Solving an imperfect EPQ model with safety stock for type-I and type-II screening error under constrained fuzzy Newton interpolation approach

Abstract

This article deals with an industrial production process of a single item with safety stock and deterioration over time. First of all, we have considered an economic production quantity (EPQ) inventory model where the items are screened multiple times and the screening process itself has Type-I and Type-II errors. Some parts of the imperfect items are reworkable (serviceable) and the unusable items are discarded from the inventory instantly. Incorporating rework cost, disposal cost and screening cost in the inventory process, a total average system cost function has been studied and it has been optimized analytically. But to capture the flexibilities of the demand rate and all unit cost components (for comparative analysis) a fuzzy model has been developed. Indeed, we know that the defuzzification is a crucial step in any fuzzy inferential system, aimed at converting fuzzy outputs into equivalent crisp values for final decision-making. To get the model optimum we optimize the fuzzy membership function developed with the help of Newton’s general interpolation formula for the proposed constrained non-linear optimization problem. The major novelties of this work include the construction of a new fuzzy membership function and techniques of decision making by means of a solution algorithm. For model validation, a numerical example has been analyzed on the basis of a case study and it has been compared with some of the existing methods. Findings reveal that the proposed method dominates others and up to 39.36% cost reduction is possible as a whole. Finally, sensitivity analysis and graphical illustrations have been carried out, followed by scope of future work.