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
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