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Therapy Schedule

Problem Statement

To optimize the scheduling of individual and group therapy sessions, given the following variables:

  • Number of available rooms
  • Number of session blocks per week
  • Number of therapeutic staff
  • Number of patients
  • Number of groups and max size per group
  • Mapping of topics to staff, patients, and groups based on interest or relevance

Challenge 1: Double-sided Random Assignment

With the following variables fixed:

  • Number of available rooms and their capacity
  • Number of session blocks per week
  • Number of therapeutic staff per category

And the following constraints specified:

  • Staff members cannot hold multiple sessions (group or individual) during the same session block
  • Patients must be in exactly one session (individual or group) during a given session block
  • Rooms can hold a maximum of one session (individual or group) per session block
  • Each group must have at least one therapeutic staff member present
  • No group can exceed its maximum capacity
  • All individual sessions a patient has in a given therapeutic category must be with the same staff member
  • Individuals and staff members can't be matched to a group unless they can attend all sessions for that group in a week

Given the following inputs:

  • Number of patients
  • Number of group sessions
  • Number of times per week each group must meet
  • Number of individual sessions per week each patient must have in each therapeutic category

Produce a function that:

  • Decision: Checks if its possible to schedule the preferred number of individual and group sessions without violating any of the constraints
  • Assignment: Returns the following assignments without violating the constraints
    • Patients to staff
    • Patients and staff to groups
    • Individual and group sessions to rooms and session blocks

Vaccination Schedule

Summary

Algorithm to optimize the scheduling of vaccination

Inputs

Vaccine Production Facility

The following attributes define each facility:

  • Number of cases of vaccines produced each month
  • Number of vaccines doses per case
  • Number of hours in which all vaccines must be administered once a case is opened
  • Maximum number of vaccine deliveries per month
  • Maximum number of cases that can be shipped per delivery

Vaccination Facility

The following attributes define each facility:

  • Maximum number of cases the facility can store
  • Number of workers supporting supporting registration
  • Number of workers administering vaccines
  • Number of hours of operation per day
  • Number of minutes required to register a patient
  • Number of minutes required to vaccinate a patient
  • Number of minutes required to monitor a patient for symptoms

Population Variables

  • Population distribution
  • Maximum number of miles

Outputs

  • Maximize:
    • Number of patients vaccinated
  • Minimize:
    • Number of vaccines wasted
    • Number of workers per category
    • Average wait time for patients
  • Optimize:
    • Number of vaccine shipments per month
    • Number of vaccine cases per shipment
    • Number and placement of vaccination facilities

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