A fast procedure for computing the total system cost of an appointment schedule for medical and kindred facilities

Scheduling outpatients and medical operation rooms has the following struct ure: N users are given appointment times to use a facility, the duration re quired by the facility to service each user is stochastic. The system incur s a "user idle cost" if a user arriving at the appointed time finds the fac ility still engaged by preceding users, while a "facility idle cost" is inc urred if the facility becomes free before the next user arrives. We develop an accurate procedure to compute the expected total system costs for any g iven appointment schedule. Compared to earlier related procedures, ours is much faster and can handle larger problems as well as very general service- time distributions. We then show that this fast computation procedure enabl es one to determine easily the "lowest-cost appointment schedule" for any g iven "job" (i.e., "user") sequence. This in turn will enable one to search for the optimal job sequence that has the best "lowest-cost appointment sch edule".