Math Problem: You have an upstream Picking department that feeds two downstream packing departments: A and B. 75% of your Pick volume goes to department A, which has a packing rate of 150 unites per labor hour (uph). 25% of the Pick volume goes to department B, which is for large items, and has a pack rate of 25 units per labor hour. Your pickers pick both large and small items throughout the day at an overall average rate of 100 units per labor hour. You have 25 people today for all 3 departments, and you absolutely must pack 7,500 units in department A 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. Department % of volume Rate (uph) People Daily Volume Pick 100% 100 ?? ?? Pack A 75% 150 ?? 7,500 Pack B 25% 25 ?? ??

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Upstairs is sending 10,000 units downstairs at an average of 100 per hour so they would need 10 people......Dept A will be receiving 7,500 units @ 150/hour = 50 hrs so they need 5 people....Dept B will be receiving 2,500 units @ 25/hour= 100 hours so they need 10 people.....10/5/10

Assign 10 people to picking. 10 people x 100uph = 1000uph x 10 hrs = 10,000 units. 75% (7,500) goes to department A and 25% (2,500) goes to department B. Assign 5 people to department A. 5 people x 150uph = 750uph x 10 hrs = 7,500 small units packed. Assign remaining 10 people to department B. 10 people x 25uph = 250uph x 10 hrs = 2,500 large units packed. And a partridge in a pear tree...

10 in Pick Area 5 in Pack Area A 10 in Pack Area B

Pick 10 people × 100 uph × 10 hours = 10000 units Pack A 5 people × 150 uph × 10 hours = 7500 units. Pack B 10 people × 25 uph × 10 hours = 2500 units .

The question is about balancing the flow in the whole process Department A has the fastest rate of 150uph. if we just use 3 people 1 at each station we will have 8 such combinations and one is left idle. this will not be able to pack 7500 small items We need 2 people manning upstream picking + 2 at dept B and 1 at Dept A. Total 5 people as a group this gives us 5 such group. this group can pick 200 units per hr. this gets distributed to 150 units to Dept A and 50 units to Dept B. In an hour they will be able to pack 150 units in A and 50 units in B. In 10 Hrs a group of 5 can fo 1500 in dept A and 500 in Dept B 5 groups can do 7500 in dept A: condition met 5 groups can to 2500 in dept B. with this there are no bottle necks, no blocking no starving. the flow is smooth and uniform

7500 units for A so 2500 units for B (25%)=10000 units 10000 units at 100 uph/10 hrs=10 pickers 7500 units/10 hrs/150 up =5 packers A 2500 units/10 hrs/25 uph =10 packers B

Stream Vol % Units/Hr Total Volume Hrs Reqd Staff Reqd Pick 100% 100 10000 100 10 Pack A 75% 150 7500 50 5 Pack B 25% 25 2500 100 10

7500 units to be picked. 7500 / 150 units = 50 labor hours. However. only 75% of the picks are sent to Dept A, so you need to increase the labor hours to account... Thus, 67 labor hours are needed to achieve 7500 units minimum. Each person works 10 hours...7 people minimum needed to meet the customer metric promise.