Clinical Trial Scan Scheduling Optimization

📌 Overview

This project develops a Mixed-Integer Linear Programming (MILP) model to optimize scheduling for a neuroimaging clinical trial requiring:

• MRI scans
• Amyloid PET scans
• Tau PET scans

The model minimizes the total number of distinct visit days per patient, subject to scanner availability, clinical constraints, and biological safety constraints.

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📓 Python Notebook

The Pasaye_Final Project.ipynb contains the first simulated a patient list, scanner availability, scan time slots, and capacity for each facility. Additionally, the Jupyter Notebook details the decision variables, constraints, objective function, and finds an optimal solution using PuLP. Lastly, after the solution has been determined, a Gantt visualization, highlighting the patient schedule of the model, a scan utilization plot, determining how much each facility was used during in the model, and a daily usage plot, illustrates the number of days each facility was used in the model.

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🎯 Problem Statement

We aim to schedule 24 participants for three different imaging modalities within a 6-month window, while satisfying operational and biological constraints.

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🏥 Facility Constraints

• MRI Facility:
  • 90-minute sessions
  • Available Monday–Friday, 8:30 AM – 4:30 PM
• PET Facility:
  • 2 sessions/day
  • Available Tuesday–Thursdays at:
    • 4:30 PM – 5:00 PM
    • 5:00 PM – 5:30 PM

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⚠️ Biological Constraints

• PET scans cannot occur on the same day and must be ≥ 24 hours apart
• Amyloid PET: Available Tuesday–Thursday
• Tau PET: Available Thursday only
• All scans must occur within 6 months for each participant

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🔢 Model Formulation

Decision Variables

• $x_{p,d,t,s} \in {0,1}$: 1 if patient $p$ has scan $s$ on day $d$ at time $t$
• $y_{p,d} \in {0,1}$: 1 if patient $p$ has any scan on day $d$

Objective

$$ \min \sum_p \sum_d y_{p,d} $$

Minimize the total number of distinct scan days.

Key Constraints

1. Linking Constraint: If any scan is assigned on day $d$, then $y_{p,d} = 1$
2. One Scan per Type per Patient
3. Facility Capacity Constraints
4. Biological Constraints (PET spacing)

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🛠️ Summary of Techniques Used

• Mixed-Integer Linear Programming (MILP) with binary decision variables
• Big-M linking constraints to track patient visit days
• Operational constraint modeling for:
  • Time-specific scan slots
  • Day-of-week restrictions
  • Sequential scan rules
• Visualization outputs:
  • Gantt chart of scan schedules
  • Resource utilization line chart
  • Daily scan usage bar chart