Mathematical Models for Studying the Value of Motivational Leadership in Teams

Mathematical models are presented for studying the value of leadership in a team where the members interact with each other. The models are based on a leader’s role of motivating each team member to perform closer to his/her maximum ability. These models include controllable parameters whose values reflect the amount of task interdependence among the workers as well as the motivational skill and variability in the skill of the leader. Confirming results—such as the fact that the skill level of the leader is a critical factor in the expected performance of the team—establish credibility in the models. Mathematical analysis and computer simulations are used to provide new managerial insights into the value of the leader—such as the fact that the skill of the leader can be more important than controlling the amount of interdependence among the team members and that having a choice of multiple leaders with no particular motivating skill is beneficial to the performance of small teams but not to large teams.Daniel Solow received a B.S. in Mathematics from Carnegie-Mellon, an M.S. in Operations Research from the University of California at Berkeley, and a Ph. D. in Operations Research from Stanford University. He has been a professor at Case Western Reserve University since 1978. His research interests include complex systems, discrete, linear, and nonlinear optimization. He has also developed systematic methods for teaching mathematical proofs, computer programming, and operations research.Sandy Kristin Piderit is an assistant professor of organizational behavior at the Weatherhead School of Management at Case Western Reserve University, and earned her Ph.D. from the University of Michigan. She studies the roles of relationships among coworkers on their performance and satisfaction with their work environments, and has published studies in the Academy of Management Review, the Journal of Management Studies, and Management Science.Apostolos Burnetas received a Diploma in Electrical Engineering from National Technical University in Athens, Greece, and an M.B.A. and Ph.D. in Operations Research from Rutgers University. He has been at the Department of Operations at Case Western Reserve University and is currently an Associate Professor at the Department of Mathematics at the University of Athens. His research interests include stochastic models and optimization, complex systems, and applications in queueing systems, supply chain and the interface of operations with finance.Chartchai Leenawong received a B.S. in Mathematics from Chulalongkorn University in Bangkok, an M.S. in Computer Science from the Asian Institute of Technology in Bangkok, and a Ph.D. in Operations Research from Case Western Reserve University. His research interests include mathematical modeling of complex systems as applied to business organizations. He has been a professor at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand since 2002.