... efficiency of suppliers. Design/methodology/approach The authors propose a modified data model considering undesirable output and dual-role factors. The study integrates the modified data envelopment analysis model into the distance function of the Malmquist–Luenberger index. Moreover, this study uses...

.../methodology/approach By using data envelopment analysis models, the authors propose to maximize the sale allocating efficiency scores to satisfy the hypothesis that the shampoo market is efficient, and then, the sales functions, linear and exponential, can be determined and specified. Findings...