A product mix problem based on maximization of the total profit and reduction of excessive inventories including uncertainty

This paper considers a product mix problem both maximizing the total future profit and reducing excessive inventories including uncertainty with respect to future profits and customers' demands. Furthermore, since a decision maker has a goal with respect to the total future profit and each inventory of the product, in this paper, aspiration levels for them are also introduced. The proposal product mix problem is formulated as a multi-criteria programming problem considering maximizing all aspiration levels assumed to be fuzzy goals. Then, since each future return and customer's demand are assumed to be random variables, this problem including randomness is basically formulated as a multi-criteria stochastic programming problem. Since it is hard to solve it analytically, the transformations into deterministic equivalent problems are introduced and the efficient solution methods are constructed.