Hindawi Publishing Corporation Advances in Decision Sciences Volume 2012, Article ID 638060, 16 pages doi:10.1155/2012/638060 Research Article A Warehouse Imperfect Fuzzified Production Model with Shortages under Inflationary Conditions S. R. Singh, 1 Shalini Jain, 2 and Sarla Pareek 2 1 Department of Mathematics, D.N. College, Meerut 250001, India 2 Centre for Mathematical Sciences, Banasthali University, Banasthali, Rajasthan 304022, India Correspondence should be addressed to S. R. Singh, shivrajpundir@gmail.com Received 30 April 2012; Revised 17 October 2012; Accepted 9 November 2012 Academic Editor: S. Dempe Copyright q 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. 1. Introduction One of the weaknesses of some production-inventory models is the unrealistic assumption that all items produced are of good quality. But production of defective units is a natural phenomenon in a production process. Defective items should be treated as a result of imperfect quality production. The effect of an imperfect process on production run time and EPQ was initially studied by Rosenblatt and Lee 1. In their study, the elapsed time until the process shift was assumed to be exponentially distributed. The optimal production run was found to be shorter than that of classical EPQ model. In recent years, numerous research efforts have been undertaken to extend the work of Rosenblatt and Lee 1. Kim and Hong 2 extended the work of Rosenblatt and Lee 1 by assuming that elapsed time