This paper considers the ranking of alternative replenishment policies for a single-location inventory when customer demand is confined to a single product. It is supposed that customer demand is uncertain and described by imprecise linguistic terms defined by fuzzy sets. For example, ‘demand is about d’ or ‘demand is more or less between dL and dU’, or more complex ‘demand is about d, but there is a possibility to be 2d’, etc. Four alternative replenishment policies are considered in particular: (1) fixed cycle–fixed order quantity, (2) fixed cycle–variable order quantity, (3) variable review period–fixed 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 fill 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 defined 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 finite 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.
