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.

Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem

This paper presents an integer programming model for developing optimal shift schedules while allowing extensive flexibility in terms of alternate shift starting times, shift lengths, and break placement. The model combines the work of Moondra (1976) and Bechtold and Jacobs (1990) by implicitly matching meal breaks to implicitly represented shifts. Moreover, the new model extends the work of these authors to enable the scheduling of overtime and the scheduling of rest breaks. We compare the new model to Bechtold and Jacobs' model over a diverse set of 588 test problems. The new model generates optimal solutions more rapidly, solves problems with more shift alternatives, and does not generate schedules violating the operative restrictions on break timing.