Bayesian assessment of profitability for products with highly uncertain demand based on multiple samples

Abstract Accepted by: M. Zied BABAI The achievable capacity index (ACI) is well suited to measuring the profitability of a newsboy-type product, wherein profitability is defined as the probability of achieving a target profit under the optimal order quantity. In retail/manufacturing situations where storage and production capacity are limited, profitability evaluation using ACI can be considered to select advantageous products. Although frequentist approaches are useful towards estimating the true ACI, the Bayesian approach may be preferable when prior information about the demand is available. In estimating the ACI, it may be necessary to deal with situations in which the demand is highly uncertain, the sample data consist of distinct subsets drawn from a demand population (i.e., multiple samples), and sampling error must be eliminated to avoid overestimates of profitability. This study seeks to overcome these issues by developing a Bayesian procedure for testing profitability based on multiple samples, focusing on exponentially distributed demand that can exhibit high uncertainty. The lower confidence bound of ACI is derived to express profitability estimates without sampling error. We also provide some tables to facilitate decision-making in evaluating profitability. We find that variations in confidence level and the evaluated criterion significantly influence the direction of decision-making, guiding managers to focus on controlling these factors. The practicality of the proposed method was demonstrated through a case study.