Title: A deterministic two warehouse inventory model for deteriorating items with stock-dependent demand and shortages under the conditions of permissible delay

Authors: S.R. Singh; Rachna Kumari; Neeraj Kumar

Addresses: Department of Mathematics, D.N. College, Meerut (U.P.), 250001 India. ' Department of Mathematics, Meerut College, Meerut (U.P.), 250001 India ' Department of Applied Science, IIMT Engineering College, Meerut (U.P.), 250001 India

Abstract: In this paper, a deterministic inventory model for deteriorating items with two warehouses and shortages is developed. It is observed that in supermarkets, the demand rate is usually influenced by the amount of the stock level, i.e., the demand rate may go up or down with the on-hand inventory level. Influenced by this, we develop a model where the demand is dependent on the present stock level. Trade credit is provided to the customer to attract them and boost up the demand. A rented warehouse (RW) is used when the ordering quantity exceeds the limited capacity of the own warehouse. Due to different storage conditions, deterioration rate in two warehouses may be different. In addition, shortages are neither completely backlogged nor completely lost assuming the backlogging rate to the inversely proportional to the waiting time for the next replenishment. The associated cost minimisation is illustrated by numerical example and also its sensitivity analysis is carried out by using Mathematica-5.2 for the feasibility and applicability of our model.

Keywords: two-warehouse inventory modelling; shortages; stock-dependent demand rate; time-dependent partial backlogging rate; permissible delay; payment delays; deteriorating items.

DOI: 10.1504/IJMMNO.2011.043084

International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.4, pp.357 - 375

Received: 05 Mar 2010
Accepted: 19 May 2010

Published online: 14 Oct 2011 *

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