Long-term inventory policy-making through fuzzy decision-making models

The inventory policy, meant as a replenishment rule, has a considerable impact on most firms. The paper considers the determination of optimal inventory policy of firms from a global viewpoint of top management. The inventory is represented as a fuzzy system with the fuzzy inventory level as the output, the fuzzy replenishment as the input and fuzzy demand. The control problem is formulated in terms of decision-making in a fuzzy environment with fuzzy constraints imposed on replenishments, a fuzzy goal for preferable inventory levels to be attained and the fuzzy decision as the intersection of fuzzy constraints and the fuzzy goal at subsequent stages. The planning horizon is infinite. The problem is to find an optimal time-invariant strategy relating the optimal replenishments to the current inventory levels, maximizing the membership function of fuzzy decision. The existence of such a strategy is proved and an algorithm for its determination is given. The optimal time-invariant strategy obtained is represented as a fuzzy conditional statement equated with a fuzzy relation which is the firm's optimal fuzzy replenishment rule.