Question

A company producing personal computers supplies various components from its suppliers and operates 52 weeks per year. A particular component is needed at the rate of 100 items per week. The company’s inventory holding rate for this component is 20%. The administrative rate to place an order of any size to the manufacturer costs $50. The manufacturer, however, tries to have orders of larger size and comes up with the following discount policy

Discount category

1
2
3

Quantity purchased

1 to 99
100 to 199
200 to 499

Price per unit

$100
$95
$90

Note that the price in each category applies to every unit purchased (for example, the price of pur- chasing 130 units is equal to 130 × 95).

1. (a) Determine the optimal order quantity according to the EOQ model with discounts.

2. (b) With this order quantity, how many orders will be placed annually? What will be the time interval between orders?

Answer 1

EOQ = [ 2 x demand per annum x cost of ordering / cost of holding one unit]^1/2

  EOQ with highest cost range = [ 2 x 52x100x50/ 0.2x100]^1/2 = 161.24

The range corresponds to the second price band of 95 ( qty 100-199)

EOQ with this range = [ 2 x 52x100x50 / 0.2 x 95]^1/2

= 166 units

Cost with EOQ = 95x5200+166/2 x0.2x95+ (5200/166) x 50

= 494000+1577+1566

=497143

Cost with next level ( 200 units)

= 5200x90+200/2 x0.2x90+(5200/200) x 50

468000+1800+1300

=471100

The cost is lowest with 200 units order size

Number of orders = 5200/200 =26

Time between orders = 52/26 =2 weeks