Optimal Hiring and Retention Policies for Heterogeneous Workers Who Learn

We study the hiring and retention of heterogeneous workers who learn over time. We show that the problem can be analyzed as an infinite-armed bandit with switching costs, and we apply results from Bergemann and Valimaki [Bergemann D, Valimaki J 2001 Stationary multi-choice bandit problems. J. Econom. Dynam. Control 2510:1585--1594] to characterize the optimal hiring and retention policy. For problems with Gaussian data, we develop approximations that allow the efficient implementation of the optimal policy and the evaluation of its performance. Our numerical examples demonstrate that the value of active monitoring and screening of employees can be substantial. This paper was accepted by Yossi Aviv, operations management.

[1]  Louis E. Yelle.  THE LEARNING CURVE: HISTORICAL REVIEW AND COMPREHENSIVE SURVEY , 1979 .

[2]  P. Freeman.  The Secretary Problem and its Extensions: A Review , 1983 .

[3]  David A. Nembhard,et al.  The Effects of Worker Learning, Forgetting, and Heterogeneity on Assembly Line Productivity , 2001, Manag. Sci..

[4]  Ward Whitt,et al.  The Impact of Increased Employee Retention on Performance in a Customer Contact Center , 2006, Manuf. Serv. Oper. Manag..

[5]  Christian M. Ernst,et al.  Multi-armed Bandit Allocation Indices , 1989 .

[6]  C. Bailey.  Forgetting and the learning curve: a laboratory study , 1989 .

[7]  Gary P. Pisano,et al.  Organizational Differences in Rates of Learning: Evidence from the Adoption of Minimally Invasive Cardiac Surgery , 2001, Manag. Sci..

[8]  Luk N. Van Wassenhove,et al.  Behind the Learning Curve: Linking Learning Activities to Waste Reduction , 2000 .

[9]  Mustafa Uzumeri,et al.  A population of learners: A new way to measure organizational learning , 1998 .

[10]  Alessandro Arlotto,et al.  Optimal employee retention when inferring unknown learning curves , 2010, Proceedings of the 2010 Winter Simulation Conference.

[11]  Joseph B. Mazzola,et al.  The Stochastic Learning Curve: Optimal Production in the Presence of Learning-Curve Uncertainty , 1997, Oper. Res..

[12]  James O. Berger,et al.  Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown , 2010 .

[13]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[14]  P. Whittle.  Multi‐Armed Bandits and the Gittins Index , 1980 .

[15]  Avishai Mandelbaum,et al.  Service times in call centers: Agent heterogeneity and learning with some operational consequences , 2010 .

[16]  Eelke Wiersma,et al.  Conditions That Shape the Learning Curve: Factors That Increase the Ability and Opportunity to Learn , 2007, Manag. Sci..

[17]  Ming-Deh A. Huang,et al.  Proof of proposition 1 , 1992 .

[18]  J. Banks,et al.  Denumerable-Armed Bandits , 1992 .

[19]  J. Gittins.  Bandit processes and dynamic allocation indices , 1979 .

[20]  Dimitri P. Bertsekas,et al.  Stochastic optimal control : the discrete time case , 2007 .

[21]  Mark A. Huselid.  The Impact of Human Resource Management Practices on Turnover, Productivity, and Corporate Financial Performance , 1995 .

[22]  Cheryl Gaimon,et al.  Improving Manufacturing Performance Through Process Change and Knowledge Creation , 2000 .

[23]  Rangarajan K. Sundaram.  Generalized Bandit Problems , 2005 .

[24]  É. Nagypál,et al.  Learning by Doing vs. Learning About Match Quality: Can We Tell Them Apart? , 2007 .

[25]  Haipeng Shen,et al.  Non‐parametric modelling of time‐varying customer service times at a bank call centre , 2006 .

[26]  R. Leach.  The learning curve , 1992 .

[27]  David A. Nembhard,et al.  An individual-based description of learning within an organization , 2000, IEEE Trans. Engineering Management.

