In the field of inventory management, a profitability evaluation for ordered products is crucial to retailer revenue. Formulating such evaluations requires determining an appropriate order quantity, while ensuring that the product has high profitability potential. The achievable capacity index (ACI) provides a simple breakdown of profitability suitable for newsboy-type products with probabilistic distributed demand under the optimal order quantity. In this study, we investigated the lower confidence bound of ACI (LCBA) to obtain a conservative evaluation of profitability. Obtaining an explicit formula for the LCBA is difficult; therefore, we adopted parametric bootstrap methods to approximate the value for the LCBA. We also created a computational algorithm using R software to simulate the performances of various parametric bootstrap methods. Coverage rates and the corresponding ratios for various sample sizes and expected ACI values were tabulated to facilitate the selection of a suitable method and decide a required sample size with a conservative estimate. An illustrative example was presented to demonstrate the applicability of the proposed method and provide managerial insights.

In queueing systems, achieving a reasonable balance between system performance and service quality requires strict control over arrivals. $ F $-policy is a control policy that forbids the entry of new customers when the system is full, only allowing entry when the size of the system is reduced to a predetermined value $ F $. Enhancing server efficiency is another effective approach to improve service quality. This paper considers an $ F $-policy GI/M/1 queue with alternating service rates, which can be upgraded in accordance with the state of the system. Steady-state analysis is performed using a recursive method in conjunction with the supplementary variable technique. Steady-state probability is used to evaluate critical system characteristics and perform sensitivity analysis. A bi-objective optimization scheme is then formulated using the NSGA-Ⅱ and two multi-objective evolutionary algorithms (MOEAs) in accordance with the performance measures to minimize the expected cost function per unit time as well as the expected waiting time. Numerical results demonstrate that the marginal utility of increasing the budget decreases when the expected waiting time is low. Regression models are also formulated to facilitate decision-making.