Title: Advertisement policy and reliability dependent imperfect production inventory control problem in bi-fuzzy environment

Authors: Samar Hazari; K. Maity; Jayanta Kumar Dey; Samarjit Kar

Addresses: Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, 713209, India ' Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Purba Medinipur, 721 425, West Bengal, India ' Department of Mathematics, Mahisadal Raj College, Purba-Medinipur, 721628, WB, India ' Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, 713209, India

Abstract: In this study, a problem for advertising policy and an imperfect production for single item are formulated with reliability parameter over a finite time horizon. The advertisement and production rates are function of time which are taken as control variables. In a competitive market on long run business, the demand face the depreciation of sale which is at a constant rate and decrease the demand rate but the advertisement policy has the positive effect to the demand rate. The reliability of the production process is an important factor to improve the quality of product and decrease the defective rate. So the quality of the product and advertisement policy play an important role to capture the customers in a competitive market. The selling price, holding cost and advertisement cost are bi-fuzzy in nature and using bi-fuzzy technique, the problem is converted into equivalent crisp problem and solved using Pontryaginn's maximum principle and generalised reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the model.

Keywords: bi-fuzzy variables; advertisement policy; inventory control; imperfect production; reliability; Pontryaginn maximum principle; product quality; selling price; holding cost; advertisement cost; generalised reduced gradient; GRG.

DOI: 10.1504/IJOR.2015.068286

International Journal of Operational Research, 2015 Vol.22 No.3, pp.342 - 365

Received: 16 Apr 2013
Accepted: 24 Jul 2013
Published online: 09 May 2015 *

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