Final answer:
Flextime allows employees to select work schedules that accommodate their personal needs, promoting a work-family balance and aligning with Theory Y, which suggests that employees are more productive when given control over their work life.
Step-by-step explanation:
The term that identifies a system allowing employees to choose among different work start-time and end-time schedules to accommodate their personal needs is Flextime. This system provides employees with the chance to balance work and personal responsibilities effectively. In contrast with rotating shift work, which can disrupt circadian rhythms due to irregular and changing schedules, flextime offers more stable and self-determined scheduling options. It aligns with Theory Y management, which assumes workers are inherently motivated and seek to be productive when given more control over their work life. Subsequently, flextime can improve work-family balance and contribute to a positive shift in organizational culture, fostering a more transformational leadership style.