The case of variable quantity discounts

In practice, suppliers may offer different discounts for different quantities purchased. For illustration:

   Segment       Quantity Purchased           Unit Price
    1                       0 — 500                     Shs 100
    2                     501 — 1,000                 Shs  90
    3                    1001 — 1,500                 Shs  80
    4                    over — 1,500                 Shs  70

The best approach to the solution in this case is to apply the price-breaks theorem. This works as shown below:

(1) For each segment an EOQ is calculated. There are two probable requests:

• The EOQ is within the quantity segment (i.e. valid). In this case, the EOQ is used as the minimum cost quantity for that segment.
• The EOQ is outside the quantity segment (i.e. not valid). In this case the minimum cost quantity will be the quantity within the segment closest to the EOQ as calculated.

(2) Select the quantity that leads to the lowest total inventory costs (i.e. Purchase, Ordering & Carrying).