Estimating and Testing Achievable Capacity Index with Exponentially Distributed Demand

Abstract

Achievable Capacity Index proposed by Su and Pearn [12-13] is a new evaluation tool, which can accurately measure the profitability of newsboy-type product with normally distributed demand. However, in practical situations, the demand variable is non-normal distributed. In this paper, we attempt to investigate a probable case that the demand is exponentially distributed. The corresponding index denoted by is developed and the statistical properties of its estimator are derived. Based on this index, we implement a hypothesis testing for examining whether the profitability reaches a specified level. The critical values of the test are tabulated for some commonly used profitability requirements. We also carry out the sample size determination by means of designated Type I error and Type II error. Finally, a real example taken from a retail store in Taiwan is presented to illustrate the applicability of our approach.