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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 5 of 19
The real wordsTheory

Total cost and the run size

TC = (I_max / 2) H + (D / Q) S Qp = sqrt( 2 D S / H ) x sqrt( p / (p - u) )

The first square root is exactly the basic EOQ. The second is a multiplier greater than 1, so Qp is always larger than the EOQ for the same D, S and H.

Gradual delivery means lower average stock, which means holding cost bites less, which means a bigger batch is worth making.

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