PATIENT SCHEDULING AT COLUMBIA’S RADIATION ONCOLOGY TREATMENT CENTERBy David Kuo Chao and Ji Soo Han

Introduction Radiation Oncology

Treatment Center Cancer Clients Parallel Machines

Client Urgency Stage of Cancer Availability

Appointments Date Time Duration

The Problem - Current State Appointment Scheduling

Diagnosed Patients Meet with one of three oncologists Receives a treatment plan that consists of

Frequency of Visits Range of Treatable Dates Number of Visits

Operating Hours 9 AM – 5 PM Monday through Friday Exceptions for High Priority Patients

The Problem - Current State The Current System

After receiving a treatment plan, patients: Schedule an appointment on a FCFS basis Patients have individual “release dates”

The current process is “Not Broken” The system lacks:

Efficiency Can lead to overtime hours for doctors and

nurses Can lead to idle time

System Design Patients

Release Dates Referral-to-

Treatment Treatment

Duration Average time of

treatment < few minutes

Focus on set-up times Average (15-30

minutes)

Due Dates Stage of Cancer

Patient Priority System of

Weights: Urgency of Care Flexibility of Time Proximity to

Treatment Center

The Problem: The Two Areas of Concern

Appointment Scheduling Given a set of dates, a

patient schedules an appointment depending on:

Availability Frequency of Treatment Release Date Health Condition Urgency of Treatment

Daily Scheduling Three Working

Oncologists Machines in Parallel

Patients arrive by schedule

Varying: Treatment Times Set-Up Times

Area of Treatment Type of Cancer Stage of Cancer

Delayed Arrivals How do we handle a

delay more effectively?

The Problem The combination of two problems

presents: Appointment schedule will dictate daily

demand Daily capacity will directly impact the number

of appointments per day Minimizing Total Tardiness

Parallel Machines (3) NP-Hard problem

The Problem: Goals Costs/Profits

Increase Profits Increase Capacity

Reduce Costs Idle Time

Machines Staff

Additional Machine(s)

Maintenance Costs

Waiting Times Per Visit

Incentives for Promptness

Reduce Back-Log Per Appointment

Weighted System Provide Care to

Urgent Patients Equal Daily Demand

Smooth Out Peaks Reduces

Idle/Overwork

Solution: Our Approach Multifaceted problem

with too many variables

Patients need multiple treatments per week (precedence)

So we broke it down into two smaller problems Day to day operations Weekly operations

Day to day Finding an optimal

schedule for each given day of patients

Minimizes waiting time and clinic operation time

Weekly Finding an optimal day

to schedule patients during a given treatment week/window

Solution: The Models Weekly:

P3|rj , prec|ΣwjTj Model will prioritize

higher weighted patients for treatment scheduling

Accounts for days available and optimal treatment time period (due date)

Processing time is uniform

Fill days to set capacity

Daily P3|rj|Lmax model uses given

estimated processing time for treatment

Creates a schedule that minimizes probability of going over operation hours (due date)

Scheduling: Weekly P3|rj , prec|ΣwjTj Given:

Release dates Due dates Weights Any precedence (chain) Each processing time =

1 Capacity of each

machine per day Each day = a time

period of 5 units of t

Solution: The problem is Strongly

NP- hard. Number of jobs per

week can run up to >100

Unrealistic to use heavy computer algorithms that are non poly time in high variable situation that is always changing and with exceptions

Develop heuristic

Scheduling: Weekly Each machine has

capacity of 5 patients per day

For each day (time period: Monday (t = (1,5)) Set A{} contains all

jobs not scheduled and are available (released) during Monday

Precedence constraints are split into multiple jobs

Set B{} contains all jobs not scheduled and not available during Monday

Set S{} contains all scheduled jobs

Take the highest weight job in A{} and assign to available machine move to S{}

Continue until capacity for day is full (15 patients)

Increase time period Update A{}, B{}

Scheduling: Daily P3|rj|Lmax Given:

