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Sem 5 Prep
← OperationsThe economic order quantity

Formulas for this chapter

Economic order quantity

EOQ = sqrt( 2 D S / H )

Buying an independent-demand item under the six basic assumptions. Convert a percentage carrying charge into H first.

D
Annual demand in units
S
Ordering cost per order
H
Holding cost per unit per year

Total annual inventory cost

TC = (Q / 2) H + (D / Q) S At the EOQ: TC = sqrt( 2 D S H ) and the two halves are equal

Costing any order quantity, optimal or not. Use the equal-halves property to check an EOQ.

Q
Order quantity being costed
(Q/2)H
Annual holding cost
(D/Q)S
Annual ordering cost

Orders per year and cycle length

N = D / Q Cycle length = Q / D (in years) = Q / D x working days (in days) = working days / N

Immediately after computing EOQ. The exam almost always asks for at least one of these.

N
Optimum number of orders a year; may be fractional
working days
The year length the question gives, not 365

Reorder level under certainty

ROP = d x LT, where d = D / working days

When lead time and demand are both certain. The stock at ROP covers exactly one lead time.

d
Demand per day
LT
Lead time in days
Step 4 of 19
The real wordsTheory

Total cost, and why the optimum is where the costs are equal

Total cost = annual holding cost + annual ordering cost = (Q / 2) H + (D / Q) S

The class derives EOQ by differentiating this, setting the slope to zero and solving for Q. What that gives, in words, is the point where the two cost curves cross.

EOQ = square root of ( 2 D S / H )

Check your answer by computing both costs at the EOQ. They should come out equal. If they do not, the arithmetic is wrong.

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