Differential Evolution: A Tool for Global Optimization

This report describes a tool for global optimization that implements the Differential Evolution optimization algorithm as a new Excel add-in. The tool takes a step beyond Excel’s Solver add-in, because Solver often returns a local minimum, that is, a minimum that is less than or equal to nearby points, while Differential Evolution solves for the global minimum, which includes all feasible points. Despite complex underlying mathematics, the tool is relatively easy to use, and can be applied to practical optimization problems, such as establishing pricing and awards in a hotel loyalty program. The report demonstrates an example of how to develop an optimum approach to that problem.

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.