Due date All due dates are

the same: end of operations for the day

Reduces problem to P3|rj|Cmax

Processing time Use probabilistic

model

Cause of waiting times and backups are the variations of treatment time for each patient Determine the

most probably processing time for each patient and use that as an estimate for the actual

Determining Processing Times Researched current

approaches to varying processing times in scheduling PERT scheduling

Program Evaluation and Review Technique

Expected time T is given by

Optimistic time (O) Most Likely time (M) Pessimistic time (P)

Doctor gives an estimate for O, M, P T is then

determined by the formula T = (O + 4M + P)/6

T is then used as the processing time for each patient in the daily problem

Patient Case Cindy has been

diagnosed with lung cancer Has accepted a

treatment plan with the oncologist

needs 3 treatments during week 1

Is available Monday (t = 1,5) Wednesday (t = 11,15) Thursday (t = 16,20) Friday (t = 21,25)

Split Cindy into 3 jobs for week 1: C1, C2, C3

Set release dates based on availability and due dates based on latest possible treatment

Cindy(47) - Lung Cancer

job rj O M P wj dj

C1 1 45 60 80 10 15

C2 11 20 30 50 5 20

C3 16 20 30 50 8 25

Weekly schedule InstanceCindy(47) - Lung Cancer

job rj O M P wj djC1 1 45 60 80 10 15C2 11 20 30 50 5 20C3 16 20 30 50 8 25

John(76) - Head/Neck Cancerjob rj O M P wj djJ1 1 45 60 80 13 5J2 6 20 30 50 3 10J3 16 20 30 50 3 20J4 21 60 80 90 12 25

Sarah(23) - Ovarian Cancerjob rj O M P wj djS1 6 20 30 60 6 10S2 21 15 30 45 3 25

Tom(66) - Pancreatic Cancerjob rj O M P wj djT1 1 45 60 80 10 5T2 6 20 30 50 5 10T3 11 20 30 50 8 15T4 16 30 35 40 7 20T5 21 40 50 60 11 25

Kyle(87) - Prostate Cancerjob rj O M P wj djK1 1 45 60 80 10 5K2 1 20 30 50 5 5K3 6 20 30 50 8 10K4 11 15 30 45 5 15K5 16 18 45 50 11 20K6 21 10 20 60 7 25

1 Machine system, with capacity of 5 patients per day

Set all processing times to 1 for each job for weekly scheduling

Weekly Schedule

t 1 2 3 4 5Monday J1 C1 T1 K1 K2

6 7 8 9 10Tuesday K3 S1 T2 J2

11 12 13 14 15Wednesday T3 K3 C2

16 17 18 19 20Thursday K5 C3 T4 J3

21 22 23 24 25Friday J4 T5 K6 S2

Daily Schedule

Monday

job rj O M P wj dj

J1 1 45 60 80 13 300

C1 1 45 60 80 10 300

T1 1 45 60 80 10 300

K1 1 45 60 80 10 300

K2 1 20 30 50 5 300

Units of time in a day = 5 hours of clinic operating hours = 5*60 = 300 minutes

1 machine, minimize lateness = minimize make span

Get estimated T Use LPT

job TjJ1 60.83333333C1 60.83333333T1 60.83333333K1 60.83333333K2 31.66666667

Results/Conclusions Used real patient data

and estimates provided by the clinic ~20 patients over a 2

week period ~60-80 jobs per week ~200 minutes of overtime

per day using current scheduling techniques = 200 cumulative minutes waiting for patients that day

~5-6 late treatments a week

Our Model Reduced the

average amount of overtime per day ~160 minutes

~1-2 late treatments a week

Pros/Cons Pros

Some cost saving is possible along with higher utilization and lower waiting times

Less hassle with arranging appointment times with patients b/c they are assigned days and times

Cons Less patient flexibility

and patient freedom of choice for when to come in

Too much variation or exceptions (cancelations, reschedules) which would break the system

No direct relation between time saved and money gained or lost

Further Areas to Consider Referral to Treatment Times

Demand-Dependent Nearby Treatment Centers

Unforeseen Delays Service Industry

Late Patient Arrivals Machine/Technical Malfunctions Changes in Patient Condition

Profit Analysis