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 or on the model of Keith. The paper shows that both formulations have weaknesses in environments where management knows, or can attempt to identify, how different levels of customer service affect profits. These weaknesses result 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. NFLSP 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 and Keith 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 Dantzig and Keith, 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 that were simulated, NFLSP yielded a higher profit than the models of Keith and Dantzig, respectively.