Answer to Custom Vans, Inc.
CUSTOM VANS, INC.
Where would you locate the two plants, and why?
To determine whether the shipping pattern can be improved and where the two new plants should be located, the total costs for the whole transportation system for each combination of plants as well as the existing shipping pattern costs will have to be determined.
In the heading identifying the combination being discussed, Gary and Fort Wayne, will be omitted because they appear in every possible combination.
The derivation of total costs and optimal solutions for each combination is found on the succeeding pages. In summary: Total cost: Detroit—Madison $10,200 Madison—Rockford $10,550 Detroit—Rockford $11,400
Because the total cost is lowest in the Gary-Fort Wayne-Detroit-Madison combination ($10,200), then the new plants should be located in Detroit and Madison. This system is also an improvement over the existing pattern, which costs $9,000, for now an extra 300 units can be shipped at an additional cost $1,200.
In terms of average total costs: Status quo: $9,000 for 450 units $20.00/unit Proposed: $10,200 for 750 units $13.60/unit
Thus, the two new plants would definitely be advantageous, both in terms of demand and in minimizing transportation costs.
(a) Existing pattern:
Initial solution—Northwest Corner Rule:
Currently implemented solution:
Total cost 200 10 50 30 40 100 100 15
$9,000
(b) Considering Detroit and Madison:
Initial solution—Northwest Corner Rule:
Note: Because a plant at Detroit could purchase a gallon of fiberglass for $2 less than any other plant, and one Showerific takes 2 gallons of fiberglass, a systems approach to transportation warrants that $4 (2 2) be deducted from each price quoted in the case for shipments for Detroit.
Because a plant at Madison could hire a laborer for $1 less per hour than the other plants, and one Showerific takes 3 labor hours to build, then $3 (3 1) should be deducted from each price
Where would you locate the two plants, and why?
To determine whether the shipping pattern can be improved and where the two new plants should be located, the total costs for the whole transportation system for each combination of plants as well as the existing shipping pattern costs will have to be determined.
In the heading identifying the combination being discussed, Gary and Fort Wayne, will be omitted because they appear in every possible combination.
The derivation of total costs and optimal solutions for each combination is found on the succeeding pages. In summary: Total cost: Detroit—Madison $10,200 Madison—Rockford $10,550 Detroit—Rockford $11,400
Because the total cost is lowest in the Gary-Fort Wayne-Detroit-Madison combination ($10,200), then the new plants should be located in Detroit and Madison. This system is also an improvement over the existing pattern, which costs $9,000, for now an extra 300 units can be shipped at an additional cost $1,200.
In terms of average total costs: Status quo: $9,000 for 450 units $20.00/unit Proposed: $10,200 for 750 units $13.60/unit
Thus, the two new plants would definitely be advantageous, both in terms of demand and in minimizing transportation costs.
(a) Existing pattern:
Initial solution—Northwest Corner Rule:
Currently implemented solution:
Total cost 200 10 50 30 40 100 100 15
$9,000
(b) Considering Detroit and Madison:
Initial solution—Northwest Corner Rule:
Note: Because a plant at Detroit could purchase a gallon of fiberglass for $2 less than any other plant, and one Showerific takes 2 gallons of fiberglass, a systems approach to transportation warrants that $4 (2 2) be deducted from each price quoted in the case for shipments for Detroit.
Because a plant at Madison could hire a laborer for $1 less per hour than the other plants, and one Showerific takes 3 labor hours to build, then $3 (3 1) should be deducted from each price