1. PATIENT SCHEDULING AT COLUMBIA’S RADIATION ONCOLOGY TREATMENT CENTER By David Kuo Chao and Ji Soo Han

2. Introduction  Radiation Oncology Treatment Center  Cancer Clients  Parallel Machines Client Urgency Stage of Cancer Availability Appointments Date Time Duration

3. 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

4. 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

5. 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

6. 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?

7. 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

8. 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

9. 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

10. Solution: The Models  Weekly:  P3|r j, prec| Σ w j T j  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|r j |Lmax  model uses given estimated processing time for treatment  Creates a schedule that minimizes probability of going over operation hours (due date)

11. Scheduling: Weekly  P3|r j, prec| Σ w j T j  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

12. 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{}

13. Scheduling: Daily  P3|r j |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

14. 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

15. 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 jobrjOMPwjdj C114560801015 C211203050520 C316203050825

16. Weekly schedule Instance Cindy(47) - Lung Cancer jobrjOMPwjdj C114560801015 C211203050520 C316203050825 John(76) - Head/Neck Cancer jobrjOMPwjdj J11456080135 J26203050310 J316203050320 J4216080901225 Sarah(23) - Ovarian Cancer jobrjOMPwjdj S16203060610 S221153045325 Tom(66) - Pancreatic Cancer jobrjOMPwjdj T11456080105 T26203050510 T311203050815 T416303540720 T5214050601125 Kyle(87) - Prostate Cancer jobrjOMPwjdj K11456080105 K2120305055 K36203050810 K411153045515 K5161845501120 K621102060725  1 Machine system, with capacity of 5 patients per day  Set all processing times to 1 for each job for weekly scheduling

17. Weekly Schedule t12345 MondayJ1C1T1K1K2 678910 TuesdayK3S1T2J2 1112131415 WednesdayT3K3C2 1617181920 ThursdayK5C3T4J3 2122232425 FridayJ4T5K6S2

18. Daily Schedule Monday jobrjOMPwjdj J1145608013300 C1145608010300 T1145608010300 K1145608010300 K212030505300  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 jobTj J160.83333333 C160.83333333 T160.83333333 K160.83333333 K231.66666667

19. 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

20. 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

21. 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