Abstract
- With the excitement of the 2021 Olympics, the popularity of the ancient Greek sport, gymnastics, is on the rise. Gymnastics has become one of the leading summer Olympic sports to watch and children around the world are getting involved. As a result, gymnastics facilities must identify a weekly personnel schedule that seeks the most cost-effective set of coach-to-program assignments using a cross-trained workforce with varying availability. Typically, gymnastic facility business owners require 24+ hours to complete the formulation of an 8-week personnel schedule, which is not easily adjusted due to the complexity of hard copy calculations, employee job qualifications and established coach-to-gymnast relationships. We first identify the optimal (utopian) assignment plan using an integer linear programming problem. The optimal coach-to-program assignment can differ considerably from the status quo, requiring multiple reassignments from the current state to reach optimality. Making these adjustments with minimal coach reassignment maintains a level of comfort and familiarity with the children and sustains a level of staffing cost which is ideal for the business operations. We utilize the multiple objective optimization technique to identify the n best coach-to-program reassignments from the current state that provide the greatest progress toward the utopian staffing cost solution. This provides the decision maker with a summary of the trade-off between the number of program reassignments and the resulting progress achieved toward the optimal staffing cost. The decision maker can then make an informed decision about the best number of program reassignments (n) to choose based on the staffing cost objective; in other words, identifying the desired level of disruption (or reassignment) and the impact on staffing cost.