Decision-making in a single-period inventory environment with fuzzy demand

This paper first defines the profitability to be the probability of achieving a target profit under the optimal ordering policy, and introduces a new index (achievable capacity index; IA) which can briefly analyze the profitability for newsboy-type product with normally distributed demand. Note that since the level of profitability depends on the demand mean μ and the demand standard deviation σ if the related costs, selling price, and target profit are given, the index IA is a function of μ and σ. Then, we assess level performance which examines if the profitability meets designated requirement. The results can determine whether the product is still desirable to order/manufacture. However, μ and σ are always unknown, and the demand quantity is common to be imprecise, especially for new product. To tackle these problems, a constructive approach combining the vector of fuzzy numbers is introduced to establish the membership function of the fuzzy estimator of IA. Furthermore, a three-decision testing rule and step-by-step procedure are developed to assess level performance based on fuzzy critical values and fuzzy p-values.