(13 points) (You can round all quantities to the nearest whole unit, and you can
ID: 353990 • Letter: #
Question
(13 points) (You can round all quantities to the nearest whole unit, and you can round all annual costs to the nearest whole dollar.) Suppose that your firm manufactures toy flying drones. Monthly demand for the drones is 46, units. Setup cost per order is $160, and the annual holding cost percentage is 22%. The drones c $40 to produce and are sold for $89. ost a. If you have one warehouse, what is the economic order quantity for the drones? What is the total of the annual setup and holding costs of this quantity? b. Suppose that you have 81 warehouses instead of one, and total demand is equally distributed among the warehouses. If setup and holding costs are the same in the smaller warehouses as they would be for the single large warehouse, what is the EOQ for the dolls at each of the 81 warehouses? What is the total of the annual setup and holding costs at each warehouse? What is the total of the company's annual setup and holding costs? c. Using centralized warehousing as in part a means that products must be shipped over longer distances. Suppose that shipping costs $1.20 per unit when using one warehouse and $0.90 per unit when using 81 warehouses. Which option should the company choose? Support your answer. d. Based on your answers to a and b above, if total company demand is D, what is the general formula for the total company EOQ cost of using N warehouses instead of one (if the demand is spread evenly over those warehouses)?Explanation / Answer
a. If you have one warehouse, what is the economic order quantity for the drones? What is the total of the annual setup and holding costs of this quantity?
Now assume that there is one centralized warehouse with monthly demand of 46,000, therefore Annual demand, D = 46,000 *12 = 552,000 units
Setup cost per order S = $160 per order
Annual Inventory holding cost, H = 22% * $40 = $8.80 per unit per year
Formula of economic order quantity (EOQ)
EOQ = Q = (2 * Annual Demand * Setup cost per order / Inventory holding cost)
Therefore
EOQ = Q = (2 * 552,000 *$160 / $8.80)
= 4,480.26 or 4480 unit (rounding to nearest whole number)
Total Cost = Annual ordering cost + Annual inventory holding cost
= (D/Q)* S + (H*Q)/2
= (552,000 / 4480) *$160 + ($8.80*4480)/2
= $39,426
Total cost for a centralized warehouse = $39,426
b. Suppose that you have 81 warehouses instead of one, and total demand is equally distributed among the warehouses. If setup and holding costs are the same in the smaller warehouses as they would be for the single large warehouse, what is the EOQ for the dolls at each of the 81 warehouses? What is the total of the annual setup and holding costs at each warehouse? What is the total of the company’s annual setup and holding costs?
First let’s calculate the Economic order quantity and total cost for one warehouse
Annual demand for one warehouse, D1 = 552,000/ 81 = 6,815 units
Ordering cost S = $160 per order
Annual Inventory holding cost, H = 22% * $40 = $8.80 per unit per year
Formula of economic order quantity (EOQ)
EOQ = Q = (2 * Annual Demand * Ordering cost/ Inventory holding cost)
Therefore
EOQ = Q = (2 * 6,815 *$160 / $8.80)
EOQ = Q = 497.81 or 498 units
Total Cost = Annual ordering cost + Annual inventory holding cost
= (D1/Q)* S + (H*Q)/2
= (6815 / 498) *$160 + ($8.80*498)/2
= $4,380.76
Therefore total cost for 81 identical warehouses or the company’s annual setup and holding costs
= 81* $4,380.76 = $350,780
c. Using centralized warehousing as in part a means that products must be shipped over longer distances. Suppose that shipping costs $1.20 per unit when using one warehouse and $0.90 per unit when using 81 warehouses. Which option should the company choose? Support your answer.
Total cost for centralized warehousing including shipping costs = Annual ordering cost + Annual inventory holding cost + Annual shipping cost
= (D/Q)* S + (H*Q)/2 + D * 1.20
= (552,000 / 4480) *$160 + ($8.80*4480)/2 + 552,000 * $1.20
= $39,426 + $662,400
=$ 701,826
Total cost for a centralized warehouse including shipping costs =$ 701,826
Total cost using 81 warehouses including shipping costs = Annual ordering cost + Annual inventory holding cost + Annual shipping cost
Total Cost = Annual ordering cost + Annual inventory holding cost + Annual shipping cost
= (D1/Q)* S + (H*Q)/2 + D1 * $0.90
= (6815 / 498) *$160 + ($8.80*498)/2 + 6815* $0.90
= $4,380.76 + $6,133.50
= $10,514.26
Therefore total cost for 81 identical warehouses or the company’s annual setup and holding costs including shipping costs
= 81* $10,514.26 = $851,655
As the total cost including shipping cost is low for a centralized warehouse therefore company should choose centralized warehousing.
d. Based on your answers to a and b above, if total company demand is D, what is the general formula for the total company EOQ cost of using N warehouses instead of one (if the demand is spread evenly over those warehouses)?
General formula for the total company EOQ cost of using N warehouses instead of one, if the demand is spread evenly over those warehouses
EOQ= (2*(D/N)*S)/H
Where,
D is annual demand
N is number of warehouses
S is Setup cost per order
H is Annual Inventory holding cost
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