Patient-centric surgeons’ case mix problem

Abstract

This paper studies a single-period tactical planning problem to find the surgeons’ case mix of a hospital surgical unit such that the total patient value per dollar spent on healthcare resources (the TPV) is maximized. We represent the relationship between the surgeons’ volume and patient outcomes using the learning curve. We formulate the problem as a nonlinear integer programming model. The problem belongs to the class of nonquadratic transportation problems in which it is proven that no algorithm solving the problem in strongly polynomial time exists. We develop a Lagrangian-based heuristic solution approach that exploits the special structure of the problem. Using simulated and real data, we show that the diversity in surgeons’ experience complements a surgical unit in a way that good patient outcomes of experienced surgeons counterbalance the average but improving patient outcomes of less experienced surgeons while the less experienced surgeons gain more experience.

Keywords:

• Planning
• resource allocation
• healthcare management
• patient outcomes
• patient value
• operations research in healthcare
• learning curve

Acknowledgments

I am grateful to Professor Frank Dexter, Department of Anesthesiology at the University of Iowa Hospital and Clinics, for his valuable comments. I am also grateful for the valuable comments from referees and the area editor. This study has been supported by the Lary and Lori Wright Research Fellowship.

Notes

1 LINGO Global Solver primer at www.lindo.com/index.php/products/lingo-and-optimization-modeling?catid=89&id=88:powerful-lingo-solvers

2 For cost and price information, refer to LASIK eye surgery cost by Liz Segre; reviewed by Gary Heiting, OD at https://www.allaboutvision.com/visionsurgery/cost.htm (accessed April 6, 2020).

3 Refer to “What is a Learning Curve?” by James Martin, Management and Accounting Web, https://maaw.info/LearningCurveSummary.htm#Comparing, accessed on March 8, 2021.

4 See Tekkis et al. (2005) for more details on conversion to open surgery for certain patient-types.

5 Pilot testing with different number of replications shows 10 replications satisfactorily reveals the variability we could expect in the TPVs. See Rardin and Uzsoy (2001) for insights on experimental evaluation of heuristic optimization algorithms.

6 Thanks to the anonymous referee who provided this insight.