2. A local company orders a component part at $40/unit. The cost of placing an o

Question

2. A local company orders a component part at $40/unit. The cost of placing an order is $100, and the annual cost of holding a unit in inventory is 20%. Current annual demand is 10,000 units, demand is treated as known and at a constant rate, and backorders are not allowed. (16)

Check all that apply. This is a basic EOQ problem.____

The optimal order quantity is greater than 500 units.____

If their current order policy is to order 600 units, the total annual cost would increase.____

If the holding cost were to increase to 25%, the optimal order quantity would increase.____

If they started to produce this component, total cost would decline.____

If annual demand changed to 20,000 units, the optimal order quantity would double.____

If the order cost increased, the optimal number of orders/year would decrease.____

In this model, the service level is 100%.____

Explanation / Answer

Solution

Back-up Theory

The optimum order quantity, i.e., EOQ, Q = sqrt{(2DS)/(hc)}, where

D = annual demand in units, S = cost of ordering per order, h = carrying cost in percentage per annum and

c = cost per unit.

Part (a)

Substituting the given values in the above formula,

Q = sqrt{(2 x 10000 x 100)/(0.2 x 40)} = sqrt(10000 x 25) = 500. Hence,

The optimal order quantity is greater than 500 units.

NO, it is exactly 500 ANSWER

Part (b)

Number of orders per annum = 10000/600 = 50/3 and hence annual ordering cost = 100 x (50/3) = $1666.67

Average inventory = 600/2 = 300 units = $(300 x 40) = $12000 and hence annual carrying cost = $(12000 x 0.2) = $2400. (500/2) x 40 x 0.2 = 2000

Total annual cost = 1666.67 + 2400 = 4066.67.

Under EOQ, Total annual cost = {(10000/500) x 100} + {(500/2) x 40 x 0.2} = 2000 + 2000 = 4000 which is less than 4066.67. Hence,

If their current order policy is to order 600 units, the total annual cost would increase. No. it will decrease by $66.67 ANSWER

Part (c)

The new optimal order quantity = old optimal order quantity x sqrt(20/25)

= 500 x sqrt(0.8) = 447.21. Hence,

If the holding cost were to increase to 25%, the optimal order quantity would increase. No. it will decrease by 53 ANSWER

Part (d)

Since cost of producing is not known, this quaetion cannot be addressed. Hence, If they started to produce this component, total cost would decline. Cannot say

Part (e)

Now, EOQ = old EOQ x sqrt(20000/10000) = 1.44 x old EOQ. Hence,

If annual demand changed to 20,000 units, the optimal order quantity would double. No. it will increase by 44% ANSWER

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