τ 1 OR OR and and τ 2 Simulation Simulation for for Health Care Optimization Health Care Optimization OR and Simulation M Healthcare PW 2010
Two parallel servers Two parallel servers OR and Simulation M Healthcare PW 2010
1 � � 1 ������ 1, 2 1 � � ��� � � � � ��� � � � 2 � 2 �� 1, 2 2 OR and Simulation M Healthcare PW 2010
Two parallel servers Two parallel servers µ λ µ λ 2 µ 2 λ OR and Simulation M Healthcare PW 2010
Stochastic OR - group Stochastic OR - group Erik van der Sluis Nikky Kortbeek Nikky Kortbeek Jan van der Wal Jan van der Wal Michiel Jansen Michiel Jansen Sindo Núñez-Queija Sindo Núñez-Queija Nico van Dijk Nico van Dijk Ivo Adan Ivo Adan OR and Simulation M Healthcare PW 2010
Simulation Simulation Familiar Operating Theatre Great Tool OR and Simulation M Healthcare PW 2010
Purposes Purposes • Organization / Scenario’s • Process Insights • What-If • Capacities • Uncertainties • Process Times OR and Simulation M Healthcare PW 2010
Organizational Organizational • Specialization • Pooling of services • Specialized Programs (Allin) • Specialized Programs (Allin) • Triage systems / Nurse practitioners • Supply Chain and ICT Conceptualization OR and Simulation M Healthcare PW 2010
Capacities Capacities • # OK • # ICU beds • # Nurses / beds : : OR and Simulation M Healthcare PW 2010
Planning Planning • OK’s • Shifts • Part-time • Diagnosis Process • Therapeutic Treatments : : OR and Simulation M Healthcare PW 2010
Introduction Introduction Simulation Most Most Valuable Evaluation Tool But: No Optimization OR and Simulation M Healthcare PW 2010
OR OR • Insights • Scenarios • Techniques for Optimization = OR and Simulation M Healthcare PW 2010
Combination Combination Simulation OR Advantages Disadvantages Real life complexity Simple models Real life uncertainties Strict assumptions Disadvantages Disadvantages Advantages Advantages Evaluation Optimization By scenarios By techniques By numbers only Also buy insights Advantages Advantages OR and Simulation M Healthcare PW 2010
Combination of O R O R Simulation Simulation OR and Simulation M Healthcare PW 2010
Application Examples Application Examples I Pooling II II ICU dimensioning ICU dimensioning III Blood Platelet Production OR and Simulation M Healthcare PW 2010
Summarizing Summarizing Simulation Operations Research Optimization Optimization Advantages Advantages OR and Simulation M Healthcare PW 2010
Challenges Challenges For OR For OR For HC-practitioners For HC-practitioners • Language • Confidence in OR • Dare to step in • Software Development • Not just conceptual • Implementation OR and Simulation M Healthcare PW 2010
1.0 0.8 OR OR 0.6 0.4 and and Wp = Wa w w w w w w w Pw ait>0 0.2 Pw ait>tau 0.0 Simulation Simulation 0.0 0.2 0.4 0.6 0.8 1.0 for for Health Care Optimization Health Care Optimization OR and Simulation M Healthcare PW 2010
Questions and/or suggestions Questions and/or suggestions OR and Simulation M Healthcare PW 2010
I: I: Should we Pool or Not Should we Pool or Not ? OR and Simulation M Healthcare PW 2010
N.M. van Dijk & E. van der Sluis N.M. van Dijk Operations Research & Management University of Amsterdam � University of Amsterdam Operations Research & Management � � � � � � � � � � � � Pooling? OR and Simulation M Healthcare PW 2010
Two parallel servers Two parallel servers µ λ µ λ 2 µ 2 λ OR and Simulation M Healthcare PW 2010
A A Pooling: An Instructive Example Pooling: An Instructive Example 1 � � 1 ������ 1, 2 1 � � ��� � � � � ��� � � � 2 � 2 �� 1, 2 2 OR and Simulation M Healthcare PW 2010
A single server (M/M/1)-queueing model A single server (M/M/1)-queueing model 1 D = � - λ OR and Simulation M Healthcare PW 2010
