Comparison of a branch-and-bound heuristic, a newsvendor-based heuristic and periodic Bailey rules for outpatients appointment scheduling systems

Appointment-based service systems admit limited number of customers at a specific time interval to make service providers more accessible by reducing customers’ waiting time and make the costly resources more productive. A traditional approach suggests the Bailey rule, which assigns one or more customers at the initial block and only one customer at remaining blocks. We prescribe two heuristic approaches and variations of the traditional Bailey rule to appointment scheduling systems with the objective of minimizing total expected costs of delay and idle times between blocks. The first heuristic adopts a branch-and-bound approach using forward dynamic programming and tries to fully enumerate with some restrictions. The second heuristic uses a sequential-inverse newsvendor approach using a starting solution. We conduct numerical tests, which show that both heuristics get near-optimal solutions in a quicker time than a commercial solver, CPLEX and that the second approach gives near-optimal solutions far faster than the first approach. In addition, we suggest the use of a periodic Bailey rule, which can be implemented easily in practice, and provides a close solution to the best result of both heuristics, depending upon cost parameters and service-time variances.