On the accuracy of fluid approximations to a class of inventory-level-dependent EOQ and EPQ models
type: Item
instance of: scholarly article
title: On the accuracy of fluid approximations to a class of inventory-level-dependent EOQ and EPQ models
zbMATH Open document ID: 1233.90038
DOI: 10.1155/2011/301205
author: Yi Zhang
author: A. B. Piunovskiy
published in: Advances in Operations Research
publication date: 2012-03-08T00:00:00Z
review text: Summary: Deterministic economic order quantity (EOQ) models have been studied intensively in the literature, where the demand process is described by an ordinary differential equation, and the objective is to obtain an EOQ, which minimizes the total cost per unit time. The total cost per unit time consists of a ``discrete'' part, the setup cost, which is incurred at the time of ordering, and a ``continuous'' part, the holding cost, which is continuously accumulated over time. Quite formally, such deterministic EOQ models can be viewed as fluid approximations to the corresponding stochastic EOQ models, where the demand process is taken as a stochastic jump process. Suppose now an EOQ is obtained from a deterministic model. The question is how well does this quantity work in the corresponding stochastic model. In the present paper we justify a translation of EOQs obtained from deterministic models, under which the resulting order quantities are asymptotically optimal for the stochastic models, by showing that the difference between the performance measures and the optimal values converges to zero with respect to a scaling parameter. Moreover, we provide an estimate for the rate of convergence. The same issue regarding specific economic production quantity (EPQ) models is studied, too.
Mathematics Subject Classification ID: 90B05
zbMATH DE Number: 6013011
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/301205
OpenAlex ID: W2042251688
Wikidata QID: Q58655024
cites work: An EOQ model with state-dependent demand rate
cites work: An application of the EOQ model with nonlinear holding cost to inventory management of perishables
cites work: An inventory model for deteriorating items with stock-dependent demand rate
cites work: Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost
cites work: Economic order quantity models with nonlinear holding costs
cites work: Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory
cites work: Asymptotic optimality of tracking policies in stochastic networks.
cites work: Fluid approximation of a controlled multiclass tandem network
cites work: Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality.
cites work: Fluid limits of optimally controlled queueing networks
cites work: Large-deviations analysis of the fluid approximation for a controllable tandem queue
cites work: Random walk, birth-and-death process and their fluid approximations: Absorbing case
cites work: DYNAMIC PRICING AND INVENTORY CONTROL FOR A PRODUCTION SYSTEM WITH AVERAGE PROFIT CRITERION
cites work: A Queueing Model to Analyze the Value of Centralized Inventory Information
cites work: A Note on an Inventory Model with Inventory-level-dependent Demand Rate
cites work: An Inventory Model with an Inventory-Level-Dependent Demand Rate and Relaxed Terminal Conditions
cites work: Accuracy of fluid approximations to controlled birth-and-death processes: absorbing case
cites work: Q4693718
description: scientific article; zbMATH DE number 6013011