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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 3 of 19
The real wordsTheory

The assumptions

Seven, and the first four are shared with the basic EOQ.

  1. Only one item is involved
  2. Annual demand requirements are known
  3. Usage rate is constant
  4. Usage occurs continually, but production occurs periodically
  5. The production rate is constant
  6. Lead time does not vary
  7. There are no quantity discounts

Assumption 4 is the whole difference from the basic model, and it requires p to be greater than u. If p were below u the firm could never build any stock at all.

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