Title: A fuzzy random continuous review inventory model with a mixture of backorders and lost sales under imprecise chance constraint

Authors: Oshmita Dey; Bibhas C. Giri; Debjani Chakraborty

Addresses: Department of Mathematics, Jadavpur University, Kolkata-700032, India ' Department of Mathematics, Jadavpur University, Kolkata-700032, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India

Abstract: The article investigates a constrained continuous review inventory system with a mixture of backorders and lost sales. The proposed model is developed with the annual customer demand incorporated as a fuzzy random variable. The lead-time is assumed to be constant while the lead-time demand is assumed to be connected to the annual fuzzy random demand through the length of the lead-time. A budget constraint is imposed on the model in the form of an 'imprecise' chance constraint to present a possible way of quantifying fuzzily defined uncertain information of the constraint. A methodology is proposed to determine the optimal order quantity and the reorder point such that the total cost incurred is minimised subject to the constraint. A numerical example is given to illustrate the proposed methodology.

Keywords: continuous review; inventory modelling; backorders; lost sales; fuzzy random demand; imprecise chance constraints; fuzzy logic; order quantity; reorder point.

DOI: 10.1504/IJOR.2016.075648

International Journal of Operational Research, 2016 Vol.26 No.1, pp.34 - 51

Received: 28 Nov 2013
Accepted: 07 Mar 2014
Published online: 31 Mar 2016 *

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