An EPQ model for an imperfect production process with fuzzy cycle time and quality screening

This study has developed a production inventory model where the cycle timeis fuzzy, the existence of defective products is assumed in each batch andproduct screening is performed both in-production and after-production.Triangular fuzzy numbers serve to model uncertainties in the cycle time, anda fuzzified total inventory profit function is created by thedefuzzification method known as the signed distance method. The classicalapproach is used to determine the optimal policy, with the ideal cycle timematched to the total profit. Although assuming asymmetric triangular fuzzynumbers prevents the calculation of a clear analytical solution, the methodapproaches as closely as possible to an analytical solution. A numericalsolution to only one equation is needed to obtain the optimal configuration.Conversely, there is a positive trade-off, with an analytical solution tothe optimization problem if there is an assumption of symmetrical triangularfuzzy numbers. The proposed model is illustrated by a numerical example. Thepaper presents results and sensitivity analyses, in both tables and graphicillustrations. The effects on total profit are discussed in relation tovarious parameters. From the numerical studies, it is observed that thelevel of fuzziness influences the cycle time and an approximately linearrelationship, in the opposite direction, was found between the total profitand the level of fuzziness, when it was increased.