Solution of an EPQ model for imperfect production process under game and neutrosophic fuzzy approach

Abstract

This article deals with an Economic Production Quantity (EPQ) deteriorating inventory model for non-random uncertain environment. It includes rework process, screening of imperfect items and partial backlogging. The items are partially serviceable, because at the time of production some items are found to be defective which cannot be recoverable or serviceable. At first, we develop a cost minimization problem under several assumptions related to imperfect items and rework process under certain linear constraints. We solve the crisp model (primal nonlinear problem) first, and then we convert this model into equivalent game problem taking the help of the theories related to strong and weak duality theorem. However, this game problem consists of the Lagrangian function that correspond a nonlinear objective function subject to some linear constraints. The main objective of the study is to develop a solution procedure of the problem associated to an imperfect process where all unit cost components might increase or decrease neutrosophically. Thus, according to the experiences gained by the decision maker (DM) we fuzzify all cost components as sub-neutrosophic offset. To defuzzify the model we have utilized the sine cuts of neutrosophic fuzzy numbers followed by a solution procedure developed in solving the matrix game exclusively. To validate the model, a numerical example is studied then we have compared the optimal results among the original problem, the equivalent game problem and the game problem under neutrosophic environment explicitly. Our findings reveal that under negative α-cuts the value of the objective function assumes lower and higher values. Finally, sensitivity analysis, graphical illustrations, conclusions and scope of future works have been discussed.