Scheduling appointments for walk-ins

In addition to scheduled patients, most hospitals in Japan accept walk-ins, and the reduction of the waiting times of both scheduled patients and walk-ins is one of the managerial issues that need to be tackled. Under the stochastic behavior of the consultation time and the arrival of walk-ins, the present study proposes a scheduling method that assigns a scheduled time to each walk-in at the time of arrival and guides him or her to the waiting room at his or her scheduled time. It is assumed that the consultation time window of a physician is divided into several blocks, and each scheduled patient is allocated to one of the blocks in advance. A box is introduced into each block to accommodate walk-ins. A walk-in is assigned to a box if the total workload does not exceed the maximum workload level, which is one of decision variables of the proposed method. Numerical experiments reveal that the proposed method realizes shorter waiting times for walk-ins with increased waiting times for scheduled patients and increased total idle time for the physician. The proposed method also indicates better performance than a static method that allocates a fixed number of slots to walk-ins in each box in advance.