Maximizing Customer Retention in Multi-session Training Service: Model and Algorithm
研究了如何通过活动排程最大化多期培训项目的客户整体留存，构建了0-1约束指数和问题并设计了几何分支定界算法，发现奖励、难度和价值的提高分别导致U形、倒U形和递增子序列。
Training is an important business in the service sector. Usually, a training program involves multiple sessions and each session contains multiple activities. Although it is essential for customers to participate in all training sessions and activities, many customers fail to complete the program because the training experience is too stressful. Given the importance of customer retention in the training programs, we investigate the modeling and optimization of the retention-oriented training program design problem (RTDP), which maximizes overall service retention across all training sessions through activity scheduling. Customers make their participation decisions about their next training session based on the remembered holistic utility of past training activities. By our analysis, RTDP is a 0–1 constrained exponential sum problem, which we prove to be NP-hard. To resolve RTDP, we introduce a geometric branch and bound algorithm that efficiently searches for the optimal solution by resolving a series of subproblems. From a numerical study, we find that higher reward, difficulty, and value lead to more U-shaped, inverted U-shaped, and increasing subsequences in each session, respectively. The reason is that higher reward favors sequences with a pleasant start and a sharp positive gradient toward the end, higher difficulty requires warm-up and cool-down, and higher value makes customers emphasize the end experience. Finally, we extend our research by investigating RTDP with session breaks and discussing the joint retention-performance optimization. When there are breaks between sessions, we find that as the break duration increases, the optimal value first increases and then decreases. For the joint retention-performance optimization, the optimal sequence is more pulsed if the service designer cares more about customer performance and flatter if the service designer cares more about customer retention.