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Advances in Decision Sciences
Volume 2012 (2012), Article ID 638060, 16 pages
Research Article

A Warehouse Imperfect Fuzzified Production Model with Shortages under Inflationary Conditions

1Department of Mathematics, D.N. College, Meerut 250001, India
2Centre for Mathematical Sciences, Banasthali University, Banasthali, Rajasthan 304022, India

Received 30 April 2012; Revised 17 October 2012; Accepted 9 November 2012

Academic Editor: S. Dempe

Copyright © 2012 S. R. Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a two-warehouse production model with imperfect items. Production rate is taken as the linear combination of on-hand inventory and demand, while demand rate is taken as function of time. Most of the researchers consider that the production rate is independent from the demand rate. In this paper we assume production rate as being dependent on the demand rate, and this assumption is more realistic. Shortages are allowed and partially backlogged with time-dependent backlogging rate. Due to different preservation facilities we consider that the deterioration rate is time dependent in own warehouse (OW) and Weibull distribution deterioration in rented warehouse (RW). Holding cost in RW is greater than in OW. We developed a fuzzy model with fuzzifying all the costs of the model as triangular fuzzy numbers. The present model is developed in both crisp and fuzzy senses. Finally, numerical example is shown, and sensitivity is also illustrated.