1. Dynamic Master Surgical Schedules in a Medium Size Hospital A. Agnetis 1, A. Coppi 1, M. Corsini 1, G. Dellino 2, C. Meloni 3, M. Pranzo 1 1 Dipartimento di Ingegneria dell’Informazione, Università di Siena 2 IMT Institute for Advanced Studies, Lucca 3 Dipartimento di Ingegneria Elettronica, Politecnico di Bari

2. Outline of the talk Lean thinking The Master Surgical Scheduling problem MSS change policies Computational experiments Conclusions 2

3. Lean thinking Lean thinking is a management philosophy based on a number of key principles: – Focus on the value delivered – Respect for people – Continuous improvement Lean thinking aims at reducing or eliminating all sources of waste (time, money, energy etc) Well-established concept in manufacturing [since 1980s…] 3

4. Lean thinking principles 1.Define value from the customer’s perspective 2.Identify the value stream map 3.Create the conditions for a smooth flow 4.Let the customer pull the process 5.Aim at perfection 4

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7. Lean manufacturing Lean manufacturing focuses on value-adding processes rather than on production volume, and aims at delivering the right quantity, at the right time, of the right quality Lean manufacturing aims at reducing or eliminating all sources of waste, typically consisting in not-value-adding activities (waits, setups, rework…) 7

9. Lean thinking in healthcare Lean thinking in healthcare is a relatively new concept [  2000] Customers  Patients Demand for products  Demand for services Production plant  Wards, operating rooms etc Product flow  Patient flow 9

10. Value creation The value of a service is related to the ability of satisfying the customer’s needs at a given time Value-creating activities should be continuously carried out throughout the system, minimizing the time unnecessarily spent in wait, idle, rework etc This requires a major organizational shift 10

11. AcceptanceMedicineSurgeryRadiologyImage diag. Departments Surgical path (elective/non elective) ICU Medical path (elective/non elective) Outpatients Birth path Low care

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14. Pull system The customers trigger the release of a service, it is not planned in advance “None should produce goods or services until the customer requests them” [Womack and Jones 1996] In the context of the surgical process, this means that actual demand should drive the surgical plan 14

15. The surgical path (Empoli) ACCESS PRE - SURGERY SURGERY POST SURGERY Patient admitted Patient at first aid Patient admitted Visit Patient Registration Preparation Reception Surgical operation Post surgery treatment Discharge Death Follow- up Evaluate donation Pre- hospitalization

16. Surgical plan Defining next week’s surgical plan consists of two distinct decision steps: 1.Assign operating room sessions to surgical specialties (Master Surgical Schedule) 2.Select (elective) patients from waiting lists (Surgical Case Assignment) 16

17. ____ ____ ____ ____ ____ 17 ____ ____ ____ ____ ____ MonTueWedThuFri OR 1 OR 2 OR 3 OR 4 OR 5 OR 6 OrthopedicsUrology MSS SCAP Gynecology Day surgery General surgery Ear-nose- throat waiting lists

18. MSSP and SCAP Input: elective waiting lists for each specialty – Patient record: Output: one-week plan (MSS+SCA) of elective surgeries in each operating room 18 Specialty: Day surgery Case IDDecision date Duration (min) Priority class Waiting time (days) Due date 621015/06/201130B2715/08/2011

19. Objectives and methods Design an optimization model for elective surgery planning coherent with the pull concept We want to evaluate benefits vs. problems related to: – Adopting an exact approach to SCAP – Designing a long-term MSS strategy 19

20. “Drivers” Efficiency: optimizing the utilization of operating rooms Quality of service: waiting time reduction and compliance with regional regulations Safety: precedence given to highest-priority cases Sustainability: easy to apply, does not require large computational resources 20

21. 21 A very large literature exists on operating room scheduling, either: addressing the above problems separately -- Testi et al. (2007, 2009) use a sequential decomposition approach or focusing on a single problem -- Blake et al (2002), Van Houdenhoven et al. (2007), Sier et al. (1997)… relatively few papers on integration aspects – van Berkel (2011), van Oostrum et al (2008), Evers et al (2010) Literature

22. Stable MSS In many cases, hospitals adopt a stable MSS policy -- the same MSS is kept throughout one year (or so) – Allows simpler forecast of pre- and post-surgical bed occupancy – Yields repetitive schedules for surgeons and personnel but – No link with the current status of the waiting lists – Problems to accommodate unpredictable arrivals, nervousness 22

23. Fixed model The MSS is given, only the surgical case assignment has to be computed The problem is solved by a (fairly simple) integer linear program, in which decision variables are – x ish = 1 if case i of specialty s is assigned to the h-th session devoted to that specialty 23

24. 24 Duration of OR session Score K is = P is (W C − R is ) Slack time Duration

25. Lean Thinking In a lean organization, planning must be done considering the actual demand In surgical planning, the demand is represented by the current state of the waiting lists We want to investigate the advantages of a dynamic vs. a stable MSS 25

26. Dynamic MSS If the MSS varies over time, the capacity of the operating theater can be better matched with the demand for surgeries The surgical process can be more directly pulled by the demand Tradeoff between flexibility and complexity Must be accepted by personnel and processes must be designed accordingly 26

27. MSSP and SCAP The two problems can be addressed concurrently, by a single optimization model, or First the MSS is chosen, and then OR sessions are filled with cases selected from the waiting lists (decomposition approach) Adopting one approach or the other depends on available computational resources and on management policies 27

