Incorporating probabilistic fuzzy sets into the newsvendor model with hybrid data

This paper is to apply a fuzzy newsvendor inventory management approach to analyze optimal order policy based on probabilistic fuzzy sets with hybrid data so that the expected total cost is minimized. We will find that, after defuzzification, the ordering quantity and the expected total cost have slightly different between the fuzzy model and the crisp model when the variation of demand is small. As a result, we verify that the fuzzy newsvendor model is one extension of the crisp models. Most importantly, one may conclude that the fuzzy methodology leads to a better result than using a single point estimate of the unknown demand under the example of exponential distribution.