Estimating conservative profitability of a newsboy-type product with exponentially distributed demand based on multiple samples

In the present inventory management, the manager must determine an appropriate order quantity, while ensuring that the product has high potential profitability. However, the following issues may be encountered when estimating product profitability: (i) a newly launched product may belong to high uncertainty demand; (ii) the market demand is obtained from multiple samples; (iii) the sampling error probably leads to overestimating profitability. To explore the above issues, our study developed an estimation method based on multiple samples for assessing the conservative profitability of a newsboy-type product with exponentially distributed demand. Note that profitability is defined as the maximum probability of achieving a target profit. First, we adopted an achievable capacity index (ACI) with a streamlined form to measure the extent of profitability. The unbiased and efficient estimator of ACI and its statistical properties were also derived. Then, the lower confidence bound of ACI (LCBA) was derived to express the conservative profitability of the newsboy-type product. The LCBA values for various number of groups, sample sizes, confidence levels, and estimates were tabulated. These generic tables can guide the direction of decision-making in some policies. For example, by looking up these tables, the retailers can decide which items are worth selling, and the manufacturers can decide to accept or reject the contract renewal of production orders. Considering the impact of high cost for sampling, the minimum data size requirement meeting an acceptable criterion is also presented. Finally, a real-world example regarding the production order of vacuum molding products was performed to illustrate the practicality of our method. Some managerial insights for the explored example were also presented according to the results of the sensitivity analysis.