Multi-item Supplier Selection Model with Fuzzy Risk Analysis Studied by Possibility and Necessity Constraints

Three different supplier selection models have been developed in crisp and fuzzy environments. Here two objective functions have been considered, profit and risk. In this paper, profit has been maximized and risk has been minimized with some constraints. Each supplier has an limited capacity. The purchasing cost of each item from different supplier as well as associative risk is known. The total space and budget of a retailer are constant. In Model I, all the parameters are considered as crisp. In Model II, the demand has been considered as fuzzy. In Model III, the risk values and demand have been considered as fuzzy. To defuzzyfy the fuzzy constraints, necessity and possibility have been introduced. To defuzzyfy the fuzzy objective, two different methods, credibility measure and alpha-cut method have been introduced. All the models have been illustrated numerically using multi-objective genetic algorithm (MOGA). Also a sensitivity analysis has been done taking different sets of risk values and a comparison result has been shown for credibility measure and alpha-cut-method-for Model-III.