Applying mathematical models to surgical patient planning

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Chapter 2 27 2.3. Planned slack and the portfolio effect The financial world deals with uncertainty by using the portfolio effect. This ensures that the expected return of a stock portfolio is less vulnerable to fluctuations on the stock market. The term “portfolio effect” then indicates that portfolio risk decreases with increasing diversity, as measured by the absence of correlation (covariance) between portfolio components (16). We earlier found application of the portfolio effect to surgical case scheduling to be successful in increasing OR efficiency, since it reduces the required amount of planned slack, given an accepted risk of overtime (11). The approach clustered surgical cases with similar variability in the same OR block, assuming these to be uncorrelated. We illustrate the portfolio effect applied to surgical case scheduling by the following example: Consider two OR Available OR capacity Planned Slack Surgical procedure A Surgical procedure B Unused c.q. lost OR capacity Figure 1: Graphical representation of a surgical case schedule, which typically includes various surgical cases, planned slack, and unused operating room time. Figure 2: Example of planned slack reduction as a result of the portfolio effect. The sum of the shaded areas in the two operating room blocks on the left exceeds that in the two operating room blocks on the right.
28 Improving operating room efficiency by surgical case scheduling blocks, both of which have two surgical cases scheduled. One case with (mean, standard deviation) = (100, 10) and one case with (mean, standard deviation) = (100, 50) (Fig. 2) (all values are given in minutes). We assumed that case durations are described by a normal distribution function. In this example, we now compared this situation (the left side of Fig. 2) with the situation in which surgical cases with similar variance are clustered. In the first situation, the standard deviation of total duration is the same for both OR blocks: √(50 2 + 10 2 ) = 51.0 min. The total planned slack for the two blocks is thus 102.0β min, where β is a risk factor to deal with risk of overtime. Since the sum of the durations follows a normal distribution the following holds: P(mean + β standard deviation) ~ accepted risk of overtime, such that given a certain accepted risk of overtime the risk factor can be calculated. In the second situation, the total planned slack is: (√(50 2 + 50 2 ) + √(10 2 + 10 2 ))β = 84.9β min. This means a 17.1β min reduction in the total required planned slack time, and thus an equal increase in available capacity. This portfolio profit will increase with higher variability of the cases concerned. This example illustrates that rescheduling a surgical case can reduce the extent of planned slack. 2.4. Organizational barriers We constructed three scenarios to investigate the impact of lowering organizational barriers imposed by block planning (Table 4). The scenarios are graded as to interdepartmental flexibility (i.e., scheduling cases of different departments in the same OR on 1 day) and flexibility of rescheduling surgical cases between days of the week compared with the current situation. Rescheduling of surgical cases throughout the week does not affect patients, since they have not yet been scheduled. In this study, we assumed application of the scenarios directly after the construction of the surgical case schedules, approximately 2 wk before the actual execution of the schedule (Fig. 3). This enables OR departments to take necessary steps to ensure feasibility; for example regarding material logistics, ranging from specific surgical material to complete navigation system for complex craniotomy Scenario Interdepartmental flexibility Flexibility over the week 1 2 3 OR block consists of surgical cases of a single department OR block consists of surgical cases of a single department OR block consists of surgical cases of a department within one unit Rescheduling on the same day Rescheduling within the same week Rescheduling on the same day See Table 1 for the clustering of surgical departments in organizational units. The flexibility is applied to the construction of surgical schedules 2 wk in advance. OR = operating room. Table 4: Description of scenarios representing various flexibility levels
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
Page 10 and 11: Contents v 5.2. Modeling resource d
Page 12 and 13: Contents vii 4.4. Step 4: Define a
Page 14: Chapter 1 Introduction Parts appear
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 36 and 37: Chapter 2 Improving operating room
Page 38 and 39: Chapter 2 25 Unit1 Unit 2 Unit 3 Un
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
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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 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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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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