How do you allocate your staffing for the first 5 hours of the shift for all departments?

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you have an upstream Picking department that feeds two downstream Packing departments:
Pack Singles and Pack Multis. Those Packing departments feed to a Shipping department that loads the outgoing trucks.
30% of your Pick volume goes to Pack Singles and has a packing rate of 171 units per labor hour (uph). 70% of the Pick volume goes to Pack Multis and has a pack rate of 266 units per labor hour.
Your pickers pick both Single and Multi items throughout the day at an overall average rate of 114 units per labor hour. All units that are packed in both processes go through the Ship process at a rate of 570 units per hour.
You have 102 people today for all 4 departments and you absolutely must pack 47,880 units in Pack Multis Items to meet a customer promise metric.
How do you allocate labor to balance the flow in your department if you work a 10 hour shift? Do not assume breaks or lunches in your answer.
Please fill out the table below.
Department
% of volume
Rate (uph)
People
Daily volume
Pick
 
Pack Singles
 
Pack Multis
Ship
 
Redirect:
You now need to process all of the Pack Singles Volume in the first 5 hours of the shift. All of the constraints and parameters are the same as the original problem. Again, assume no breaks and lunches.
How do you allocate your staffing for the first 5 hours of the shift for all departments?
How do you allocate your staffing for the second 5 hours of the shift for all departments?
Overall Thought Process:
The Pick and Ship departments do not change. The total volume for Pack Singles is not greater than 50% of the total volume so they would process at the normal pace to solve for the entire shift.

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