Question

Autos orders their tires from a wholesaler. Every year Radfors requires 10,000 tires of a certain type. Cost is $150 per tire from their supplier.

The estimated cost of orderingat the suppliers and paying shipping fees is $80 per order. K = $80

The holding cost per tire is estimated to be 10% of the cost of the tire. h = .01 * $150 = $15

Using the economic ordering quantity model, the order size that would minimize the total costs is equal to

a. 103

b. 194

c. 287

d. 327

e. 10000

Answer 1

Let the order size that minimises the total cost be N.

Write the total cost interms of N.

Total cost T = total cost of purchase + (cost of ordering + shipping per order) + holding cost.

A total of 10,000 tyres are required. If N tyres are ordered at a time, then the number of orders per year is 10,000 / N.

So total cost of purchase = cost of 1 tyre x total order size = 150 X 10,000.

cost of ordering + shipping = number of orders x cost of ordering and shipping per order = 80 x 10,000 / N.

Holding cost per tyre is 15. In the economic ordering quantity model, on average, we expect there to be N/2 number of tyres in holding, so holding cost = 15 x N/2.

Combining all the above, the total cost as a function of N is

The total cost as a function of the order size N has to be minimised. The value of N which does this can be found by taking the derivative of T with respect to N and then setting it equal to 0.

The order size that would minimise the total cost is .

Rounding off, the order size should be 327.