The schedules illustrated in our examples are assumed to be fixed. Each employee works a specific cyclic pattern with specified days off. Because of the desire for free weekends, there is the possibility of workers rotating through the several schedules. This creates a different problem because the number of work days between the individual schedules will vary. For example, the schedule that we used to explain the day-off algorithm resulted in the following:
Workdays Days off
Worker 1 M – F S — Su
Worker 2 Su – Th F – S
Worker 3 M – F S – Su
Worker 4 W – Su M – T
If one rotates through these schedules, the number of workdays between days off is variable. Shifting from the first schedule to the second, there are only four workdays between days off; from the second to the third, there are six workdays; and from the third to the fourth, there are zero workdays, there being two consecutive sets of days off. If the sequence of the schedules is changed, the patterns of work days between days off will also change, but the new pattern will probably also have problems. These variations in the numbers of workdays between rotating schedules are often unacceptable, even though they average out over a period of time.
Additional Work Rule Constraints: Baker and Magazine (1977) provide algorithms for days off constraints in addition to the two consecutive days off constraint that we have discussed. These more constraining situations include the following:
1) Employees are entitled to every other weekend off and to four days off every two weeks.
2) Employees are entitled to every other weekend off and to two pairs of consecutive days off every two weeks.
When part time workers can be used, the problem of scheduling personnel is eased somewhat. The scheduling of the part time workers then becomes an interesting problem.
Using Part time Workers:
When demand for service varies significantly but follows a fairly stable weekly pattern, the use of part time employees can give managers added flexibility. Mabert and Raedels (1976) reported such an application involving eight branch offices of the Purdue National bank.
Daily Work shift Scheduling:
Here are many situations where services for operations are required on a 24 hour basis and where the demand for services is highly fluctuating. For example, Figure shows the number of incoming calls at a telephone exchange during a 24 hour period. It is clear from this figure that the telephone company must schedule operators judiciously so that the load is met and the costs are minimized. Hospitals, banks, supermarkets, and police departments all face similar problems in meeting a highly varying demand.
Buffa, Cosgrove, and Luce (1976) have developed an approach for scheduling workers or operators so that requirements are met as closely as possible. The approach begins with a forecast of daily demand (the daily number of calls in the telephone exchange example) that considers seasonal, weekly, and special day effects as well as trends. This forecast is converted to a distribution of operator requirement by half hour increments. Based on the distribution of operator requirements, a schedule of tours or shifts is developed and, finally specific operators are assigned to tours. The key idea in designing shifts to meet load is to utilize flexibility in shift lengths and in the positioning of lunch hours and rest periods. The shifts should meet the constraints imposed by state and federal law, union agreements, company policy, and other practical considerations.
Work shift scheduling problems can be formulated as integer programming problems. However, the solution of large size, real world problems by these methods is computationally prohibitive except for some problems with very special structures. Heuristic solutions have been used to obtain very good, though not optimal, solutions for large problems. Integrated systems for scheduling work shifts have been developed in the telephone industry, in the postal service, and for nurse scheduling. These integrated systems make it possible to schedule shifts and personnel for fairly large operations, based on forecasts. Managers of such systems can meet service performance requirements at minimum costs on a routine basis.