Final answer:
To foster balance and manage his limited discretionary time effectively, Robert's most effective option would be to inform his friend about his busy schedule and postpone the dinner, while still considering alternative arrangements.
Step-by-step explanation:
To foster balance and manage his limited discretionary time effectively, Robert's most effective option would be to inform his friend about his busy schedule and postpone the dinner (option b). This allows Robert to communicate his time constraints honestly and prioritize his commitments while still maintaining his friendship. By postponing the dinner, Robert can create a plan to schedule a quick coffee meeting during a break in his schedule (option a) or delegate some tasks to free up time for the dinner (option c), depending on the urgency and importance of his other commitments.