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 I _E 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.

Key Words:

• Achievable capacity index
• exponential
• hypothesis testing
• newsboy problem
• sample size determination.

Additional information

Notes on contributors

Rung-Hung Su

Rung-Hung Su is a Project Manager in SEDA Chemical Products CO., LTD, Taiwan. He received his Ph.D. in Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan and M.S. in Management Science, Tamkang University, Taiwan. His research interests include applied statistics, process capability indices, and production/inventory control

Dong-Yuh Yang

Dong-Yuh Yang is an Associate Professor in Institute of Information and Decision Sciences at National Taipei University of Business, Taiwan. He received his Ph.D. in Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan and M.S. in Applied Mathematics, National Chung Hsing University, Taiwan. His research interests include applied statistics, process capability analysis, fuzzy theory, and queuing theory.

W. L. Pearn

W. L. Pearn is a Chair Professor in Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan. He received his Ph.D. in Operations Research, University of Maryland, USA. His research interests include process capability indices, quality management, applied statistics, network optimization, and queueing system.