Skip to content
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 3 of 18
The real wordsTheory

The piecewise curve

The class's schedule: 1 to 44 boxes at $2, 45 to 69 at $1.70, 70 or more at $1.40.

Each price has its own U-shaped total-cost curve. The one you are actually on depends on how much you order, so the real curve is a piece of one, then a drop, then a piece of the next.

The drops at the price breaks are what make this problem different: the cheapest point on the whole curve is often at a break, not at the bottom of any single U.

← BackContinue →