17-13. (Comprebensive EOQ calculations) Knutson Products Inc. is involved in the
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Question
17-13. (Comprebensive EOQ calculations) Knutson Products Inc. is involved in the production of airplane parts and has the following inventory, carrying, and storage costs 1. Orders must be placed in round lots of 100 units 2. Annual unit usage is 250,000. (Assume a 50-week year in your calculations.) 3. T 4. The purchase price is $10 per unit. 5. The ordering cost is $100 per order 6. The desired safety stock is 5,000 units. (This does not include delivery-time stock.) 7. The delivery time is 1 week. he carrying cost is 10 percent of the purchase price Given the forgoing information a. Determine the optimal EOQ level b. How many orders will be placed annually? c. What is the inventory order point? (That is, at what level of inventory should a new order be placed?) d. Wha at is the average inventory leve l e. What would happen to the EOQ if annual unit sales doubled (all other unit costs and safety stocks remaining constant)? What is the elasticity of EOQ with respect to sales? (That is, what is the percentage change in EOQ divided by the percentage change in sales?) If carrying costs double, what will happen to the EOQ level? (Assume the original sales level of 250,000 units.) What is the elasticity of EOQ with respect to carrying costs? f. g. If the ordering costs double, what will happen to the level of EOQ? (Again assume original levels of sales and carrying costs.) What is the elasticity of EOQ with respect to ordering costs h. If the selling price doubles, what will happen to EOQ? What is the elasticity of EOQ with respect to selling price?Explanation / Answer
Given,
Parameters
Values
ANNUAL UNIT USAGE (d)
250,000
ORDER LOT NUMBER (q)
100
ORDERING COST (s)
100
PURCHASE PRICE PER UNIT (c )
10
CARRYING COST (i)
10%
SAFETY STOCK
5,000
DELIVERY TIME
1 WEEK
NUMBER OF WEEKS
50
Parameters to be calculated:
Holding Cost = Carrying Cost (i) X Purchase Price Per Unit (c )
= 10% x $10
= $1
a) Economic Order Quantity (EOQ) = Square Root Of { (2 X Ordering Cost X Annual Unit Usage)/Holding Cost}
= ?(2sd/h)
=?(2x100x250000)/1
= 7071 units (approx.)
b)Number of Orders = Annual Unit Usage (d) X Order Lot Number (q)
= 250,000/100
= 2,500
c) Delivery Time Consumption = Annual Unit Usage/ Total Number Of Weeks
= 250,000/50
= 5,000 units per week
Inventory Order Point = Safety Stock + Delivery Time Consumption
= 5000 + 5000
= 10,000 units
d) Average Inventory Level = (0 + EOQ)/2
= (7071/2) units
= 3536 units (approx.)
e) When annual unit sales are doubled, Annual Unit Usage (d) = 500,000
So % change in Annual Unit Usage = 100%
Therefore,
= 10,000 units
So, % change in EOQ = 41%
The elasticity of EOQ with respect to sales = (41%/100%) = 0.41
f) When carrying cost is doubled, Carrying Cost (i ) = 20%
So % change in Carrying Cost = 10%
Now, in this case, Holding Cost = 20% x $10 = $2
Therefore,
= 5,000 units
So, % change in EOQ = 29%
The elasticity of EOQ with respect to carrying cost = (29%/10%) = 2.9
g) When orderings costs are doubled, Ordering Cost (s) = $200
So % change in Ordering Cost = 100%
Therefore,
= 10,000 units
So, % change in EOQ = 41%
The elasticity of EOQ with respect to ordering cost = (41%/100%) = 0.41
h) When selling prices are doubled, Purchase Price (c ) = $20
So % change in Purchase Price = 100%
Now, in this case, Holding Cost = 10% x $20 = $2
Therefore,
EOQ = ?(2x100x250000)/2
= 5,000 units
So, % change in EOQ = 29%
The elasticity of EOQ with respect to sales = (29%/100%) = 0.29
Parameters
Values
ANNUAL UNIT USAGE (d)
250,000
ORDER LOT NUMBER (q)
100
ORDERING COST (s)
100
PURCHASE PRICE PER UNIT (c )
10
CARRYING COST (i)
10%
SAFETY STOCK
5,000
DELIVERY TIME
1 WEEK
NUMBER OF WEEKS
50
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