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Production-inventory system with finite production rate,stock-dependent demand, and variable holding cost

Published online by Cambridge University Press:  10 January 2014

Hesham K. Alfares
Hesham K. Alfares*
Affiliation:
P.O. Box 5067, Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.. alfares@kfupm.edu.sa
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Abstract

In general, traditional production-inventory systems are based on a number of simplifying– but somewhat unrealistic – assumptions, including constant demand rate, constant holdingcost, and instantaneous order replenishment. These assumptions have been individuallychallenged in numerous variations of production-inventory models. Finite production ratemodels, such as economic production quantity (EPQ) systems consider gradual orderreplenishment. Stock-dependent demand models assume the demand rate to be an elasticfunction of the inventory level. Variable holding cost models assume the holding cost perunit per time period to be a function of the time spent in storage. In this paper, thethree simplifying assumptions are simultaneously relaxed in a new production-inventorysystem with a finite production rate, stock-level dependent demand rate, and variableholding cost. Mathematical models and optimum solution procedures, including nonlinearprogramming, are presented for two functional forms of holding cost variability. The maincontribution of this paper is the formulation and solution of a new production-inventorymodel that more closely represents real-world situations. The realistic assumptions andefficient solution algorithms should make the model practical and useful for industrialapplications.

Keywords

Production-inventory systemstock-dependent demandvariable holding costnonlinear programming
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 1 , January 2014 , pp. 135 - 150
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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