Question

In: Operations Management

Suppose we have an Economic Order Quantity (EOQ) problem with discounts. A (annual demand)= 10000, k...

Suppose we have an Economic Order Quantity (EOQ) problem with discounts.

A (annual demand)= 10000, k (order cost)= 10, c1 (item cost)= 8, h (holding cost)= 0.1

For orders of 2000 or more, the cost is discounted from 8 to 7.3728.

What is the optimal TAC (total annual cost, including order and holding, and also including the purchase costs)?

Expert Solution

In this situation we know that EOQ is provided using the formula

EOQ = sqrt ( 2*Annual demand*Order cost / Holding cost)

Thus with the original given information, the EOQ is

EOQ = sqrt (2*10000*10/0.1) = 1414.214

Let’s keep the number in fraction for the intermediate calculation. In ideal situations this should be rounded to nearest whole number.

Now we know that for orders more than 2000 units, the price of the product drops to 7.3728 from 8. This means at the EOQ, the total annual cost is the sum of product cost, ordering cost and holding cost. These are given by

Annual product cost = 10000*8 = 80000

Annual ordering cost = Annual demand*Order cost/Quantity = 10000*10/1414.214 = 70.71

Annual holding cost = Holding cost*Quantity/2 = 0.1*1414.214/2 = 70.71

The total annual cost will be 80000 + 70.71 +70.71 = 80141.42

Now there is a discount if we order more than 2000 units. However since our EOQ is lesser than 2000, the best price we shall get is when the quantity is at the edge that is nearest to the EOQ. This means even though 2000 or more units will give us a discount, the best annual cost will be incurred at 2000 units. Thus let’s change the above calculation with Quantity = 2000 and check the total annual cost. We have

Total annual cost = 10000*7.3728 + 10000*10/2000 + 0.1*2000/2 = 73878

This cost is lower than the cost incurred at EOQ. This means the optimal quantity to order is 2000 units.

keosha answered 10 months ago

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