A Simulation Model to Predict the Performance of an Endoscopy Suite
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1 A Simulation Model to Predict the Performance of an Endoscopy Suite Brian Denton Edward P. Fitts Department of Industrial & Systems Engineering North Carolina State University October 30, 2007
2 Collaborators Hari Balasubramanian (Mayo) Angela Bailey (Mayo) Bjorn Berg (Mayo) Keith Lindor (Mayo) Heidi Nelson (Mayo) Ahmed Rahman (Mayo) Supported by National Science Foundation DMI
3 Summary Endoscopy Suite process Simulation model Optimization of appointment schedules Results Future research
4 Endoscopy Process Patient Intake: patient checks-in, administrative activities, gowning, patient roomed Procedure: endoscopist enters room, patient sedated, colonoscopy starts, polyps removed, patient extubated Recovery: post anesthesia care unit (PACU), patient discharged Intake Procedur e Recovery
5 Complicating Factors Many types of resources: endoscopists, nurses, equipment, materials High cost of resources and fixed time to complete activities Large number of activities to be coordinated in a highly constrained environment Uncertainty in duration of activities Many competing criteria
6 Endoscopy Suite Decisions Number of cases to schedule each day Anticipated procedure room utilization How to staff the suite (nurses, endoscopists) Allocation of procedure rooms to endoscopists Arrival time scheduling patients
7 Simulation Model
8 Process Map
9 Example Data Instance_ID Location Room Proc Endoscopist Primary Nurse Appt Time Pt. Status Status time /6/05 WAITING 7:27 7: /6/05 CHECK_IN 7:42 7: /6/05 HOLDING 7:47 7: Gonda 250 Colon Dr.X Nurse Y 12/6/05 ROOMING 7:47 7: Gonda 250 Colon Dr.X Nurse Y 12/6/05 MD_IN_ROOM 8:04 7: Gonda 250 Colon Dr.X Nurse Y 12/6/05 INTUBATION 8:10 7: Gonda 250 Colon Dr.X Nurse Y 12/6/05 EXTUBATION 8:23 7: /6/05 BEDDED 8:28 7: /6/05 DISCHARGED 9:04 7: /6/05 SIGN_OFF 12:22 7:30 Intake Procedure Recovery
10 Intake, Procedure, and Recovery
11 Model Patient Arrivals Patient Check-in Waiting Area Recovery Area Patient Discharge Intake Area Preoperative Waiting Area Procedure Rooms Dependent (Waiting) Independent (Process) Dependent (Waiting) Independent (Process) Dependent (Waiting) Independent (Process)
12 Model Outputs Maximum patient throughput Waiting time: Patients Endoscopists Utilization Procedure room Endoscopists Recovery beds Length of day Overtime
13 Questions Number of cases to schedule each day? Anticipated procedure room utilization? How to staff the suite (nurses, endoscopists)? Allocation of procedure rooms to endoscopists?
14 Endoscopist-to-OR Allocation
15 General Insights Economies of Scale: No observed efficiencies in patient throughput due to increasing the number of Ors. Some benefits for up and down stream resources. Turn-over Times: The impact of reducing turnover times for ORs on all performance measures is limited to staffing scenarios is which endoscopists have 1 or 1.5 ORs. Utilization: The maximum achievable endoscopist utilization is 90% and the maximum achievable OR utilization is 67%.
16 Appointment Scheduling
17 Endoscopy Suite Patient Waiting Time Recovery Area Schedule Patient Arrivals Patient Check-in Waiting Area Patient Discharge 1 st Patient Arrival Preoperative Waiting Area Intake Area Length of Day Operating Rooms nth Patient Completion
18 Optimization Model Average Cost of Waiting Average Cost of Idling Average Cost of Overtime n min{ w s L C i * E Z [ W i] + C * E Z [ S i] + C * E Z [ L i = 1 n i = 1 ]} Customer Server W S i i = i max( Wi 1 + Zi 1 x 1,0) = i max( W i 1 Z i 1 + x 1,0) Arrival Process Service Process L = max( W n + Z n + Σ x i d,0 )
19 Endoscopy Suite Optimizer Decision variables: scheduled start times to be assigned to n patients each day Goal: Generate the Pareto set of (non-dominated) schedules to optimally tradeoff patient waiting time and session length Schedules generated using a genetic algorithm (GA) Non-dominated sorting used to identify the Pareto set and rank solutions in the GA
20 Pareto Set Non-dominated sorting genetic algorithm (NSGA-II) of Deb et al.(2000) Session Length Rank 1 Solutions Rank 2 Solutions Rank 3 Solutions Waiting Time
21 Main features of the GA: Genetic Algorithm Randomly generated initial population of schedules Single point crossover: z 1 z 2 z 3.. z n z 1 z 2 - y 3.. y n y 1 y 2 y 3.. y n y 1 y 2 - z 3.. z n Parents Children Selection based on Pareto set ranking Mutation
22 Example
23 Questions?
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