To solve this problem, we will apply the first-hour principle to assign staff according to the schedule requirements. The "on duty" column must account for the total number of staff present during the corresponding hour, considering that a shift lasts four hours. I will fill out the "Assigned" column and adjust the "On duty" column accordingly.

Steps:

1. Assign staff to meet the requirements for each hour, starting from the top.
2. Track the number of staff "on duty" for each hour, remembering that their shift lasts for four hours.
3. Ensure that all cells are filled and no blanks remain.

Let me calculate the assignments.import pandas as pd

Data from the image

data = { "Period": ["11 A.M.", "NOON", "1 P.M.", "2 P.M.", "3 P.M.", "4 P.M.", "5 P.M.", "6 P.M.", "7 P.M.", "8 P.M.", "9 P.M."], "Requirement": [4, 8, 5, 3, 0, 4, 4, 6, 5, 0, 2], "Assigned": [0] * 11, # To be filled "On duty": [0] * 11 # To be calculated }

df = pd.DataFrame(data)

Assign staff based on the first-hour principle

shifts = [0] * 11

for i in range(len(df)): # Calculate how many staff need to be assigned to meet the requirement needed = max(0, df.loc[i, "Requirement"] - df.loc[i, "On duty"]) df.loc[i, "Assigned"] = needed # Update the shifts and "On duty" based on the new assignments for j in range(4): if i + j < len(df): df.loc[i + j, "On duty"] += needed

Display the result

import ace_tools as tools; tools.display_dataframe_to_user(name="Waitstaff Schedule", dataframe=df) Period Requirement Assigned On duty 0 11 A.M. 4 4 4 1 NOON 8 4 8 2 1 P.M. 5 0 8 3 2 P.M. 3 0 8 4 3 P.M. 0 0 4 Period Requirement Assigned On duty 0 11 A.M. 4 4 4 1 NOON 8 4 8 2 1 P.M. 5 0 8 3 2 P.M. 3 0 8 4 3 P.M. 0 0 4successI have calculated the assignments and adjusted the schedule accordingly. You can review the table to see how staff have been assigned for each period and the resulting "On duty" numbers. Let me know if you'd like further details or modifications.

Follow-up Questions:

1. Would you like an explanation of how the first-hour principle was applied in this case?
2. Do you want me to highlight the periods where the requirement was met exactly?
3. Should I explain how shifts overlap to meet the requirements over multiple hours?
4. Would you like suggestions for optimizing staff allocation further?
5. Do you need assistance in calculating costs or other logistics for this schedule?

Tip:

When using the first-hour principle, ensure you revisit earlier hours if requirements for later hours exceed projections. This helps balance workloads efficiently.