Multicriteria ranking of inventory replenishment policies in the presence of uncertainty in customer demand

This paper considers the ranking of alternative replenishment policies for a single-location inventory when customer demand is con"ned to a single product. It is supposed that customer demand is uncertain and described by imprecise linguistic terms de"ned by fuzzy sets. For example, `demand is about da, or `demand is more or less between d and d a, or more complex `demand is about d, but there is a possibility to be 2da, etc. Four alternative replenishment policies are considered in particular: (1) "xed cycle}"xed order quantity, (2) "xed cycle}variable order quantity, (3) variable review period}"xed order quantity, and (4) variable review period}variable order quantity. With each replenishment policy a number of criteria are associated. Typical criteria examined are: (a) average "ll rate, (b) inventory holding cost per item delivered, (c) regularity of the replenishment orders with regard to time and quantity of ordering. Criteria values for each replenishment policy can be obtained either analytically or by using a simulation technique, or they are linguistic subjective judgements de"ned by fuzzy sets, like, for example, the values of criterion (c). In order to choose the best replenishment policy, a procedure for selecting a compromised optimistic}pessimistic solution is developed and applied. It enables the comparison of a "nite number of alternative replenishment policies with respect to a number of criteria, simultaneously, when the criteria values are either cardinal or linguistic terms, and the relative weights of the criteria are vaguely expressed. An illustrative example is given. 2001 Elsevier Science B.V. All rights reserved.