With arrival patterns on both day-of-the-week and an hour-of-the-day basis and with highly service times depending on the type of patient, important problems result. First, what can be done to schedule appointments so as to smooth the patient load on physicians? How should appointment schedules be arranged through the week and during the day in light of demand variation? What overall capacity for service is actually needed? How long can patients reasonably be expected to wait for service? Is physician idle time justified? Would a system of priorities help to level loading?
Schedules for Service System:
Service oriented organizations face unique scheduling problems. In all of these kinds of systems, demands for service and the time to perform the service may be highly variable. It often appears that no sensible schedule can be constructed if arrivals for service and service times are random. The result would be to maintain the capability for service at levels sufficient to keep the waiting line to certain acceptable average level, the service facility would be idle for some fraction of the time in order to be able to provide service if needed. In a sense, the scheduling of personnel and physical facilities is simple in such situations, being controlled by policies for the hours during which the service is to be available and for the service level to be offered. Schedules are then simple statements of capacity for service, and personnel and other resources are keyed to these levels. The design for the size of maintenance crews has often been on this basis.
However we can improve on the system response of simply keeping hours. Sometimes overall performance can be improved by a priority system, taking arrivals on other than a first come first served basis. Also, improvements often result from examining the demand to see if there is a weekly and/or daily pattern. When a pattern exists, it may be possible the schedule more effectively to improve service facility utilization, shorten average waiting time, or both. Thus, we have three broad groups of situations: one described by random arrivals at a service center that performs a service requiring variable time, one where priority systems are the basis for improved scheduling and one in which arrivals follow some dominant pattern.
The random arrival, variable service time case is the classic waiting line or queuing problems. When the distribution of arrivals and service times follow certain known mathematical functions, fairly simple equations describe the flow through the system. These computations can be performed for simple situations such as a single chair barber shop, for a multiple server system such as super market check out stands, or for a serial of operations such as assembly line.
One of the variables that may be controllable in waiting line systems is the order of processing of arrivals. For example, in medical facilities, patients will tolerate a priority system that allows emergency cases to be taken first. In machine shops, priority systems are often used to determine the sequence of processing jobs through a service center. Recall that computer simulation of alternate priority rules has shown that certain rules are more effective in getting work through the system on schedule.
When arrivals follow a dominant pattern, we can use that information to schedule personnel and facilities. For example, if arrivals of patients at a clinic followed the weekly pattern shown, we could use an appointment system to counterbalance the pattern and smooth the load over the week. Similarly if the typical daily pattern for physicians’ services in a clinic followed that shown, it could be counterbalanced both by an appointment system and by having a larger number of physicians on duty during the afternoon hours. If physicians could work different periods or shifts, we might be able to find quite good capacity service solutions. Thus the entire subject of work shift scheduling becomes an important issue.