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