Applying mathematical models to surgical patient planning

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Chapter 2 Improving operating room efficiency by applying bin-packing and portfolio techniques to surgical case scheduling Abstract BACKGROUND: An operating room (OR) department has adopted an efficient business model and subsequently investigated how efficiency could be further improved. The aim of this study is to show the efficiency improvement of lowering organizational barriers and applying advanced mathematical techniques. METHODS: We applied advanced mathematical algorithms in combination with scenarios that model relaxation of various organizational barriers using prospectively collected data. The setting is the main inpatient OR department of a university hospital, which sets its surgical case schedules 2 wk in advance using a block planning method. The main outcome measures are the number of freed OR blocks and OR utilization. RESULTS: Lowering organizational barriers and applying mathematical algorithms can yield a 4.5% point increase in OR utilization (95% confidence interval 4.0%–5.0%). This is obtained by reducing the total required OR time. CONCLUSIONS: Efficient OR departments can further improve their efficiency. The paper shows that a radical cultural change that comprises the use of mathematical algorithms and lowering organizational barriers improves OR utilization. 1. Introduction Optimal use of scarce and expensive facilities such as operating rooms (ORs) requires efficient planning. The Erasmus University Medical Center (Erasmus MC), Rotterdam, The Netherlands, developed an OR business model based on controlled surgical case scheduling and management contracts. Nevertheless, OR department managers still explore new ways to improve OR efficiency. The main inpatient OR department in Erasmus MC is run as a facilitating department that provides staffed and fully equipped ORs for the various surgical departments. A block planning approach has been adopted in which blocks of OR time are made available to surgical departments in advance (1,2). Departments may only assign patients to OR blocks that were made available to them. Regrettably, these organizational barriers result in suboptimal use of OR time. The OR business model furthermore incorporates the annual management contracts specifying the yearly amounts of OR time available for each surgical department. Capacity for emergency cases and uncertainty of case durations is accounted for by determining target OR utilizations for each surgical department independently. Any surgical case schedule, therefore, must include free OR
24 Improving operating room efficiency by surgical case scheduling time, or “planned slack.” Since target utilizations differ, planned slack also differs among surgical departments. In summary, for the planning of surgical cases the surgical departments must adhere to the following rules: 1. Submit elective case schedules 2 wk in advance; 2. Maximize use of OR time and not exceed block times; 3. Plan elective cases using historical mean case durations; 4. Include planned slack to deal with emergency cases and variability of case durations. Provided these rules are adhered to, the OR department “guarantees” that all scheduled surgical cases and emergency cases will be performed, whatever happens during the day. Moreover, applying these rules consequently helps surgical departments in their yearly contract negotiations about OR time with the hospital board. The hypothesis to be tested was: combining advanced mathematical algorithms with lowering of organizational barriers among surgical departments improves OR efficiency. Several methods to improve efficiency have been proposed in the literature. Strum et al. (3) reported a benefit of approaching the OR planning problem as a newsvendor problem. Dexter et al. (4) recently showed the benefits of various approaches to surgical case scheduling. A broad overview of relevant literature is presented by McIntosh et al. (5). Mathematical algorithms to optimize surgical case schedules is a widely researched topic (3,6–8). Several studies addressed the application of bin packing techniques, such as the Best Fit Descending heuristic (9,10) or Regret-Based Random Sampling (RBRS) (11), yet within single departments. Finally, there is evidence that approaching the OR scheduling problem as a portfolio problem (12) may deal with the unpredictability of case durations and improve efficiency (11). Similar portfolio techniques are already in use for case mix management problems (13,14). Given the business model used by the main OR department of Erasmus MC, efforts are still focused on improving the current OR utilization. The aforementioned mathematical methods were examined. In addition, we report a computer simulation study assessing promising methods for creating efficient surgical schedules within scenarios that represent various degrees of lowering organizational barriers. 2. Methods 2.1. Data Erasmus MC is a university hospital and tertiary referral center in Rotterdam, The Netherlands. Erasmus MC has 1237 beds and admits 34,500 patients per year, 60%– 70% of whom undergo operation. The main inpatient OR suite consists of 16 ORs,
Page 1 and 2: JEROEN VAN OOSTRUM Applying mathema
Page 4 and 5: Applying Mathematical Models to Sur
Page 6 and 7: Acknowledgements This thesis is a p
Page 8 and 9: Contents iii Contents Acknowledgeme
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Page 12 and 13: Contents vii 4.4. Step 4: Define a
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Page 17 and 18: 4 Introduction high-level care to p
Page 19 and 20: 6 Introduction The OR department is
