Dynamic Master Surgical Schedules in a Medium Size Hospital

1. Dynamic Master Surgical Schedules in a Medium Size Hospital A. Agnetis1, A. Coppi1, M. Corsini1, G. Dellino2, C. Meloni3, M. Pranzo1 1 Dipartimento di Ingegneria dell’Informazione, Università di Siena 2 IMT Institute for Advanced Studies, Lucca 3 Dipartimento di Ingegneria Elettronica, Politecnico di Bari MOGISA group meeting, Narbonne, June 28, 2012

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

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…]

4. Lean thinking principles • Definevaluefrom the customer’s perspective • Identify the value stream map • Create the conditions for a smooth flow • Let the customer pull the process • Aim at perfection

5. Leanmanufacturing • 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. 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

8. 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. Departments Acceptance Radiology Image diag. Medicine Surgery ICU Surgical path (elective/non elective) Medical path (elective/non elective) Outpatients Birth path Low care

11. 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 the actual demand should drive the surgical plan

12. Surgical plan • Defining next week’s surgical plan consists of two distinct decision steps: • Assignoperatingroomsessionstosurgicalspecialties (Master Surgical Schedule) • Select (elective) patientsfromwaitinglists (Surgical Case Assignment)

13. MSS Mon Tue Wed Thu Fri OR1 SCAP OR2 OR3 waiting lists OR4 Gynecology Urology Daysurgery General surgery Ear-nose-throat Orthopedics OR5 ____________________ ____________________ ____________________ ____________________ ____________________ ____________________ OR6

14. MSSP and SCAP • Input: electivewaitinglistsforeachspecialty • Patient record: • Output: one-weekplan (MSS+SCA) ofelectivesurgeries in eachoperatingroom Specialty: Day surgery Case ID Duration (min) Priority class Decision date Waiting time (days) Due date 6210 30 B 15/06/2011 27 15/08/2011

15. 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

16. “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

17. Literature • A verylargeliteratureexists on operatingroomscheduling, 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 Houdenhovenet al. (2007), Sieret al. (1997)… • relativelyfewpapers on integrationaspects – vanBerkel (2011), vanOostrumet al (2008), Everset al (2010)

18. 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

19. 1. Fixedmodel • The MSS isgiven, only the surgical case assignmenthastobecomputed • The problem is solved by a (fairly simple) integer linear program, in which decision variables are • xish= 1 if case i of specialty s is assigned to the h-th session devoted to that specialty

20. Case duration Kis = PisWis Waiting time (adjusted by priority class) Score Duration of OR session

21. 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

22. 2. (Totally) flexiblemodel • The MSS and SCA are concurrentlycomputedfrom scratch • The problem is solved by an integer linear program, in which decision variables are • ysjwz= 1 if specialty s is performed in room j, on day w, in a session of type z • xisjwz= 1 if case i of specialty s is performed in room j, on day w, in a session of type z

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

24. 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,D): • the MSS remains the same for b weeks • a new MSS has distance at most D from the reference MSS

25. 3. Bounded-distancemodel • To restrict the search to MSSs having distance at most D from a reference MSS, a modified version of the Flexible model is solved, adding

26. 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

27. Case study • 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

28. Case study • The analysis focuses on the first 6 ORs of the operating theater of San Giuseppe • 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

29. specialty

31. Change policies • D(b,D): the MSS remains the same for b weeks, at the end of which at most D changes are allowed from the last MSS • S(b,D): 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 Dfrom a given MSS

32. 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)

33. 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, the appropriate model (fixed, bounded-distance or flexible) was solved

34. Experiments • All tests have been performed using OPL Studio 6.1 and the CPLEX 11.2 MILP solver • Symmetry-breaking constraints have been added to the mathematical programming models • Time limits were set to 1 minute for the fixed-MSS model and 15 minutes for bounded-distance or flexible model • Average gap below 2%

35. Avg. weekly performance - base

36. Avg. weekly performance - stressed

37. Final vs. initialwaitinglists

38. Final vs. initialwaitinglists (byclass)

39. Conclusions • Solving SCAP every week (even in the stable policy) is highly beneficial, however… • …anychange policy improves over the stable policy in terms of all indices • No major differencesamongchangepolicies, 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

40. Ongoing and future research • Heuristics for flexible and bounded-distance • 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