* Corresponding author. Tel./fax: +91 33 24146717. E-mail addresses: bibhas_pnu@yahoo.com (B. C. Giri), © 2010 Growing Science Ltd. All rights reserved. doi: 10.5267/j.ijiec.2010.04.001 International Journal of Industrial Engineering Computations 2 (2011) 179–192 Contents lists available at GrowingScience International Journal of Industrial Engineering Computations homepage: www.GrowingScience.com/ijiec Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochastic/fuzzy demand rate K. A. Halim a , B. C. Giri a and K. S. Chaudhuri a a Department of Mathematics,Jadavpur University, Kolkata 700 032, India A R T I C L E I N F O A B S T R A C T Article history: Received 1 May 2010 Received in revised form 8 July 2010 Accepted 9 July 2010 Available online 9 July 2010 In this article, we consider a single-unit unreliable production system which produces a single item. During a production run, the production process may shift from the in-control state to the out-of-control state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models. © 2010 Growing Science Ltd. All rights reserved. Keywords: Inventory Production planning Imperfect production Fuzzy number Graded mean integration representation method 1. Introduction Inventory represents an important asset to any business organization. After the pioneering work by Harris (1915) who developed the classical economic order quantity (EOQ) model with known constant demand, a great deal of researches on inventory modeling have been conducted to capture many interesting and realistic situations. However, in real world inventory systems, there exist parameters and variables which are uncertain or almost uncertain. When these uncertainties are significant, they are usually treated by probability theory. Of course, to address such an uncertainty, we need to prescribe an appropriate probability distribution. In some cases, uncertainties can be defined as fuzziness or vagueness, which are characterized by fuzzy numbers of the fuzzy set theory. Zadeh (1965) introduced fuzzy set theory to deal with quality-related problems with imprecise demand. Bellman and Zadeh (1970) distinguished the difference between randomness and fuzziness by showing that the former deals with uncertainty regarding membership or non-membership of an