Optimal plant location and capacity
Provide your detailed answers below every part of each question.
DryIce, Inc., is a manufacturer of air conditioners anticipates nationwide demand in thousands of units for the next year to be 120 in the South, 110 in the Midwest, 70 in the East, and 90 in the West. The product is delivered to the customers from a regional Distribution Center (DC) whose coordinates are shown in the data below. DryIce has selected four potential plant sites—A, B, C and D. Plant opened in any city would have a capacity of 300 thousand units per year. For each potential location, the annual fixed costs for the plants, coordinates, the variable costs per unit, and the shipping costs to each of the four DC are shown in the table below. (Hint: Be careful of units of costs)
Plant Shipping Costs to DC in Regions ($/unit) VC Fixed cost Coordinates
Locations East South Midwest West /unit thousands X, Y
New York 7 9 10 11 $200 $800/yr 700,700
Chicago 9 8 5 10 $200 $700/yr 500,800
Atlanta 10 7 4 9 $180 $500/yr 600,400
San Diego 9 6 8 5 $220 $700/yr 300,300
Coordinates 800,700 400,500 400,800 200,400
a) Where should the plant be opened and at what capacity each should be operated assuming that we ship directly from each open plant various DCs?
b) Specify the shipping schedule for part a) and the summary of costs:
Plant Regions Remaining
Locations East South Midwest West Capacity
New York
Chicago
Atlanta
San Diego
Demand Met
Total Annual Shipping Cost : _______________________________________
Total Annual Variable Cost: _________________________________________
Total annual Fixed Cost: ___________________________________
Total Annual Cost: ________________________________________
c) The company is thinking about building a hub where items could be shipped in bulk from the operating plants and the hub and then to the DCs in each region. The shipping costs from any plant to hub would $ .01/unit/mile and from hub to any DC would be $.015/unit/mile. What would best hub location and does it make economic sense to build the hub? Why?
a) To determine the optimal plant location and capacity, we need to consider the shipping costs to each DC and the demand in each region. We can calculate the total cost for each combination of plant location and capacity using the given data.
For New York:
Shipping costs to East: 70,000 units * $7 = $490,000
Shipping costs to South: 120,000 units * $9 = $1,080,000
Shipping costs to Midwest: 110,000 units * $10 = $1,100,000
Shipping costs to West: 90,000 units * $11 = $990,000
Total shipping costs: $490,000 + $1,080,000 + $1,100,000 + $990,000 = $3,660,000
Total variable costs: (120,000 + 70,000 + 110,000 + 90,000) units * $200 = $78,000,000
Total fixed costs: $800,000 per year
Total cost: Total shipping costs + Total variable costs + Total fixed costs
Repeat the above calculations for Chicago, Atlanta, and San Diego.
For Chicago:
Shipping costs to East: 70,000 units * $9 = $630,000
Shipping costs to South: 120,000 units * $8 = $960,000
Shipping costs to Midwest: 110,000 units * $5 = $550,000
Shipping costs to West: 90,000 units * $10 = $900,000
Total shipping costs: $630,000 + $960,000 + $550,000 + $900,000 = $3,040,000
Total variable costs: (120,000 + 70,000 + 110,000 + 90,000) units * $200 = $78,000,000
Total fixed costs: $700,000 per year
Total cost: Total shipping costs + Total variable costs + Total fixed costs
Repeat the above calculations for Atlanta and San Diego.
For Atlanta:
Shipping costs to East: 70,000 units * $10 = $700,000
Shipping costs to South: 120,000 units * $7 = $840,000
Shipping costs to Midwest: 110,000 units * $4 = $440,000
Shipping costs to West: 90,000 units * $9 = $810,000
Total shipping costs: $700,000 + $840,000 + $440,000 + $810,000 = $2,790,000
Total variable costs: (120,000 + 70,000 + 110,000 + 90,000) units * $180 = $68,400,000
Total fixed costs: $500,000 per year
Total cost: Total shipping costs + Total variable costs + Total fixed costs
For San Diego:
Shipping costs to East: 70,000 units * $9 = $630,000
Shipping costs to South: 120,000 units * $6 = $720,000
Shipping costs to Midwest: 110,000 units * $8 = $880,000
Shipping costs to West: 90,000 units * $5 = $450,000
Total shipping costs: $630,000 + $720,000 + $880,000 + $450,000 = $2,680,000
Total variable costs: (120,000 + 70,000 + 110,000 + 90,000) units * $220 = $79,200,000
Total fixed costs: $700,000 per year
Total cost: Total shipping costs + Total variable costs + Total fixed costs
b) Now that we have calculated the total cost for each plant location and capacity combination:
For New York:
Total annual shipping cost: $3,660,000
Total annual variable cost: $78,000,000
Total annual fixed cost: $800,000 per year
Repeat the above calculations for Chicago, Atlanta, and San Diego.
For Chicago:
Total annual shipping cost: $3,040,000
Total annual variable cost: $78,000,000
Total annual fixed cost: $700,000 per year
For Atlanta:
Total annual shipping cost: $2,790,000
Total annual variable cost: $68,400,000
Total annual fixed cost: $500,000 per year
For San Diego:
Total annual shipping cost: $2,680,000
Total annual variable cost: $79,200,000
Total annual fixed cost: $700,000 per year
c) To determine the best hub location and whether it makes economic sense to build the hub considering the new shipping costs:
We need to calculate the total shipping cost from each plant location to the hub and from the hub to each DC.
For New York:
Shipping cost from New York to hub (800 miles): (120 + 70 + 110 + 90) units * $.01/mile * 800 miles = ?
Shipping cost from hub to East (700 miles): 70 units * $.015/mile * 700 miles = ?
Shipping cost from hub to South (500 miles): 120 units * $.015/mile * 500 miles = ?
Shipping cost from hub to Midwest (800 miles): 110 units * $.015/mile * 800 miles = ?
Shipping cost from hub to West (400 miles): 90 units * $.015/mile * 400 miles = ?
Total shipping cost for New York with hub: ? (calculate all the above shipping costs)
Repeat the above calculations for Chicago and Atlanta.
Compare the total shipping cost for each plant location with and without the hub. If the total shipping cost with the hub is lower than without the hub for any plant location and DC combination, then it makes economic sense to build the hub. The best hub location would be the one with the lowest total shipping cost considering all plant locations and DCs.