Title: Periodic review inventory model with service level constraint in fuzzy environment

Authors: Nita H. Shah, Hardik Soni

Addresses: Department of Mathematics, School of Science, Gujarat University, Ahmedabad-09, India. ' Chimanbhai Patel Post Graduate Institute of Computer Applications, Ahmedabad-15, India

Abstract: In the current world of high service levels and tight delivery schedules, companies need to adjust their actions to deal with smaller orders that are made more frequently. In this regard, a periodic review inventory system with service level constraint has been analysed in which (R, T) policy jointly minimises the cost function when single product having demand function of selling price which is imprecise in nature. The holding cost which is influenced by selling price comprises two components viz. holding cost for base stock and holding cost for critical stock, i.e., the amount of inventory reserved during stock out for high priority customers| demand. Critical stock is maintained at high carrying rate as compared to carrying rate of base stock. The characteristic of the lead time is taken as fuzzy. The arithmetical operations of fuzzy total cost are performed under function principle and the manager|s k-preference integration representation method is applied to defuzzify the fuzzy total cost. Trapezoidal distribution of fuzzy number is used to work out the stock out. Then the model is solved jointly for (R, T) policy through Kuhn-Tucker conditions. A rigorous numerical study has been carried out and explained as managerial view point.

Keywords: periodic review systems; function principle; modified graded mean integration representation; Kuhn-Tucker conditions; service levels; inventory modelling; holding cost; base stock; holding cost; critical stock; fuzzy total cost.

DOI: 10.1504/IJADS.2011.039515

International Journal of Applied Decision Sciences, 2011 Vol.4 No.2, pp.129 - 147

Published online: 29 Sep 2014 *

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