Shift Scheduling in Services When Employees Have Limited Availability: An L. P. Approach

This paper compares two linear programming (LP) models for shift scheduling in services where homogeneously-skilled employees are available at limited times. Although both models are based on set covering approaches, one explicitly matches employees to shifts, while the other imposes this matching implicitly. Each model is used in three forms—one with complete, another with very limited meal break placement flexibility, and a third without meal breaks—to provide initial schedules to a completion/improvement heuristic. The term completion/improvement heuristic is used to describe a construction/ improvement heuristic operating on a starting schedule. On 80 test problems varying widely in scheduling flexibility, employee staffing requirements, and employee availability characteristics, all six LP-based procedures generated lower cost schedules than a comparison from-scratch construction/improvement heuristic. This heuristic, which perpetually maintains an explicit matching of employees to shifts, consists of three phases which add, drop, and modify shifts. In terms of schedule cost, schedule generation time, and model size, the procedures based on the implicit model performed better, as a group, than those based on the explicit model. The LP model with complete break placement flexibility and implicitly matching employees to shifts generated schedules costing 6.7% less than those developed by the from-scratch heuristic.

Improving the Utilization of Front-Line Service Delivery System Personnel

There are two types of work typically performed in services which differ in the degree of control management has over when the work must be done. Serving customers, an activity that can occur only when customers are in the system is, by its nature, uncontrollable work. In contrast, the execution of controllable work does not require the presence of customers, and is work over which management has some degree of temporal control. This paper presents two integer programming models for optimally scheduling controllable work simultaneously with shifts. One model explicitly defines variables for the times at which controllable work may be started, while the other uses implicit modeling to reduce the number of variables. In an initial experiment of 864 test problems, the latter model yielded optimal solutions in approximately 81 percent of the time required by the former model. To evaluate the impact on customer service of having front-line employees perform controllable work, a second experiment was conducted simulating 5,832 service delivery systems. The results show that controllable work offers a useful means of improving labor utilization. Perhaps more important, it was found that having front-line employees perform controllable work did not degrade the desired level of customer service.