Improving Chemotherapy Scheduling at the

BC Cancer AgencyCIHR Team in

Operations Research for Improved Cancer Care

The Challenge

Increasing Volumes of Chemotherapy Patients New therapies More cases

Antiquated scheduling methodology Burdensome on staff

• Schedulers• Pharmacy

Inconvenient for patients• Most notified one day before treatment

Goals Increase time between notification and appointment Simplify and automate process Put changes into practice

2

Optimization Problem DescriptionG

IFU

RC

RT

Nur

sing

tim

e

Cha

ir

time

Protocol name

Start of shift

Prep time

Lunch break

Break

Time CH

AIR

25

CH

AIR

26

CH

AIR

27

CH

AIR

28

8:008:158:308:459:009:159:309:4510:0010:1510:3010:4511:0011:1511:3011:4512:0012:1512:3012:4513:0013:1513:3013:4514:0014:1514:3014:4515:0015:1515:3015:4516:0016:1516:3016:4517:0017:1517:3017:4518:0018:1518:3018:45

NURSE07

CTC

HB

RA

JFE

CD

UG

IFFI

RB

BR

AJ

TR

GU

EP

BR

AJ

TR

BR

AJ

DTF

EC

Break

Break

Treatment slots

End of shift

A Daily Chemotherapy Schedule

Optimization Problem Description1 2 3 4 Nurse 5 6 7 8 Nurse 9 10 11 12 Nurse 13 14 15 16 Nurse

8:008:158:308:459:009:159:309:45

10:0010:1510:3010:4511:0011:1511:3011:4512:0012:1512:3012:4513:0013:1513:3013:4514:0014:1514:3014:4515:0015:1515:3015:4516:0016:1516:3016:4517:0017:1517:3017:4518:0018:1518:3018:45

chair: 3:30 5:00 2:30 1:00 12:00nurse: 1:15 2:00 0:30 0:15 4:00cplxity: 5 5 3 1 14

Nurse 1 Nurse 2

Prep Time

Nurse … Nurse 9Time Slot

Prep Time

Prep Time Prep Time

chai

r: 1:

30nu

rse:

0:3

0cp

lx: 2

chai

r: 5:

00nu

rse:

2:0

0cp

lx: 5

chai

r: 2:

30nu

rse:

0:3

0cp

lx: 3

chai

r: 1:

00nu

rse:

0:1

5cp

lx: 1

chai

r: 2:

00nu

rse:

0:4

5cp

lx: 3

List of Patients

Decision Variables

= 1 if patient p is scheduled at treatment slot i in chair j of nurse k, 0 otherwise

pijkx

1,0∈pijkx

Auxiliary Variables

= 1 if nurse k has patients scheduled, 0 otherwise= 1 if chair j of nurse k has patients scheduled, 0

otherwise= maximum nurse workload= shortfall in number of patients with respect to

second part of the shift for nurse k= shortfall in number of patients with respect to

first part of the shift for nurse k

Λ+kδ

−kδ

0,,

1,0,

≥Λ

∈ΩΘ−+kk

kk

δδ

kΘ

jkΩ

Parameters

: chair time for patient p: nurse time for patient p: complexity for patient p: maximum number of patients to be assigned to nurse k: maximum chair time to be assigned to nurse k: maximum nurse time to be assigned to nurse k: maximum complexity to be assigned to nurse k: maximum number of patients for nurse k that can start

treatment simultaneously (nursing constraint): maximum number of patients for all nurses that can

start treatment simultaneously (pharmacy constraint)

pξpνpχ

kΠ

kΞkΝkΧ

kΓ

Ψ

Constraints

All patients need to be scheduled

At most one patient can be scheduled in a given chair at each treatment slot

At most one patient receiving nursing care in any of the chairs of each nurse

1=∑ijk

pijkx p∀

1ˆ

ˆ ≤∑ ∑≤≤−p iii

pjki

p

xξ

kji ,,∀

1ˆ

ˆ ≤∑ ∑ ∑≤≤−p iii j

pjki

p

xν

ki,∀

Constraints

Maximum scheduled:

number of patients

chair time

nurse time

complexity per nurse Maximum number of patients to start treatment

simultaneously (same slot)

