How to crate a Hybrid Work Model roster simulation

Question

My office is currently manually creating employee rosters for our Hybrid work model.

A roster is a weekly or biweekly calendar, stating which all employees should come to office on which day of the week.

Can we automate the process in Python/Pandas?

Rules for creating a 2 week roster:

• in a week (5 working days)
  • maximum days in office: 3 days
  • minimum days in office: 2 days
• in 2 weeks (10 working days)
  • number of days in office: 5 days
• coinciding days
  • atleast 1 day in the week, the employee (Id column) should be on office on the day when his/her manager (ManagerId column) is also in office
• Roster should be randomly generated and employees should get reporting days randomly assigned, in order to avoid repetitive pattern reoccurring

E.g. for team mappings:

EmpId	Name	Team	ManagerId
0	Z	Z	90
1	Abc	A	0
2	Ade	A	1
3	Afg	A	1
4	Bmn	B	0
5	Bop	B	4
6	Bqr	B	4
7	Bst	B	4
8	Ctu	C	0
9	Cvw	C	8
10	Cxy	C	8
11	Djk	D	0
12	Dlm	D	11
13	Dno	D	11
14	Dpq	D	11

Results in a roster that looks like (can be any format/shape, below is only for visual representation):

Mon1	Tue1	Wed1	Thu1	Fri1	Mon2	Tue2	Wed2	Thu2	Fri2
Z	Z	Afg	Ctu	Ctu	Abc	Z	Z	Z	Djk
Abc	Abc	Cvw	Abc		Ade	Ctu	Ctu	Ctu	Cvw
Ade	Ade	Cxy	Cvw	Ade	Afg	Cvw	Cvw	Bmn	Cxy
Afg	Afg	Bop	Cxy		Dlm	Cxy	Cxy	Dlm	Dlm
Dlm	Bmn	Bqr	Bmn		Dno	Abc		Dno	Dno
Dno	Bop	Bst	Bop		Dpq	Afg	Ade	Dpq	Dpq
Dpq	Bqr	Dlm	Bqr			Bmn	Bmn
	Bst	Dno	Bst			Bop	Bop
		Dpq				Bqr	Bqr
						Bst	Bst

If you want to play around, the dataset:

import pandas as pd
import numpy as np
EmpId =  np.arange(15)
Name = ['Z', 'Abc', 'Ade', 'Afg', 'Bmn', 'Bop', 'Bqr', 'BSt', 'Ctu', 'Cvw', 'Cxy', 'Djk', 'Dlm', 'Dno', 'Dpq']
Team = ['Z', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'C', 'C', 'C', 'D', 'D', 'D', 'D'] 
ManagerId = [90, 0, 1, 1, 0, 4, 4, 4, 0, 8, 8, 0, 11, 11, 11]

team_mapping_df = pd.DataFrame(zip(EmpId , Name, Team, ManagerId), columns = ['EmpId ', 'Name', 'Team', 'ManagerId'])
team_mapping_df