Journal of Intelligent & Fuzzy Systems 30 (2016) 3527–3541 DOI:10.3233/IFS-162098 IOS Press 3527 A fuzzy random EPQ model with fuzzy defective rates and fuzzy inspection errors Sushil Kumar Bhuiya and Debjani Chakraborty ∗ Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India Abstract. In this paper, we consider an economic production quantity (EPQ) model for imperfect production process under fuzzy random variable demand considering inspection errors. Due to the first stage inspection errors, some proportion of defective items are returned because of dissatisfaction of the customers. In the previous traditional models, the defective rates and the inspection errors follow some probability distributions. However, in real life situation, it is almost impossible to obtain the statistical information precisely. Thus, this study proposes the fuzzy defective rates and the fuzzy inspection errors. In addition, this model interpolates two more stages of inspections, one is after the production run time, and another is after the beginning of the rework process. The purpose of this study is to establish a fuzzy random EPQ model with the fuzzy defective rates and inspection errors. The expected profit per unit time is calculated by using fuzzy random renewal reward theorem. This model maximizes the expected profit per unit time in fuzzy sense. We develop a methodology for finding the global optimal solutions. A numerical example is also provided to illustrate our proposed model. Furthermore, sensitivity analysis is also carried out in order to present some managerial inferences. Keywords: Inventory, imperfect item, inspection error, fuzzy type-I and type-II error, fuzzy random variable 1. Introduction The economic production quantity (EPQ) is one of the most applicable and effective model in the industry. The EPQ model is mostly used to solve the problem of the optimal lot size and the production run-time for maximization of the expected profit. One of the basic assumptions of the classical economic production quantity model is that, the items produced are of perfect quality. However, in the realistic situ- ations, the manufacturer’s production process is not perfect. Thus, the assumption of perfect quality is not realistic in the industrial applications. Shih [36] was the first, who introduced an inventory model to explore the effect of defective products on the ∗ Corresponding author. Debjani Chakraborty, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, India. Tel.: +91 3222 283638; Fax: +91 3222 282276; E-mail: debjani@maths. iitkgp.ernet.in. production lot size and the annual cost of the inven- tory system. Since then, during the last few decades, several researchers have developed EPQ models with imperfect quality of items under various assumptions. The previous existing classic imperfect-quality EPQ model can be mainly categorized into two parts with regard to inspection method of defects connected to the imperfect production process. In the first category, the production system deteriorates in each cycle dur- ing the production process and thus produces some defect items. Those defective items are inspected in regular interval with a constant hazard rate. In the sec- ond category, the inspection of an entire lot screening of the production process with no deterioration has been performed. The survey on the development of the inventory model with imperfect production can be found in [2, 18, 35]. Another unrealistic assumption of the EPQ model with imperfect production process is that the inspec- tion of defective items is 100% correct. In an EPQ 1064-1246/16/$35.00 © 2016 – IOS Press and the authors. All rights reserved