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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 - PowerPoint PPT Presentation
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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 Siena2 IMT Institute for Advanced Studies, Lucca
3 Dipartimento di Ingegneria Elettronica, Politecnico di Bari
MOGISA group meeting, Narbonne, June 28, 2012
Outline of the talk
• Lean thinking• The Master Surgical Scheduling problem• MSS change policies• Computational experiments• Conclusions
2
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
Lean thinking principles
1. Define value from the customer’s perspective2. Identify the value stream map3. Create the conditions for a smooth flow4. Let the customer pull the process5. Aim at perfection
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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…)
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Lean thinking in healthcare
• Lean thinking in healthcare is a relatively new concept [2000]
Customers PatientsDemand for products Demand for servicesProduction plant Wards, operating rooms etcProduct flow Patient flow
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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
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Acceptance Medicine SurgeryRadiology Image diag.
Departments
Surgical path (elective/non elective)
ICU
Medical path (elective/non elective)
Outpatients
Birth path
Low care
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
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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)
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____________________ 13
____________________
____________________
____________________
____________________
____________________
Mon Tue Wed Thu Fri
OR1
OR2
OR3
OR4
OR5
OR6
OrthopedicsUrology
MSS
SCAP
Gynecology Day surgery
General surgery
Ear-nose-throat
waiting lists
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
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Specialty: Day surgery
Case ID Decision dateDuration(min)
Priority class
Waiting time (days) Due date
6210 15/06/201130 B 27 15/08/2011
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
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“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
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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
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
personnelbut
– No link with the current status of the waiting lists– Problems to accommodate unpredictable arrivals,
nervousness18
1. 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– xish = 1 if case i of specialty s is assigned to the h-th
session devoted to that specialty
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Duration of OR session
Score
Kis = PisWisWaiting time (adjusted by priority class)
Case duration
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
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2. (Totally) flexible model
• The MSS and SCA are concurrently computed from 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
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Duration of OR session
Min/max no. of sessions for each specialty
Min/max no. of parallel sessions for each specialty
Score
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 MSS26
3. 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
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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
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• 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
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
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specialty
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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
33
Change policies selected(52,0) - keep the same MSS throughout the yearD(13,∞) - a new MSS every three monthsD(4,2) - two changes at the end of a 4-week periodD(1,1) - one change per week from previous MSSD(1, ∞) - a new MSS every weekS(1,1) - one change per week from a given MSS (the
MSS presently in use in the hospital)
34
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
35
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%36
Avg. weekly performance - base
37
# cases # late cases
% empty
t.u.
% empty t.u.*
mean lateness
max lateness
mean tardiness
(52,0) 185 53 4,62% 4,59% -14 42 11D(13, ) 193 49 0,17% 0,00% -17 30 9
D(4,2) 194 32 0,03% 0,00% -18 16 7D(1,1) 194 29 0,02% 0,00% -17 14 7
D(1, ) 193 30 0,04% 0,00% -17 13 7S(1,1) 193 32 0,10% 0,00% -17 15 7
Avg. weekly performance - stressed
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# cases # late cases
% empty
t.u.
% empty t.u.*
mean lateness
max lateness
mean tardiness
(52,0) 187 77 3,88% 3,87% -5 58 17D(13, ) 193 55 0,02% 0,00% -5 47 15
D(4,2) 194 52 0,01% 0,00% -6 37 13D(1,1) 193 46 0,00% 0,00% -5 29 12
D(1, ) 193 44 0,03% 0,00% -5 27 12S(1,1) 193 43 0,08% 0,00% -5 28 12
Final vs. initial waiting lists
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# cases # late cases
mean lateness
max lateness
mean tardiness
waiting time
(52,0) 1500 246 -31 47 3 54D(13, ) 1159 13 -46 -1 0 34D(4,2) 1049 9 -50 -4 0 30D(1,1) 1057 2 -53 -11 0 28D(1, ) 1056 0 -53 -13 0 21S(1,1) 1327 117 -37 23 1 40Initial 1373 777 16 180 33 90
Final vs. initial waiting lists (by class)
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A B C# cases Wait # cas Wait # cas Wait
(52,0) 102 24 534 38 843 37
D(13, ) 41 7 319 21 719 23
D(4,2) 30 2 266 16 757 24
D(1,1) 29 2 252 15 776 23
D(1, ) 27 2 258 14 781 24
S(1,1) 28 2 262 15 775 24
Initial 157 55 413 78 803 103
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
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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 testing43