Two parallel servers Two parallel servers µ λ 1 D = � - λ µ λ 1 D = 2 � - 2 λ 2 µ 2 λ OR and Simulation M Healthcare PW 2010
� 1 ≠ � 2 � 1 ≠ � 2 Pooling (A): Pooling (A): 1 � 1 � ? ? 1, 2 1, 2 � � ��� � � � � ��� � � � � ��� � � � � ��� � � 2 � 2 � 1, 2 1, 2 And yet? OR and Simulation M Healthcare PW 2010
Pollaczek-Khintchine’s Formula Pollaczek-Khintchine’s Formula M / G / 1 c + 2 W = ½(1 )W G exp Squared Coefficient of Variation OR and Simulation M Healthcare PW 2010
Example Example Mix ratio k =10 ρ = 0.83 Deterministic OR and Simulation M Healthcare PW 2010
Pooling or separate queue Pooling or separate queue 1 1 � � � � 1 1 ������ ������ 1 1 1, 2 1, 2 � � ��� � � � � ��� � � � � � � 2 � 2 � 2 2 2 2 � � 2 2 �� �� �� �� 1, 2 1, 2 2 2 W 1 = 6.15 W 1 = 2.50 W 2 = 6.15 W 2 = 25.0 W A = 6.15 W A = 4.55 OR and Simulation M Healthcare PW 2010
Can we do better? Can we do better? 1 � 1 � ? ? 1, 2 1, 2 � � ��� � � � � ��� � � � � ��� � � � � ��� � � 2 � 2 � 1, 2 1, 2 OR and Simulation M Healthcare PW 2010
Overflow scenario(s) Overflow scenario(s) 1 , 2 � Type 1 Type 1 � 2 , 1 Type 2 OR and Simulation M Healthcare PW 2010
Overflow Result Overflow Result 1 1 � � � � � � 1 1 1 1 ������ ������ ������ ������ 1, 2 1, 2 1 1 1, 2 1, 2 � � ��� � � � � ��� � � � � � � 2 2 2 2 � � � � �� �� 2 2 �� �� 1, 2 1, 2 1, 2 1, 2 2, 1 2, 1 2, 1 2, 1 2 2 2 W 1 = 6.15 W 1 = 2.50 W 1 = 3.66 W 2 = 6.15 W 2 = 25.0 W 2 = 8.58 W A = 6.15 W A = 4.55 W A = 4.11 OR and Simulation M Healthcare PW 2010
How? How? Result Queueing Simulation OR and Simulation M Healthcare PW 2010
Overflow scenario(s) Overflow scenario(s) 1 , 2 � Type 1 Type 1 Simulation Simulation � 2 , 1 Type 2 OR and Simulation M Healthcare PW 2010
Can we do better? Can we do better? 2.50 1 1 � � � � 1 1 ������ ������ 1 1 1, 2 1, 2 � � ��� � � � � ��� � � 4.55 6.15 � � 2 2 � � 2 2 �� �� 1, 2 1, 2 1, 2 1, 2 25.0 25.0 2 2 2 3.66 1.80 � � � � 1 1 1 1 ������ ������ ������ ������ 1, 2 1, 2 1 1 4.11 3.92 � � � � 2 2 2 2 �� �� �� �� 8.58 25.2 2, 1 2, 1 2, 1 2, 1 OR and Simulation M Healthcare PW 2010
By OR and Simulation By OR and Simulation 120% W A Rank No. Scenario 100% 7 1 0.71 Pooled 6 5 0.68 80% Thr(Opt) 5 2 0.63 Unpooled 60% 60% 4 3 0.58 Two-way 3 4 40% 0.52 One-way 2 6 0.38 Prio(1,N) 20% 1 7 0.20 Prio(1,P) 0% 1 5 2 3 4 6 7 Average waiting time for s = 10 OR and Simulation M Healthcare PW 2010
B Pooling: MRI-scans B Pooling: MRI-scans � U 10% W 1 < 3 days R 90% W 2 < 9 days � OR and Simulation M Healthcare PW 2010
� W < 3 days ? W < 3 days ? U + R U + R � OR and Simulation M Healthcare PW 2010
Results Results Pool if: W P < W 1 By Queueing (OR) ρ ≤ ρ + ρ − ρ 2 ½ 8 ½ 2 1 1 1 OR and Simulation M Healthcare PW 2010
Pooling or Not? Pooling or Not? ρ ↑ 1.0 2 No Pooling 0.8 Pooling 0.6 0.4 W P = W 1 Wp = Wa wwwwwww P { W P > 0} = P { W 1 > 0} Pwait>0 0.2 P { W P > τ } = P { W 1 > τ } Pwait>tau 0.0 0.0 0.2 0.4 0.6 0.8 1.0 → ρ 1 OR and Simulation M Healthcare PW 2010
RT – application RT – application (# consults per week) Capacity needed for SL-1 SL-1 6 days 5 days 4 days 3 days (spare) P 34.5 35.5 36.5 39 6.5 NP 35 35.5 36 36.5 4 OR and Simulation M Healthcare PW 2010
C C Pooling: Nurse Practitioner Pooling: Nurse Practitioner Overflow � 1 � 2 Necessarily Simulation OR and Simulation M Healthcare PW 2010
Pooled scenario Pooled scenario Next τ 1 Next τ 2 OR and Simulation M Healthcare PW 2010
Overflow scenario Overflow scenario Overflow τ 1 τ 2 Necessarily Simulation OR and Simulation M Healthcare PW 2010
Comparison Comparison Next τ 1 τ 1 τ 1 = 1 Next τ 2 τ 2 τ = 1.4 τ 2 = 1.4 Pooled Overflow W A = 2.59 W A = 2.37 OR and Simulation M Healthcare PW 2010
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