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This study has developed a production inventory model where the cycle time is fuzzy, the existence of defective products is assumed in each batch and product screening is performed both in-production and after-production. Triangular fuzzy numbers serve to model uncertainties in the cycle time, and a fuzzified total inventory profit function is created by the defuzzification method known as the signed distance method. The classical approach is used to determine the optimal policy, with the ideal cycle time matched to the total profit. Although assuming asymmetric triangular fuzzy numbers prevents the calculation of a clear analytical solution, the method approaches as closely as possible to an analytical solution. A numerical solution to only one equation is needed to obtain the optimal configuration. Conversely, there is a positive trade-off, with an analytical solution to the optimization problem if there is an assumption of symmetrical triangular fuzzy numbers. The proposed model is illustrated by a numerical example. The paper presents results and sensitivity analyses, in both tables and graphic illustrations. The effects on total profit are discussed in relation to various parameters. From the numerical studies, it is observed that the level of fuzziness influences the cycle time and an approximately linear relationship, in the opposite direction, was found between the total profit and the level of fuzziness, when it was increased. |
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