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Sem 5 Prep
← OperationsQuantity discounts

Formulas for this chapter

Total cost with quantity discounts

TC = (Q / 2) H + (D / Q) A + P D

Whenever the unit price depends on the order quantity. All three terms, every time.

H
Holding cost per unit per year; recompute it if it is a fraction of price
A
Ordering cost per order, written S in the basic EOQ slides
P
Unit price applying to the quantity being tested
D
Annual demand in units

Holding cost as a fraction of price

H = carrying fraction x P

When the question gives a carrying-cost fraction rather than a rupee amount. H then changes at every price break, and so does the EOQ.

carrying fraction
Annual carrying cost as a fraction of unit value, e.g. 0.15
P
The price being tested

Discount decision procedure

1. EOQ = sqrt(2 D A / H) 2. Feasible? Is EOQ inside the range for that price? 3. TC at the feasible EOQ, all three terms 4. TC at the lowest qualifying quantity of each cheaper price above 5. Choose the lowest TC

Every quantity discount problem. Never test quantities below the feasible EOQ.

Feasible
The EOQ lies within the quantity range that earns the price used to compute it
lowest qualifying quantity
The smallest order that still earns that lower price
Step 1 of 18
The ideaTheory

Ten for the price of nine

The shop says a pack of one costs Rs 20, but a box of a hundred works out at Rs 16 each. Suddenly the size of your order changes what you pay, not just how often you shop.

Once the price moves, the money spent on the goods themselves has to enter the comparison. In every earlier model it was a constant and dropped out.

That single change makes the total-cost curve break into pieces, and the answer is usually to jump to a price break rather than to sit at the EOQ.

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