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

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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…]

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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

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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)

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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

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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

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# 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