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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.

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.

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.

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.

This study assumes image size and location, product substitution, and product supply to be factors influencing the purchase decision. Under such assumption, shelf-space allocation and inventory theories are integrated, and operating profit and cost of the online store under the supply policy that prevent stockouts are analyzed to develop an optimal model for inventory control and product image allocation. The paper aims to discuss these issues.

The developed model takes both order cost and holding cost into account when calculating the total cost. As the model presented is an integer non-linear programming problem, this study adopts genetic algorithm to solve the problem.

Numerical examples are provided in this study to demonstrate the applicability of the model and to illustrate the search for parameters that possess greater influence over the operating profit of the store.

This study provides a mixed integer non-linear programming model for the joint optimization of graphic design and inventory control problem. Online store owners may take the results of this study as a reference for decision-making purposes.

The purpose of this paper is to re‐evaluate the performance of the adaptive control charts which allow some of their design parameters to change during production depending on the collected information from samples over time. Instead of employing a single performance measure (average time to signal process changes), a set of measures, associated with the inspection efficiency and effort, is taken into account in the evaluation process.

A multivariate analysis of variation (MANOVA) approach along with the post hoc analysis are applied to investigate the performance of different adaptive control charts based on different measures.

The findings indicate that different adaptive control charts may have different performance, depending on the measure regarded and the value of shift in process mean. In general, the VSSC, VSSI, and VSI control charts would be recommended for a process with a small, moderate, and large shift, respectively. The SS chart is still the best choice for a process with an extremely large shift.

Up to now, the proposed procedure has been developed for the comparative analyses of adaptive X¯ charts, but it could be adjusted for other adaptive charts as well.

This paper provides a review of the performance of adaptive control charts from a novel perspective.