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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

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