Takt Time Calculation

TAKT time calculations ask for demand at peak, so from the limited information I have to assume your demand is for 10000 pieces on Monday, 20000 pieces on Tuesday, 30000 pieces on Wednesday, 40000 pieces on Thursday and 50000 pieces on Friday.
Short of getting your customers to average their demand, or giving them an incentive for smoothing requirements to you, you must calculate TAKT based on 10 people on 1 line making 50000 pieces, @ 85% efficentcy on 1 shift for an availble production time of 382.5 minutes or 22950 seconds making your TAKT time .459 seconds.
Not very realistic, but I suspect you knew that.
When you run 40000 on Thursdays, you’ll only need to run the line with 8 people, all switching off in perfect unision to do the job before or after their normal work station to balence the flow, like wise on Wednesday it is run with 6 people, Tuesdays with 4 and Monday 2 people get to bounce all over the line with only 10000 to run.
 
Hope this helps

Takt Time does not care whether your stations are independant, coupled, etc…
Takt time is calculated as (Available time / Demand)
You are required to determine how to meet your takt time whether it is more stations, more employees, more automation, overtime, etc…
Per the example by ramblinwreck, your output has to meet the takt time or you will not be able to support customer demand.

I root for the DAWGS 48 weeks of the year, but TAKT time has nothing to do with weather the stations are coupled or independent. It has only to do with Availbile time and demand. If you had two line set up TAKT time would double as staffing it would provide more availbile production time, likewise if you ran the line 3 shifts instead of 1 you TAKT time would triple due to more availible production time.
 
Hope this helps and we’ll see see who wins this weekend.
ramblinwreck

The availalbe time does not change based on headcount!   Available time is the actual time less planned breaks meetings, lunch etc,. that the line is shceduled to work. Overtime, flex work force  etc. is a mechanism to utilize to meet the TAKT time is the number don’t work
 
Takt time is availalbe time / demand or ADD (Average Daily Demand)
To estimate the number of people needed to meet takt time you have to divide the cycle time by the takt time.
I.e. you have a takt time of 5 minutes you have a cycle time of ten minutes. to meet the Takt time you need to either reduce cycle time to 2.5 minutes or add an additional head.

Given the conditions you’ve stated, as your volume changes you should alter Takt, and staff your line appropriately. 
Here’s the way I see it – (resources are both operations and people, in this case)  I’m assuming a one shift operation with daily available time as 408 minutes (85% of 8 hours) and a product cycle time of 10 seconds.  On Monday, you’ll have 16 workstations sitting idle, and Friday you’ll be fully staffed with 20 stations running.

10000
20000
30000
40000
50000
Daily Volume

2.448
1.224
0.816
0.612
0.4896
Takt (sec)

10
10
10
10
10
Cycle time (sec)

5
9
13
17
21
# of resources required
Hope this is helpful
Flowguy

sir.. please send calculation of takt time