A firm is trying to decide whether to have a centralized warehouse or regional w

Question

A firm is trying to decide whether to have a centralized warehouse or regional warehouses. A centralized warehouse would be cheaper than four regional warehouses, but the expenses for shipping would be higher with a centralized warehouse. The cost of a centralized warehouse is $1,700,000 and the per-unit shipping cost is $5/unit. If the firm decided to use the regional warehouse model, each of the four warehouses would cost $500,000 and the per-unit shipping cost would be $3.50/unit.

a. If the firm ships 150,000 units, should the firm use the centralized warehouse or the regional warehouses?

b. If the firm ships 300,000 units, should the firm use the centralized warehouse or the regional warehouses?

c. What number of shipments would make the cost the same for the two plans?

Explanation / Answer

Given that the fixed cost of a centralized warehouse is $1,700,000 and the variable cost is $5/unit. Fixed cost of each warehouse would cost $500,000 and the variable cost would be $3.50/unit.

a) If the firm ships 150,000 units, under centralized warehouse, the total cost becomes $1,700,000 + $750,000 = $2,450,000. And under regional warehouse, the total cost becomes $500,000*4 + 525,000 or $2,525,000. Since TC(CW)<TC(RW), the firm should use the centralized warehouse

b) If the firm ships 300,000 units, under centralized warehouse, the total cost becomes $1,700,000 + $1,500,000 = $3,200,000. And under regional warehouse, the total cost becomes $500,000*4 + 1,050,000 or $3,050,000. Since TC(CW)>TC(RW), the firm should use the Regional warehouse

c) Let the number of shipments be y:

$1,700,000 + 5y = $2,000,000 + 3.5y

1.5y = 300,000

y = 200,000

Hence,  200,000 shipments would make the cost the same for the two plans.

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