per nurse

overall

kpij

pijkx Π≤∑

kpij

ppijkx Ξ≤⋅∑ ξ

kpij

ppijkx Ν≤⋅∑ ν

kpij

ppijkx Χ≤⋅∑ χ

k∀

k∀

k∀

k∀

kpj

pijkx Γ≤∑

Ψ≤∑pjk

pijkx

ki,∀

i∀

Constraints

Definition of maximum nurse workload in terms of:(only one of the following active at a time)

number of patients

chair time

nurse time

complexity

Λ≤∑pij

pijkx

Λ≤⋅∑pij

ppijkx ξ

Λ≤⋅∑pij

ppijkx ν

Λ≤⋅∑pij

ppijkx χ

k∀

k∀

k∀

k∀

Constraints

Relationship between scheduling variables and indicators per nurse

Relationship between scheduling variables and indicators per chair-nurse

Balance between number of patients in first and second part of nursing shift

kpijkx Θ≤

kpijkx Ω≤

−

∈

+

∈

+=+ ∑∑ kPMpij

pijkk

AMpij

pijk xx δδ

)()(

kjip ,,,∀

kjip ,,,∀

k∀

Objective Function

Where Ф can be chosen as: Maximum nurse workload (defined as number of

patients, chair time, nurse time or complexity)

Number of nurses scheduled

Number of chairs used

( )∑ −+ ++Φk

kkMin δδ

Λ=Φ

∑Θ=Φk

k

∑Ω=Φjk

jk

The Model in Numbers

Typical scenario: 40 to 50 patients to be scheduled 8-9 nurses (8-hr shift; 6-hr of effective treatment) 4 chairs per nurse 11-hr workday (8:00 to 19:00) divided in 15’ slots

Resolution: Decision variables: over 100,000 (most binary) Constraints: over 40,000 Solution time: ~1-5’ to optimality

(30” for gap < 5%) Modeling platform: GAMS/CPLEX Database platform: MS Access Tool platform: VBA

Output Report – Nursing ScheduleNURSE01 NURSE02 NURSE03 NURSE04 NURSE05 NURSE06 NURSE07

Time8:00 08:15 08:30 08:45 09:00 29:15 09:30 19:45 110:00 110:15 110:30 110:45 311:00 211:15 011:30 011:45 112:00 112:15 112:30 212:45 113:00 113:15 213:30 013:45 214:00 114:15 214:30 214:45 115:00 215:15 415:30 115:45 216:00 116:15 016:30 016:45 017:00 117:15 017:30 017:45 018:00 018:15 018:30 018:45 0

# Patients 40 2 6 7 6 6 6 7Total Time 39:0 3:0 6:0 6:15 5:45 6:15 6:0 5:45Booked Time 30:45 2:30 4:45 4:45 4:45 4:30 4:45 4:45% Booked 79% 83% 79% 76% 83% 72% 79% 83%Chair Time 72:15 4:30 11:0 12:0 11:0 8:45 13:0 12:0

# Patient Starts

UGIAJFFOX (45min)

GIIR (45min)

GUEP (30min)

CTCH (60min)

UGIFFIRB (45min)

BRAJTR (30min)

BRAJDTFEC (30min)

BRAJFECD (60min)

BRAJTR (30min)

BRAJTR (30min)

BRAJACTT (90min)

UBRAVGEMP (45min)

BRAJTR (30min)

BRCH (75min)

BRCH (75min)

BRAJTR (30min)

BRLAACDT (75min)

UGIFFIRB (45min)

BRAJTR (30min)

GIPGEM (30min)

GIFOLFIRI (45min)

BRAVTR (45min)

GUEP (30min)

BRAVTR (45min)

UGIFFIRB (45min)

UGIFFIRB (45min)

BRAJTR (30min)

GUAVPG (30min)

CTCH (60min)

BRAVTR (45min)

BRAJTR (30min)

Nurse

GIFURCRT (60min)

BRLAACD (90min)

LYFLUDR (45min)

USA0 (90min)

BRAJTR (30min)

UGIFOLFOX (45min)

BRAJTR (30min)

GIFOLFIRI (45min)

ULYRMTN (30min)

