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An EPQ model for deteriorating items with imperfect production, inspection errors, rework and shortages : a type-2 fuzzy approach

  • Chayanika Rout
  • Ravi Shankar Kumar
  • Debjani Chakraborty
  • Adrijit GoswamiEmail author
Theoretical Article


In this paper, a production inventory model is studied considering imperfect production and deterioration of item, simultaneously. Both the serviceable and reworkable items are assumed to deteriorate with time. A cost-minimizing model is developed incorporating both Type I and Type II inspection errors. Shortages are allowed that are completely backlogged. All the screened items are reworked at the end of the production process. To encounter a more practical situation, the deterioration rate is considered to be a type-2 fuzzy number. Such a situation arises when the vendor assigns, with similar priority, a number of experts to determine the rate of deterioration and the decision given by each expert is in linguistic term, which may be replaced by a fuzzy number. The aim of the proposed model is to calculate the maximum back-order quantity allowed and the optimal lot size that must be produced in order to minimize the overall inventory cost. The problem is solved for both the crisp and fuzzy models and a numerical example with practical application is also presented to exemplify the procedure. A novel method for solving a type-2 fuzzy optimization problem is developed which results in a set of Pareto optimal solutions for the proposed problem. It is followed by presenting a sensitivity analysis of various parameters involved on the decision variables and the cost function for a better illustration of the model.


EPQ Deterioration Imperfect production Type I and Type II inspection errors Rework Shortages Type-2 fuzzy 



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© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Government PolytechnicSaharsaIndia

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