Developing a Multi-Methodology Operating

Theatre Scheduling Support System

Marion PennWith: Prof. Chris Potts and Prof. Paul Harper

IMA 29th March 2010

Outline• Introduction to topic and literature

• Soft OR - Understanding the problem

• Hard OR - Master Timetable

– Set Up

– Formulation

– Results to date

– Future Work

Background Hospitals face the challenges of;

• Demanding Targets– Shorter waits for operations– Reduced cancellations

• Financial Constraints

• Resource Constraints

Theatre Scheduling

My Objective

• To develop a methodology that can be used in hospitals to produce efficient theatre schedules.

Literature • Over 100 papers

• Methods – LP, Simulation, Queuing …

• Whole system … narrow aspects

• Factors – Theatre Time– Staff– Beds

Gaps in the Literature

• Key Factors not brought together

• Lack of Implementation

• Addressing Stochastic Elements

Cognitive mapping

• Visual

• Brings together ideas

• Enables joint understanding

• Explores links

• Causal relationships

Meet Targets

Reduce Cancellations

Reduce waiting lists/

times

Do more work

Reduce clinical cancellations

Reduce patient cancellations

Reduce number of appt

inconvenient

Reduce no. of operation not

required

Reduce no. of unfit for surgery

Reduce no. of Pre-op guidance

not followed

Reduce no of DNA

Include more in pre-assessments

More opportunity for patients to

understand what is involved /

consent at pre-assessent

Introduce contacting

patients 48 hours before op

Reduce occurrence of missing notes/

admin error

More beds available

Bring more patients in early

to make sure they get beds

Reduce use of beds by medical

patients

-

-

Improve predictability of medical case

load

Understand seasonal variationsIncrease

understanding of variability of

demand

-

Ability to predict bed

usageImproved ability predict to LOS

Use a diary system, booking

only if bed, theatre time, equipment all

available

Ability to plan to smooth demand

for beds

Ability to book patients further in

advance

Ability to include bed usage in

planning

Have Matron to oversee bookings/

theatres

Reduce over booking/overruns

Increase capacity

Reduce demand for

surgery

Increasing proportion of out

patients need surgery

-

More filtered by physio

More well being activities in the

community

Reduce Outpatient numbers

Raise GP awareness of when to refer and fitness

for surgery

Raise GP awareness of capacity and

surgeons specialisations so refer appropriately

Introduce regular GP newsletter/

booklet of surgeon info/website

Increase face to face contacts with GPs e.g.

quarterly meetings cycling through specs

Advertise via practice managers

Increase proportion of sessions that start on time

Have notes ready Have necessary

facilities open, before surgery

due to start

Get ordered list to wards

sooner

Run 3 session days

Whole hospital work later on specific days

Increased staff flexibility

More theatre staff (out side divisions

control!)

Use capacity when surgeons

on leave etc

Increase matching of bookings to available time

Purchase more equipment so not a limiting factor

Book in front of target i.e. shorter

waits

Book at decision to

operate

Cognitive Map Showing My Understanding of IssuesSurrounding Theatre Management

June, 2007

Reduce number of self heal/die

on list

More theatres, surgeons and anaesthetists

Where appropriate have two juniors running

surgeries with seniors moving between them.

Designate sessions of all major/minor

cases

Allow patients to opt in to receive info. By email

Assign beds in advance and treat as though patient

present

More all day lists

-

Increase time available for

infection control

Computerise notes

Constraints on system e.g. theatre type

required

Follow up if DNA pre-

assessment

Optimise Theatre

Timetable

-

Hard OR – From Literature

• Strategic– Planning work load– Dividing theatre time

• Longer term tactical planning– Developing a Master Theatre Timetable

• Day to day scheduling of electives– Booking into slots– Live changes to the schedule

Master Timetable

• What– Assigns slots of theatre time to surgeons– Cyclic

• How– Linear / Goal Programming– Heuristics– Simulation– Column Generation

Inputs

• Theatre types and availability

• Numbers of theatre slots required

• Surgeon (and other staff) availability

• Surgeon preferences

• Expected bed usage (by ward)

• Equipment availability

• Bed availability and usage

Variables•Xi,t,d,s Assigns surgeons to slots.

•Yi,t,d,s If a slot has been assigned to a surgeon with a low preference score for it.

•Ui,t,d,s If surgeon in same theatre for consecutive slots.

•Vi,t,d,s If surgeon in different theatres for consec. slots.

•Wi,t,d,s If slot repeated weekly.

• Expected beds required each day. •Z Min difference between beds required and beds

available.X, Y, U, V and W are all binary variables.Index i represents an individual surgeon, t a theatre, d a dayin the cycle and s a daily theatre slot.

d

Significant Parameters

• Gh,t Types of theatres 1 if t is of type h, 0 otherwise

• Rh,t Number of slots of type h required by surgeon i

• Bi,t,j,w Expected number of patients in beds in ward k, j days after surgeon i

has a slot in theatre t• Dd,w Number of beds available on day d

in ward k

‘Straightforward’ Constraints

• Only use available slots

• Surgeons can only be in one place

• Surgeons availability

• Limit on surgeons no. slots per day

• Equipment constraint

Demand Constraints

•

Cover demand by theatre type

•

Meet each surgeon’s overall demand exactly

•

Surgeons don’t use any theatre more than

their total demand for its type(s)

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Bed Constraints

• Assigns

• Assigns Z

• Based on Gallivan & Utley’s formulation

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Gallivan S. and Utley M. (2005) ‘Modelling admissions booking of elective in-patients into a treatment centre’, IMA Journal of Management Mathematics 16, p. 305-315

Other Constraints

• Assign values to;– U– V– W– Y

• Based on the values in X

Objectives• Find a feasible timetable

• Smooth Bed usage

• Max surgeon pref. score

• Min low pref. scores

• Max all day slots

• Repeat slots weekly

• Avoid consecutive slots in

different theatres

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Output

• Weekly / Monthly Schedule– Slots for Surgeons

• Expected Bed Usage

• Ratings against objectives

Early Results

Indicator Original Timetable

LP Timetable

Max beds used 90 83

No. Surgeons changing theatres

0 0

No. of all day slots 30 55

Repeat weekly 166 178

Bed SmoothingComparing current and suggested timetables bed usage.

0

20

40

60

80

100

120

140

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 Day 13 Day 14

Day of Cycle

Nu

mb

er

of

be

ds

Max. number of beds availableBeds required by current timetableMax. beds required by current timetableBeds required by suggested timetableMax. beds required by suggested timetable

Future Work

• Further Develop Master Timetable

• Day to day scheduling tool

• Warning systems

Questions/ Comments