28. (Totally) flexible policy The MSS and SCA are concurrently computed from scratch The problem is solved by an integer linear program, in which decision variables are – y sjwz = 1 if specialty s is performed in room j, on day w, in a session of type z – x isjwz = 1 if case i of specialty s is performed in room j, on day w, in a session of type z 28

29. 29 Duration of OR session Min/max no. of sessions for each specialty Min/max no. of parallel sessions for each specialty Score

30. Changing MSS An intermediate policy between flexible and stable is to allow a limited number of changes (distance) with respect to a reference MSS A change consists in reallocating one OR session from one specialty to another Change policy (b,  ): – the MSS remains the same for b weeks – a new MSS has distance at most  from the reference MSS 30

31. Bounded-distance model To restrict the search to MSSs having distance at most  from a reference MSS, a modified version of the Flexible model is solved, adding 31

32. Change policies Key question: How much flexibility is needed to get significant improvements in service quality while keeping complexity acceptable? The idea is to evaluate such tradeoff simulating various scenarios 32

33. 33 San Giuseppe is a public general hospital located in Empoli, Tuscany (Italy) Almost 500.000 square feet, over 400 beds Recently, the hospital started a major revision of its processes, also favored by the regional government policy The hospital managers want to evaluate the effectiveness of their current MSS planning policy against alternative solutions, from the viewpoint of OR utilization and due date performance Case study

34. The analysis focuses on the first 6 ORs of the operating theater in Empoli hospital – Each case is assigned a score related to the current waiting time and priority class – To accommodate emergencies, there must always be either an empty OR or an OR with a short case in process – Various constraints on the number of OR sessions for each specialty, specialty-to-room assignments, parallel sessions etc 34

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37. Change policies D(b,  ): the MSS remains the same for b weeks, at the end of which at most  changes are allowed from the last MSS S(b,  ): the MSS remains the same for b weeks, at the end of which the MSS can be replaced by a new one, having distance at most  from a given MSS 37

38. Change policies selected (52,0) - keep the same MSS throughout the year D(13,∞) - a new MSS every three months D(4,2) - two changes at the end of a 4-week period D(1,1) - one change per week from previous MSS D(1, ∞) - a new MSS every week S(1,1) - one change per week from a given MSS (the MSS presently in use in the hospital) 38

39. Experiments We simulated the behavior of the system in 10 one-year realizations Actual arrival rates for each surgical discipline All simulations started from the real waiting lists For each week, either the fixed-MSS model, the buonded-distance or the flexible model was solved 39

40. Avg. weekly performance - base 40 # cases# late cases % empty t.u. % empty t.u.* mean lateness max lateness mean tardiness (52,0)185534,62%4,59%-144211 D(13,  ) 193490,17%0,00%-17309 D(4,2)194320,03%0,00%-18167 D(1,1)194290,02%0,00%-17147 D(1,  ) 193300,04%0,00%-17137 S(1,1)193320,10%0,00%-17157

41. Avg. weekly performance - stressed 41 # cases# late cases % empty t.u. % empty t.u.* mean lateness max lateness mean tardiness (52,0) 187773,88%3,87%-55817 D(13,  ) 193550,02%0,00%-54715 D(4,2) 194520,01%0,00%-63713 D(1,1) 193460,00% -52912 D(1,  ) 193440,03%0,00%-52712 S(1,1) 193430,08%0,00%-52812

42. Final vs. initial waiting lists 42 # cases# late cases mean lateness max lateness mean tardiness waiting time (52,0) 1480180-3839237 D(13,  ) 10819-56-2022 D(4,2) 10540-59-16022 D(1,1) 10590-60-20021 D(1,  ) 10680-60-20021 S(1,1) 10670-59-18022 Initial 1373777161803390

43. Final vs. initial waiting lists (by class) 43 ABC # casLat.Wait# casLat.Wait# casLat.Wait (52,0) 102-524534-2138843-5237 D(13,  ) 41-227319-3821719-6623 D(4,2) 30-272266-4316757-6524 D(1,1) 29-282252-4415776-6623 D(1,  ) 27-282258-4514781-6524 S(1,1) 28-272262-4415775-6524 Initial 1572555413187880313103

44. Final vs. initial waiting lists 44 General surgery Urology Gynecology General surgery Urology Gynecology Day surgery Ear-nose-throat Orthopedics Day surgery Ear-nose-throat Orthopedics Day surgery Ear-nose-throat Orthopedics Flexible policy Stable policy D(4,2) D(1,1)

45. Interaction among specialties With the Stable policy, otolaryngology has depleted significantly, but this occurs at the expense of other specialties! 45 Day surgery Ear-nose-throat Orthopedics Stable policy

46. Lateness 46 StableFlexibleD(4,2)D(1,1)

47. Conclusions Solving SCAP every week (even in the stable policy) is highly beneficial, however… …any change policy improves over the stable policy in terms of all indices No major differences among change policies, only D(13,  ) slightly worse than the others Allowing even a small degree of flexibility largely pays off in room utilization, waiting list balancing and waiting time reduction Small, frequent changes are better than large, infrequent changes 47

48. Ongoing and future research Model refinement, including stochastic issues such as: Variable demand patterns over time Stochastic surgical case durations Integration with the surgical path: Bed management Pre-hospitalization Field testing 48