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1 OR OR and and 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. 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

  2. Two parallel servers Two parallel servers OR and Simulation M Healthcare PW 2010

  3. 1 � � 1 ������ 1, 2 1 � � ��� � � � � ��� � � � 2 � 2 �� 1, 2 2 OR and Simulation M Healthcare PW 2010

  4. Two parallel servers Two parallel servers µ λ µ λ 2 µ 2 λ OR and Simulation M Healthcare PW 2010

  5. 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

  6. Simulation Simulation Familiar Operating Theatre Great Tool OR and Simulation M Healthcare PW 2010

  7. Purposes Purposes • Organization / Scenario’s • Process Insights • What-If • Capacities • Uncertainties • Process Times OR and Simulation M Healthcare PW 2010

  8. 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

  9. Capacities Capacities • # OK • # ICU beds • # Nurses / beds : : OR and Simulation M Healthcare PW 2010

  10. Planning Planning • OK’s • Shifts • Part-time • Diagnosis Process • Therapeutic Treatments : : OR and Simulation M Healthcare PW 2010

  11. Introduction Introduction Simulation Most Most Valuable Evaluation Tool But: No Optimization OR and Simulation M Healthcare PW 2010

  12. OR OR • Insights • Scenarios • Techniques for Optimization = OR and Simulation M Healthcare PW 2010

  13. 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

  14. Combination of O R O R Simulation Simulation OR and Simulation M Healthcare PW 2010

  15. Application Examples Application Examples I Pooling II II ICU dimensioning ICU dimensioning III Blood Platelet Production OR and Simulation M Healthcare PW 2010

  16. Summarizing Summarizing Simulation Operations Research Optimization Optimization Advantages Advantages OR and Simulation M Healthcare PW 2010

  17. 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

  18. 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

  19. Questions and/or suggestions Questions and/or suggestions OR and Simulation M Healthcare PW 2010

  20. I: I: Should we Pool or Not Should we Pool or Not ? OR and Simulation M Healthcare PW 2010

  21. 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

  22. Two parallel servers Two parallel servers µ λ µ λ 2 µ 2 λ OR and Simulation M Healthcare PW 2010

  23. 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

  24. 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

  25. 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

  26. � 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

  27. 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

  28. Example Example Mix ratio k =10 ρ = 0.83 Deterministic OR and Simulation M Healthcare PW 2010

  29. 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

  30. 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

  31. Overflow scenario(s) Overflow scenario(s) 1 , 2 � Type 1 Type 1 � 2 , 1 Type 2 OR and Simulation M Healthcare PW 2010

  32. 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

  33. How? How? Result Queueing Simulation OR and Simulation M Healthcare PW 2010

  34. 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

  35. 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

  36. 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

  37. 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

  38. � W < 3 days ? W < 3 days ? U + R U + R � OR and Simulation M Healthcare PW 2010

  39. 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

  40. 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

  41. 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

  42. C C Pooling: Nurse Practitioner Pooling: Nurse Practitioner Overflow � 1 � 2 Necessarily Simulation OR and Simulation M Healthcare PW 2010

  43. Pooled scenario Pooled scenario Next τ 1 Next τ 2 OR and Simulation M Healthcare PW 2010

  44. Overflow scenario Overflow scenario Overflow τ 1 τ 2 Necessarily Simulation OR and Simulation M Healthcare PW 2010

  45. 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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