B r e a k

B r e a k

Brea

k

Brea

k

Bre

akBr

eak

Brea

k

Brea

kBr

eak

B r e a k

Brea

k

Output Report – Chair Schedule

Time# Patient

Starts CH

AIR

01

CH

AIR

02

CH

AIR

03

CH

AIR

04

CH

AIR

05

CH

AIR

06

CH

AIR

07

CH

AIR

08

CH

AIR

09

CH

AIR

10

CH

AIR

11

CH

AIR

12

CH

AIR

13

CH

AIR

14

CH

AIR

15

CH

AIR

16

CH

AIR

17

CH

AIR

18

CH

AIR

19

CH

AIR

20

CH

AIR

21

CH

AIR

22

CH

AIR

23

CH

AIR

24

CH

AIR

25

CH

AIR

26

CH

AIR

27

CH

AIR

28

8:00 08:15 08:30 08:45 09:00 29:15 09:30 19:45 110:00 110:15 110:30 110:45 311:00 211:15 011:30 011:45 112:00 112:15 112:30 212:45 113:00 113:15 213:30 013:45 214:00 114:15 214:30 214:45 115:00 215:15 415:30 115:45 216:00 116:15 016:30 016:45 017:00 117:15 017:30 017:45 018:00 018:15 018:30 018:45 0

1 1 0 0 2 0 3 1 2 1 2 2 3 1 0 2 3 1 1 1 3 1 1 1 2 2 3 01:00 1:30 0 0 2:15 0 2:00 0:30 1:15 0:30 1:15 1:45 2:30 1:15 0 1:00 2:30 0:45 0:30 0:45 1:45 0:45 0:45 1:30 2:00 1:15 1:30 03:00 1:30 0 0 6:00 0 3:15 1:45 5:00 0:45 1:30 4:45 6:00 2:30 0 2:30 4:30 0:45 0:45 2:45 3:00 1:45 3:00 5:15 4:30 3:00 4:30 0

UG

IFFI

RB

BR

AJ

TR

GU

EP

BR

AJ

TR

BR

AJ

DTF

EC

BR

AJA

CTT

CTC

HB

RA

JFE

CD

GIIR

UG

IAJF

FO

X

BR

AJ

TRU

BR

AV

GE

MP

BR

AJ

TR

BR

AV

TR

BR

AJ

TR

GIF

OLF

IR

I

BR

LAA

CD

TU

GIF

FIR

BG

IPG

EM

BR

CH

ULY

RM

TNB

RA

JTR

BR

AJ

TRG

IFO

LFI

RI

BR

CH

BR

AJ

TR

BR

AJ

TRB

RA

VTR

UG

IFFI

RB

CTC

H

GU

EP

UG

IFFI

RB

GU

AV

PG

LYFL

UD

RB

RA

JTR

BR

AV

TR

NURSE06 NURSE07NURSE01 NURSE02 NURSE03 NURSE04

Chair time

# PatientsNursing time

NURSE05

GIF

UR

CR

T

BR

LAA

CD

US

A0

UG

IFO

LFO

X

Break

Break

Brea

k

Brea

k

Bre

akBr

eak

Brea

k

Brea

kBr

eak

Break

Brea

k

Scheduling Tool Concept

Visual interface for managers to review and modify schedule

Initial schedule loaded from optimization model

Patients can be re-scheduled across nurses Constraints are checked “on the fly” and

warnings/error messages reported to user Workload stats are updated after every change Web-based platform

Schedule Modifier Tool ConceptPatients can be re-scheduled (drag & drop)

Stats are updated after changes in

schedule

Initial schedule loaded from

optimization model

Discussion

Implementation plan being developed Daily optimization model Requires expert involvement Must interface with system• Inputs•Outputs•Standalone tool

Ignores variability Many inputs are arbitrary now

18

Overall Concluding Comments

Concluding Remarks Just touched the tip of the iceberg of potential applications Many challenging optimization (OR) problems arise in

healthcare They can significantly effect practice both at the operational

and strategic levels They offer great research potential Often solutions cannot be delivered easily so guidelines are

necessary Researchers must be cognizant of needs of staff and work

collaboratively to develop applications