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.

Accounting for the Multi-Period Impact of Service When Determining Employee Requirements for Labor Scheduling

Providing good customer service, inexpensively, is a problem commonly faced by managers of service operations. To tackle this problem, managers must do four tasks: forecast customer demand for the service; translate these forecasts into employee requirements; develop a labor schedule that provides appropriate numbers of employees at appropriate times; and control the delivery of the service in real-time. This paper focuses upon the translation of forecasts of customer demand into employee requirements. Specifically, it presents and evaluates two methods for determining desired staffing levels. One of these methods is a traditional approach to the task, while the other, by using modified customer arrival rates, offers a better means of accounting for the multi-period impact of customer service. To calculate the modified arrival rates, the latter method reduces (increases) the actual customer arrival rate for a period to account for customers who arrived in the period (in earlier periods) but have some of their service performed in subsequent periods (in the period). In an experiment simulating 13824 service delivery environments, the new method demonstrated its superiority by serving 2.74% more customers within the specified waiting time limit while using 7.57% fewer labor hours.