business
- 2010

In this article, it is shown that an easily computed and simply structured policy for making work-order decisions is optimal in the Clark–Scarf inventory model. That is a model of a make-to-stock…

### Optimal Policies for a Capacitated Two-Echelon Inventory System

- BusinessOper. Res.
- 2004

This paper demonstrates optimal policies for capacitated serial multiechelon production/inventory systems by demonstrating that a modified echelon base-stock policy is optimal in a two-stage system when there is a smaller capacity at the downstream facility.

### Capacitated Multiechelon Inventory Systems: Policies and Bounds

- Computer ScienceManuf. Serv. Oper. Manag.
- 2016

This work considers the use of echelon base-stock policies for this multiechelon serial inventory system (even though they are known to be suboptimal) and proposes algorithms for finding base- stock levels that are easy to understand and implement and is shown to be asymptotically optimal.

### Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models

- Business, Computer ScienceMath. Oper. Res.
- 2017

We develop the first algorithmic approach to compute provably good ordering policies for a multi-echelon, stochastic inventory system facing correlated, nonstationary and evolving demands over a…

### Continuous-Review Policies for a Multi-Echelon Inventory Problem With Stochastic Demand

- Business
- 2017

This paper considers a multi-stage, serial inventory system. The demand for the end item is stochastic and stationary. The relevant costs include a fixed ordering cost and an echelon inventory…

### A Multiechelon Inventory Problem with Secondary Market Sales

- BusinessManag. Sci.
- 2011

A novel class of policies, referred to as the disposal saturation policies, are introduced and it is established that there exists a disposal saturation policy, determined recursively by a single base-stock level at each echelon, that achieves the decomposition of this problem.

### The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies

- BusinessEur. J. Oper. Res.
- 2001

### Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information

- BusinessManuf. Serv. Oper. Manag.
- 2003

This work shows how to optimally incorporate advance demand information into periodic-review, multiechelon, inventory systems in series, and proves the optimality of state-dependent, echelon base-stock policies for finite and infinite horizon problems.

## References

SHOWING 1-10 OF 25 REFERENCES

### Approximations of Dynamic, Multilocation Production and Inventory Problems

- Business
- 1984

Consider a central depot or plant which supplies several locations experiencing random demands. Orders are placed or production is initiated periodically by the depot. The order arrives after a fixed…

### Allocation policies and cost approximations for multilocation inventory systems

- Economics, Business
- 1984

This work considers a central depot that supplies several locations experiencing random demands, and considers the special case where the penalty‐cost/holding‐cost ratio is constant over the locations.

### Optimal Policy for a Multi-product, Dynamic Non-Stationary Inventory Problem

- Business
- 1965

This paper is concerned with a multi-product dynamic nonstationary inventory problem in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has…

### Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem

- Mathematics
- 1963

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…

### Optimality of Myopic Inventory Policies for Several Substitute Products

- Business
- 1969

Multiproduct inventory systems with proportional ordering costs and stochastic demands are studied. New conditions are obtained under which a myopic ordering policy (a policy of minimizing expected…

### Designing a Multi-Product Multi-Echelon Inventory System,

- Business
- 1979

A reformulation of the nonlinear programming model as a 0-1 linear programming model is presented, to incorporate capacity constraints at the retail stores and warehouses, and illustrate the use of the new model.

### Exact and Approximate Cost Functions for Product Aggregates

- Economics, Business
- 1982

We show that certain large, multiproduct problems can be well approximated by smaller models of the same form, representing only one aggregate product or a few such products. This reduction follows…

### An Efficient Algorithm for Computing Optimal (s, S) Policies

- Computer ScienceOper. Res.
- 1984

This paper presents an algorithm to compute an optimal s, S policy under standard assumptions stationary data, well-behaved one-period costs, discrete demand, full backlogging, and the average-cost…

### Nonstationary Markov decision problems with converging parameters

- Mathematics
- 1981

This paper considers the solution of Markov decision problems whose parameters can be obtained only via approximating schemes, or where it is computationally preferable to approximate the parameters,…

### Least d-Majorized Network Flows with Inventory and Statistical Applications

- Mathematics
- 1971

It is shown that for any feasible network flow model, there is a flow which simultaneously minimizes every d-Schur convex function of the flows emanating from a single distinguished node called the…