Title: Optimal ordering policies of an inventory model for deteriorating items with demand inversely proportional to the on-hand inventory

Authors: V.V.S.S.V. Prasad Rao Patnaik; K. Srinivasa Rao

Addresses: Department of Mathematics and Statistics, M.R. College (Autonomous), Vizianagaram 535 002, Andhra Pradesh, India ' Department of Statistics, Andhra University, Visakhapatnam 530 003, Andhra Pradesh, India

Abstract: In this paper, we develop and analyse an inventory model for deteriorating items with the assumption that the lifetime of the commodity is random and follows an exponential distribution and the demand is inversely proportional to the stock on-hand, having variable cycle lengths declining in arithmetic progression. It is further assumed that the shortages are allowed and fully backlogged. Using the differential equations, the instantaneous level of inventory is derived. With suitable cost consideration, the total cost function is obtained. By minimising the total cost, the optimal cycle length and ordering quantities are derived. The sensitivity of the model with respect to the parameters and costs is also performed. This model is extended to the case of without shortages. This model is useful in practical situations arising at places such as textile markets, fruit and vegetable markets.

Keywords: inventory modelling; deteriorating items; stock-dependent demand; variable cycle lengths; sensitivity analysis; ordering policies; optimisation; total cost function; textile markets; fruit and vegetable markets; fruit and veg.

DOI: 10.1504/IJOR.2012.045187

International Journal of Operational Research, 2012 Vol.13 No.2, pp.200 - 218

Published online: 11 Jan 2015 *

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