PATIENT SCHEDULING AT COLUMBIAS RADIATION ONCOLOGY TREATMENT CENTER
PATIENT SCHEDULING AT COLUMBIA’S RADIATION ONCOLOGY TREATMENT CENTER By 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: Daily Scheduling � � Three Working Oncologists Machines in Parallel Patients arrive by schedule Varying: Availability Frequency of Treatment Release Date Health Condition Urgency of 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 � Reduce Idle Capacity Costs Time Machines Staff Additional Machine(s) Maintenance Costs Waiting Times � Per Visit Incentives for Promptness Reduce Back-Log � Per Appointment Weighted Provide Care to Urgent Patients Equal System 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: � P 3|rj , prec|Σwj. Tj � 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 Daily � P 3|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 P 3|rj , prec|Σwj. Tj 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 P 3|rj|Lmax Given: � Due date All due dates are the same: end of operations for the day Reduces problem to P 3|rj|Cmax � Processing Use time 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 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 scheduling Program = (O + 4 M + 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 accepted a treatment plan with the oncologist � needs 3 treatments during week 1 � Is available � Has Monday (t = 1, 5) Wednesday (t = 11, 15) Thursday (t = 16, 20) Friday (t = 21, 25) Split Cindy into 3 jobs for week 1: C 1, C 2, C 3 Set release dates based on availability and due dates based on latest possible Cindy(47) - Lung Cancer treatment job rj O M P wj dj C 1 1 45 60 80 10 15 C 2 11 20 30 50 5 20 C 3 16 20 30 50 8 25
Weekly schedule Instance job C 1 C 2 C 3 rj 1 11 16 O 45 20 20 Cindy(47) - Lung Cancer M P 60 80 30 50 wj 10 5 8 dj 15 20 25 job J 1 J 2 J 3 J 4 rj 1 6 16 21 John(76) - Head/Neck Cancer O M P 45 60 80 20 30 50 60 80 90 wj 13 3 3 12 dj 5 10 20 25 job S 1 S 2 rj 6 21 Sarah(23) - Ovarian Cancer O M P 20 30 60 15 30 45 wj 6 3 dj 10 25 job T 1 T 2 T 3 T 4 T 5 rj 1 6 11 16 21 Tom(66) - Pancreatic Cancer O M P 45 60 80 20 30 50 30 35 40 40 50 60 wj 10 5 8 7 11 dj 5 10 15 20 25 job K 1 K 2 K 3 K 4 K 5 K 6 rj 1 1 6 11 16 21 Kyle(87) - Prostate Cancer O M P 45 60 80 20 30 50 15 30 45 18 45 50 10 20 60 wj 10 5 8 5 11 7 dj 5 5 10 15 20 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 Monday 1 J 1 2 C 1 6 Tuesday K 3 7 11 K 5 Friday J 4 C 3 K 2 9 10 13 14 15 18 19 20 24 25 J 2 T 4 22 T 5 5 C 2 17 21 K 1 T 2 K 3 4 8 12 16 Thursday T 1 S 1 Wednesday T 3 3 J 3 23 K 6 S 2
Daily Schedule Monday job rj O M P wj dj J 1 1 45 60 80 13 300 C 1 1 45 60 80 10 300 T 1 1 45 60 80 10 300 K 2 1 20 30 50 5 300 job J 1 C 1 T 1 K 2 Tj 60. 83333333 31. 66666667 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
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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