Applying the bootstrap method to newsvendor model incorporating group buying for optimal price discount and order quantity

Abstract

Purpose Group buying (GB) is a shopping strategy through which customers obtain volume discounts on the products they purchase, whereas retailers obtain quick turnover. In the scenario of GB, the optimal discount strategy is a key issue because it affects the profit of sellers. Previous research has focused on exploring the price discount and order quantity with a fixed selling price of the product assuming that customer demand is uncertain (but follows a known distribution). This study aims to look at the same problem but goes further to examine the case where not only customer demand is certain but also the demand distribution is unknown. Design/methodology/approach In this study, optimal price discount and order quantity of a GB problem cast as a price-setting newsvendor problem were obtained assuming that the distribution of customer demand is unknown. The price–demand relationship is considered in addition form and product form, respectively. The bootstrap sampling technique is used to develop a solution procedure for the problem. To validate the usefulness of the proposed method, a simulated comparison of the proposed model and the existing one was conducted. The effects of sample size, demand form and parameters of the demand form on the performance of the proposed model are presented and discussed. Findings It is revealed from the numerical results that the proposed model is appropriate to the problem at hand, and it becomes more effective as sample size increases. Because the two forms of demand indicate restrictive assumptions about the effect of price on the variance of demand, it is found that the proposed model seems to be more suitable for addition form of demand. Originality/value This study contributes to the growing literature on GB models by developing a bootstrap-based newsvendor model to determine an optimal discount price and order quantity for a fixed-price GB website. This model can assist the sellers in making decisions on optimal discount price and order quantity without knowing the form of customer demand distribution.