I have created a function in python to generate a roster for inspection by selecting a pair of inspectors each for two teams (Team A and B) each week for the whole year. The function accepts two lists, one list is optional. A pair cannot be formed exclusively from list2, the optional list. The count of each person in each Team should be almost the same.

The function works well except that there is little variety in the selection process. I want different pairs to be selected for the same team until all possible pairs are exhausted. I want each person to have a different partner each time he/she is selected for Team A. For example, if Kay, Pat are selected in Team A for Week 4, Kay should have a different partner the next time Kay is selected in Team A.

This is the code I have so far.

import pandas as pd
import random

def generate_roster(list1, list2=None):
    if list2:
        people = list1 + list2
    else:
        people = list1
    
    # Ensure there are at least 4 people to form two pairs for Team A and Team B
    if len(people) < 4:
        raise ValueError("There should be at least four people to form two pairs for Team A and Team B.")
    
    # Initialize dictionaries to keep track of when each person was last selected for Team A and Team B
    last_selected_a = {person: -2 for person in people}  # Start with -2 to allow immediate selection
    last_selected_b = {person: -2 for person in people}
    
    # Initialize dictionaries to count appearances in Team A and Team B
    appearances_a = {person: 0 for person in people}
    appearances_b = {person: 0 for person in people}

    roster = []

    for week in range(1, 53):  # 52 weeks in a year
        valid_selection = False

        while not valid_selection:
            # Sort people by their appearances in Team A and Team B to prioritize those with fewer appearances
            sorted_people_a = sorted(people, key=lambda p: (appearances_a[p], last_selected_a[p]))
            sorted_people_b = sorted(people, key=lambda p: (appearances_b[p], last_selected_b[p]))
            
            selected_people = []

            # Select two people for Team A ensuring no pair is formed exclusively from list2
            for _ in range(2):
                for person in sorted_people_a:
                    if person not in selected_people and (person in list1 or any(p in list1 for p in selected_people)):
                        selected_people.append(person)
                        break
            
            # Select two people for Team B ensuring no pair is formed exclusively from list2
            for _ in range(2):
                for person in sorted_people_b:
                    if person not in selected_people and (person in list1 or any(p in list1 for p in selected_people[2:])):
                        selected_people.append(person)
                        break

            team_a = selected_people[:2]
            team_b = selected_people[2:]

            # Check if this is the first week or if the same person is selected for the same team in successive weeks
            if week == 1 or (not (set(team_a) & set(roster[-1]['Team A'].split(', ')) or set(team_b) & set(roster[-1]['Team B'].split(', ')))):
                valid_selection = True

        # Update the last selected week for each person
        for person in team_a:
            last_selected_a[person] = week
            appearances_a[person] += 1
        for person in team_b:
            last_selected_b[person] = week
            appearances_b[person] += 1

        roster.append({
            'Week Number': week, 
            'Team A': ', '.join(team_a), 
            'Team B': ', '.join(team_b)
        })

    df_roster = pd.DataFrame(roster)
    return df_roster