Maximum inventory (EPQ)
I_max = (Qp / p) x (p - u)
The first thing to compute once Qp is known. Read it as run length times net rate of build-up.
- Qp
- Run size (economic production quantity)
- p
- Production or delivery rate, per day
- u
- Usage rate, per day, in the same unit as p
Economic production quantity
Qp = sqrt( 2 D S / H ) x sqrt( p / (p - u) )
When the item is produced in batches while being used continuously, and p exceeds u.
- D
- Annual demand; derive it from the daily usage rate if needed
- S
- Setup cost per production run
- H
- Carrying cost per unit per year
Total cost (EPQ)
TC = (I_max / 2) H + (D / Q) S
Costing a production batch. Note I_max/2 rather than Q/2; the two halves are equal at the optimum.
- I_max / 2
- Average inventory over the cycle
- (D / Q) S
- Annual setup cost: runs a year times setup cost
Run time, cycle time, runs a year
Run time = Qp / p
Cycle time = Qp / u
Runs/year = D / Qp
Idle time = cycle time - run time
Whenever a duration is asked for. Run time uses p; cycle time uses u.
- p
- Production rate per day
- u
- Usage rate per day