A fully fuzzified, intelligent theory-of-constraints product-mix decision

Abstract

The present research work outlines a fuzzified approach using fuzzy linear programming (FLP) using a suitably designed smooth logistic membership function (MF) for finding fuzziness patterns at disparate levels of satisfaction for theory of constraints-based (TOC) product-mix decision problems. The objective of the present work is to find fuzziness patterns of product-mix decisions with disparate levels of satisfaction of the decision-maker (DM). Another objective is to provide a robust, quantified monitor of the level of satisfaction among DMs and to calibrate these levels of satisfaction against DM expectations. Product-mix decision should take into account considerations such as the DM's level of satisfaction (sometimes called ‘emotions’) in order to make the decision a robust one. Sensitivity of the decision has been focused on a bottleneck-free, optimal product-mix solution of a TOC problem. The inefficiency of traditional linear programming (LP) in handling multiple-bottleneck problems using TOC is discussed using an illustrative example. Relationships among the degree of fuzziness, level of satisfaction and the throughput of modified TOC guide decision-makers (DM) under tripartite fuzzy environment in obtaining their product-mix choice trading-off with a pre-determined allowable fuzziness.