The case of a fixed discount

When evaluating inventory decisions when a fixed discount rate exists, the appropriate procedure is to compare the total costs of the EOQ with the total costs when discounts are taken. The option giving lower costs is then chosen.

Note: The Unit (variable) cost (i.e. Purchase Price) behaves in the following manner.

C = Co        if    0 ≤ Q ≤ Qb
Co (1 - P)    if    Q ≥ Qb

Where:

Co = basic unit cost without a discount
P = Discount rate allowed.
Qb = Break-point (Quantity) - where discounts become operational.

In order to determine the optimal ordering quantity, it is necessary to include the costs of the inventory with the carrying ordering costs.

Total costs of Inventory = Total Purchase cost + Total order cost + Total carrying cost

TC = DC_o + (Q*/2) H + D_o/Q²                  If 0 ≤ Q ≤ Qb   
TC = DC. (1 - P) + (Q/2) H + D_o/Q            If Q ≥ Qb   
                               
Note:

The second equation i.e. with discounts will give a lower TC than first equation for the same. The decision whether to go for the discount lies on a trade-off between extra carrying costs vs. a decrease in acquisition costs.