Extended open shop scheduling with resource constraints: Appointment scheduling for integrated practice units

Abstract

An Integrated Practice Unit (IPU) is a new approach to outpatient care in which a co-located multidisciplinary team of clinicians, technicians, and staff provide treatment in a single patient visit. This article presents a new integer programming model for an extended open shop problem with application to clinic appointment scheduling for IPUs. The advantages of the new model are discussed and several valid inequalities are introduced to tighten the linear programming relaxation. The objective of the problem is to minimize a combination of makespan and total job processing time, or in terms of an IPU, to minimize a combination of closing time and total patient waiting time. Feasible solutions are obtained with a two-step heuristic, which also provides a lower bound that is used to judge solution quality. Next, a two-stage stochastic optimization model is presented for a joint pain IPU. The expected value solution is used to generate two different patient arrival templates. Extensive computations are performed to evaluate the solutions obtained with these templates and several others found in the literature. Comparisons with the expected value solution and the wait-and-see solution are also included. For the templates derived from the expected value solution, the results show that the average gap between the feasible solution and lower bound provided by the two-step heuristic is 2% for 14 patients. They also show that either of the two templates derived from the expected value solution is a good candidate for assigning appointment times when either the clinic closing time or the patient waiting time is the more important consideration. Sensitivity analysis confirmed that the optimality gap and clinic statistics are stable for marginal changes in key resources.

Keywords:

• Integrated practice units
• open shop scheduling
• flexible flow shop
• stochastic optimization

Additional information

Funding

This project was supported by the Dell Medical School’s Texas Health Catalyst program. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the University of Texas at Austin. Additional support was provided by a grant from the McCombs School of Business at the University of Texas.

Notes on contributors

Pengfei Zhang

Pengfei Zhang is a fourth year Ph.D. student in the McCombs School of Business at the University of Texas at Austin. He graduated from the School of the Gifted Young at the University of Science and Technology of China with a bachelor’s degree in physics. He obtained his master’s degree in industrial engineering from the University of Arizona. His research interests include modeling of healthcare delivery systems and robust optimization.

Jonathan F. Bard

Jonathan F. Bard is a professor of operations research & industrial engineering in the Mechanical Engineering Department at the University of Texas at Austin. He holds the Industrial Properties Corporation Endowed Faculty Fellowship, and serves as the Associate Director of the Center for the Management of Operations and Logistics. He received a D.Sc. in Operations Research from The George Washington University. Dr. Bard's research centers on improving healthcare delivery, personnel scheduling, production planning and control, and the design of decomposition algorithms for solving large-scale optimization problems, and has appeared in a wide variety of technical Journals. Currently, he serves on six editorial boards and previously was a Focused Issue Editor of IIE Transactions and an Associate Editor of Management Science. He is a registered engineer in the State of Texas, a fellow of IIE and INFORMS, and a senior member of IEEE. In the past, he has held a number of offices in each of these organizations, and is currently the INFORMS Vice President of Publications.

Douglas J. Morrice

Douglas J. Morrice holds the Bobbie and Coulter R. Sublett Centennial Professorship in Business. He is also Professor of Operations Management and a University of Texas Supply Chain Management Center of Excellence Senior Research Fellow in the McCombs School of Business at The University of Texas at Austin. Dr. Morrice has an ORIE Ph.D. from Cornell University. His research interests include simulation design, modeling, and analysis, healthcare delivery management, and supply chain risk management. He is a senior editor for Production and Operations Management, an editor-at-large for Interfaces, and an area editor for IISE Transactions on Healthcare Systems Engineering.

Karl M. Koenig

Karl M. Koenig is the Medical Director of the Musculoskeletal Institute at Dell Medical School and leads the Integrated Practice Unit for Joint Pain. He also leads the effort to develop IPUs for other musculoskeletal conditions including Back Pain, Fracture Care, Sports Medicine, and Foot Care. After receiving his undergraduate degree at the Massachusetts Institute of Technology, he attended Baylor College of Medicine. Dr. Koenig completed his residency at Dartmouth-Hitchcock Medical Center (Lebanon, NH) in Orthopaedic Surgery and fellowship in Adult Reconstruction at Stanford University. He is also a graduate of the Dartmouth Institute for Health Policy and Clinical Practice, where he began his work on patient outcomes and value-based healthcare delivery. Prior to joining Dell Medical School, Dr. Koenig led the Division of Adult Reconstruction at Dartmouth for 5 years and was one of the architects of GreenCare, a sweeping quality improvement initiative to create a self-improving microsystem around total joint replacement.