Title: An inventory model for Weibull distribution deterioration under price-dependent demand and partial backlogging with opportunity cost due to lost sales

Authors: T. Roy, K.S. Chaudhuri

Addresses: Department of Mathematics, Vidyasagar College for Women, 39, Sankar Ghosh Lane, Kolkata – 700006, India. ' Department of Mathematics, Jadavpur University, Kolkata – 700032, India

Abstract: In this paper, we assume not only the time-proportional backlogging rate to be related to waiting time but also the generalised form of the two-parameter Weibull distribution deterioration rate. This assumption is more appropriate and applicable in practice. The opportunity cost due to lost sales is also introduced in this paper. Pricing is a major policy for retailers to obtain its maximum profit. We develop an inventory model for deteriorating items with price-dependent demand and partial backlogging to determine its optimal selling price, optimal service time and optimal total average cost. The existence and uniqueness of the solutions of the system are also examined. Finally, a numerical example is presented to illustrate the model.

Keywords: inventory modelling; price-dependent demand; Weibull distribution deterioration; partial backlogging; opportunity cost; lost sales; deteriorating items; optimisation; selling price; service time; total average cost.

DOI: 10.1504/IJMIC.2011.040490

International Journal of Modelling, Identification and Control, 2011 Vol.13 No.1/2, pp.56 - 66

Published online: 31 May 2011 *

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