[28]  Demosthenis Teneketzis,et al.  Multi-armed bandits with switching penalties , 1996, IEEE Trans. Autom. Control..

[29]  M. Weitzman.  Optimal search for the best alternative , 1978 .

[30]  Cheryl Gaimon,et al.  Planning Information Technology-Knowledge Worker Systems , 1997 .

[31]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[32]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[33]  Avishai Mandelbaum,et al.  Statistical Analysis of a Telephone Call Center , 2005 .

[34]  Ming-Deh A. Huang,et al.  Proof of proposition 2 , 1992 .

[35]  Maqbool Dada,et al.  Monopolistic Pricing and the Learning Curve: An Algorithmic Approach , 1990, Oper. Res..

[36]  Stochastic Orders , 2008 .

[37]  Ritesh Madan,et al.  The Irrevocable Multiarmed Bandit Problem , 2011, Oper. Res..

[38]  P. W. Jones,et al.  Bandit Problems, Sequential Allocation of Experiments , 1987 .

[39]  K. Taira.  Proof of Theorem 1.3 , 2004 .

[40]  N. Kiefer,et al.  Controlling a Stochastic Process with Unknown Parameters , 1988 .

[41]  J. Bather,et al.  Multi‐Armed Bandit Allocation Indices , 1990 .

[42]  D. Bergemann,et al.  Stationary Multi Choice Bandit Problems , 2001 .

[43]  J. Banks,et al.  Switching Costs and the Gittins Index , 1994 .

[44]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[45]  W. Rudin.  Principles of mathematical analysis , 1964 .

[46]  Marco Pavone,et al.  Stochastic Optimal Control , 2015 .

[47]  D A Nembhard,et al.  Heuristic approach for assigning workers to tasks based on individual learning rates , 2001 .

[48]  J. March.  Exploration and exploitation in organizational learning , 1991, STUDI ORGANIZZATIVI.

[49]  Mustafa Uzumeri,et al.  Experiential learning and forgetting for manual and cognitive tasks , 2000 .

[50]  Joseph B. Mazzola,et al.  A Bayesian Approach to Managing Learning-Curve Uncertainty , 1996 .

[51]  Haipeng Shen.  Nonparametric regression for problems involving lognormal distributions , 2003 .

[52]  Tackseung Jun.  A survey on the bandit problem with switching costs , 2004 .

[53]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[54]  V. Farias,et al.  The Irrevocable Multi-Armed Bandit Problem , 2009 .

[55]  José Niño-Mora.  A Faster Index Algorithm and a Computational Study for Bandits with Switching Costs , 2008, INFORMS J. Comput..

[56]  Zeynep Akşin,et al.  The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research , 2007 .

[57]  Noah Gans,et al.  Managing Learning and Turnover in Employee Staffing , 1999, Oper. Res..

[58]  Boyan Jovanovic.  Job Matching and the Theory of Turnover , 1979, Journal of Political Economy.

[59]  Cheryl Gaimon,et al.  Dynamic Resource Capabilities: Managing Workforce Knowledge with a Technology Upgrade , 2011, Organ. Sci..

[60]  Mark A. McComb.  Comparison Methods for Stochastic Models and Risks , 2003, Technometrics.

[61]  José Niòo-Mora.  A Faster Index Algorithm and a Computational Study for Bandits with Switching Costs , 2008 .

[62]  Warren B. Powell,et al.  The Knowledge-Gradient Policy for Correlated Normal Beliefs , 2009, INFORMS J. Comput..

[63]  David A. Nembhard,et al.  Task complexity effects on between-individual learning/forgetting variability , 2002 .

[64]  Edieal J. Pinker,et al.  The Efficiency-Quality Trade-Off of Cross-Trained Workers , 2000, Manuf. Serv. Oper. Manag..

[65]  Matthew S Goldberg,et al.  Statistical Methods for Learning Curves and Cost Analysis , 2003 .