Using Information on Unconstrained Student Demand to Improve University Course Schedules

We examine how using information on unconstrained demand can improve operational decisions. Specifically, we examine the widespread problem of developing course schedules in not-for-profit university settings. We investigate the potential benefit of incorporating, into the scheduling process, information on the unconstrained demand of students for courses. Prior to this study, the status quo in our college, like that in a large proportion of university settings, was building the course schedule to avoid time conflicts between required courses and to minimize time conflicts between designated groups of courses, such as electives in a particular area. Compared to the status quo approach, we find that, based on three semester's worth of actual data, an approach that explicitly considers students’ course preferences improves a student-based metric of schedule quality on the order of over 4% (which is the equivalent, in our setting, of improving service for over 20% of students).

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.

Labor Scheduling Using NPV Estimates of the Marginal Benefit of Additional Labor Capacity

An extensive literature exists on the problems of daily (shift) and weekly (tour) labor scheduling. In representing requirements for employees in these problems, researchers have used formulations based either on the model of Dantzig (1954) or on the model of Keith (1979). We show that both formulations have weakness in environments where management knows, or can attempt to identify, how different levels of customer service affect profits. These weaknesses results in lower-than-necessary profits. This paper presents a New Formulation of the daily and weekly Labor Scheduling Problems (NFLSP) designed to overcome the limitations of earlier models. NFLSP incorporates information on how changing the number of employees working in each planning period affects profits. NFLP uses this information during the development of the schedule to identify the number of employees who, ideally, should be working in each period. In an extensive simulation of 1,152 service environments, NFLSP outperformed the formulations of Dantzig (1954) and Keith (1979) at a level of significance of 0.001. Assuming year-round operations and an hourly wage, including benefits, of $6.00, NFLSP's schedules were $96,046 (2.2%) and $24,648 (0.6%) more profitable, on average, than schedules developed using the formulations of Danzig (1954) and Keith (1979), respectively. Although the average percentage gain over Keith's model was fairly small, it could be much larger in some real cases with different parameters. In 73 and 100 percent of the cases we simulated NFLSP yielded a higher profit than the models of Keith (1979) and Danzig (1954), respectively.