Skip to content
Sem 5 Prep
← OperationsThe economic production quantity

Formulas for this chapter

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
Step 1 of 19
The ideaTheory

Filling the bath while the plug is out

When you buy a batch, it all lands at once and the stock jumps to Q. When you make a batch, it trickles in while customers are already taking some away.

So the stock never reaches Q. It rises slowly during the run, at the production rate minus the usage rate, then falls when the run stops.

Peak inventory is lower than in the purchase case, so holding cost is lower, so the economic batch is larger. That is the entire chapter.

← BackContinue →