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 alternative shift starting times, shift lengths, and break placement. The model combines the work of Moondra (Moondra, S. L. 1976. An L. P. model for work force scheduling for banks. J. Bank Res. 7(4) 299--301.) and Bechtold and Jacobs (Bechtold, S. E., L. W. Jacobs. 1990. Implicit optimal modeling of flexible break assignments in labor staffing decisions for service operations. Management Sci. 36(11) 1339--1351.) 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.