Page 21 and 22: 8 Introduction elective surgeries (
Page 23 and 24: 10 Introduction central planner dec
Page 25 and 26: 12 Introduction 5. A 7-stepwise app
Page 27 and 28: 14 Introduction The organization ma
Page 29 and 30: 16 Introduction room-days to a mast
Page 31 and 32: 18 Introduction Hans, E., Wullink,
Page 33 and 34: 20 Introduction
Page 38 and 39: Chapter 2 25 Unit1 Unit 2 Unit 3 Un
Page 40 and 41: Chapter 2 27 2.3. Planned slack and
Page 42 and 43: Chapter 2 29 surgery. Surgical depa
Page 44 and 45: Chapter 2 31 3. Results Applying th
Page 46 and 47: Chapter 2 33 4. Discussion The stud
Page 48 and 49: Chapter 2 35 8. Marcon E, Kharraja
Page 50: Chapter 3 A method for clustering s
Page 53 and 54: 40 A method for clustering surgical
Page 66 and 67: Chapter 4 A master surgical schedul
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Page 70 and 71: Chapter 4 57 ponents. This principl
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Page 74 and 75: Chapter 4 61 This model has two mai
Page 76 and 77: Chapter 4 63 The dual constraints o
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Page 80 and 81: Chapter 4 67 Cycle length Number of
Page 82 and 83: Chapter 4 69 Initialization heurist
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Chapter 4 73 Van den Akker JM, Hoog
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Chapter 5 Fewer intensive care unit
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78 Fewer intensive care unit refusa
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Chapter 6 Implementing a master sur
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Chapter 6 91 centers encompass all
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Chapter 6 93 approach. Creating suc
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Chapter 6 95 We define a master sur
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Chapter 6 97 difference existed bet
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Chapter 6 99 4.5. Step 5: Construct
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Chapter 6 101 unknown. However, whe
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Chapter 6 103 McLaughlin, C.P., Yan
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Chapter 7 Requirements for a full s
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Chapter 7 Requirements for a full s
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Chapter 7 109 Erasmus MC deals with
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Chapter 7 111 on in an OR that is d
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Chapter 7 113 2.4. Modeling the OR
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Chapter 7 115 Total number of guara
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Chapter 7 117 Mean number of OR tea
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Chapter 7 119 Not guaranteeing all
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Chapter 7 121 schedules are properl
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Chapter 8 Closing emergency operati
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Chapter 8 Closing emergency operati
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Chapter 8 127 Figure 1: Visualizati
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Chapter 8 129 Interrupting the exec
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Appendix to Chapter 8 Letter 1: non
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Chapter 9 A simulation model for de
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Chapter 9 A simulation model for de
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Chapter 9 137 performed at least ei
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Chapter 9 Case durations wwere draw
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Chapter 9 141 Scenarios with fewer
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Chapter 9 143 Figure 2: Proportions
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Chapter 9 145 4. Discussion A simul
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Chapter 9 147 References 1. Simoens
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Chapter 10 Concluding remarks and i
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Chapter 10 Concluding remarks and i
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Chapter 10 153 processes. Ideally,
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Nederlandse samenvatting (Summary i
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157 binnen operatiekamercomplexen w
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Curriculum Vitae Jeroen van Oostrum
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ERASMUS RESEARCH INSTITUTE OF MANAG
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Brumme, W.-H., Manufacturing Capabi
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Gilsing, V.A., Exploration, Exploit
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Iwaarden, J.D. van, Changing Qualit
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Le-Duc, T., Design and Control of E
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Mom, T.J.M., Managers’ Exploratio
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Quak, H.J., Sustainability of Urban
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Szkudlarek, B.A., Spinning the Web
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Wielemaker, M.W., Managing Initiati
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Erasmus Research Institute of Manag
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Applying mathematical models to surgical patient planning

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