Transportation Models
1. The following example demonstrates the formulation of the transportation model. Wheat is harvested in the Midwest and stored in grain elevators in three cities - Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis and Cincinnati. Grain is shipped to the mills in railroad cars, each capable of holding one ton of wheat. Each grain elevator is able to supply the following number of tons of wheat to the mills on a monthly basis.
Grain Elevator Supply
1. Kansan City 150
2. Omaha 175
3. Des Moines 275
Each mill demands the following number of tons of wheat per month.
Mill Demand
A. Chicago 200
B. St. Louis 100
C. Cincinnati 300
The cost of transporting one ton of wheat from each grain elevator to each mill differs according to the dstance and rail system. These costs are shown below. For example, the cost of shipping one ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7.
Mill
Grain Elevator Chicago (A) St. Louis (B) Cincinnati (C)
Kansan City 6 8 10
Omaha 7 11 11
Des Moines 4 5 12
2. A concrete company transports concrete from three plants to three construction sites. The supply capacities of the three plants, the demand requirements at the three sites, and the transportation cost per ton are as follows:
Plant Construction Site Supply (tons)
A B C
1 8 5 6 120
2 15 10 12 80
3 3 9 10 80
Demand (tons) 150 70 60
3. Given the following transportation tableau, determine the initial solution using any method and compute the total cost for each.
FROM/TO A B C Supply
1 10 9 5 60
2 6 8 7 30
3 4 3 2 60
Demand 40 40 70 150
FROM/TO 1 2 3 4 Supply
1 7 6 2 12 70
2 3 9 8 7 40
3 10 4 11 5 100
Demand 30 60 90 30
FROM/TO 1 2 3 Supply
A 6 7 4 100
B 5 3 6 180
C 8 5 7 200
Demand 135 175 170
4. Green Valley Mills produces carpet at plants in St. Louis and Richmond. The carpet is then shipped to two outlets located in Chicago and Atlanta. The cost per ton of shipping carpet each of the two plants to the two warehouses is as follows.
From/To Chicago Atlanta
St. Louis 40 65
Richmond 70 30
The plant at St. Louis can supply 250 tons of carpet per week; the plant at Richmont can supply 400 tons per week. The Chicago outlet has a demand of 300 tons per week, and the outlet Atlanta demands 350 tons per week. The company wants to know the number of tons of carpet to ship from each plant to each outlet to minimize the total shipping cost. Solve this transportation problem.
5. Tobacco is stored in warehouses in four cities at the end of each growing season
Location Capacity (tons)
A. Charlotte 90
B. Raleigh 50
C. Lexington 80
D. Danville 60
These warehouses supply the following of tobacco to cigarette companies in three cities.
Plant Demand (tons)
1. Richmond 120
2. Winston-Salem 100
3. Durham 110
The railroad shipping costs per ton of tobacco are shown below:
FROM/TO 1 2 3
A 7 10 5
B 12 9 4
C 7 3 11
D 9 5 7
6. Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload, supply, and demand.
FROM/TO New York Philadelphia Chicago Boston Supply
Tampa 9 14 12 17 200
Miami 11 10 6 10 200
Fresno 12 8 15 7 200
Demand 130 170 100 150
7. A manufacturing firm produces diesel engines in four cities - Phoenix, Seattle, St. Louis, and Detroit. The company is able to produce the following numnbers of engines per month.
Plant Production
1. Phoenix 5
2. Seattle 25
3. St. Louis 20
4. Detroit 25
Three trucking firms purchase the following numbers of engines for their plants in three cities.
Firm Demand
A. Greensboro 10
B. Charlotte 20
C. Louisville 15
The transportation costs per engine from sources to destinations are shown below.
FROM/TO A B C
1 7 8 5
2 6 10 6
3 10 4 5
4 3 9 11
8. The Interstate Truck Rental firm has accumulated extra trucks at three of its leasing outlets, as shown below.
Leasing Outlet Extra Outlets
1. Atlanta 70
2. St. Louis 115
3. Greensboro 60
The firm also has four outlets with shortages of rental trucks, as follows.
Leasing Outlet Truck shortage
A. New Orleans 80
B. Cincinnatri 50
C. Louisville 90
D. Pittsburgh 25
The firm wants to transfer trucks from those outlets with extras to those with shortages at the minimum total cost. The following costs of transporting these trucks from city to city have been determined.
FROM/TO A B C D
1 70 80 45 90
2 120 40 30 75
3 110 60 70 80
9. The Shotz Beer Company has breweries in two cities; the breweries can supply the folloiwng numbers of barrels of draft beer to the company's distributors each month.
Brewery Monthly Supply (barrels)
A. Tampa 3500
B. St. Louis 5000
The distributors, spread throughout six states, have the following total monthly demand:
Distributor Monthly Demand (barrels)
1. Tennessee 1600
2. Georgia 1800
3. North Carolina 1500
4. SOuth Carolina 950
5. Kentucky 1250
6. Virginia 1400
The company must pay the following shipping costs per barrel:
FROM/TO 1 2 3 4 5 6
A 0.50 0.35 0.60 0.45 0.80 0.75
B 0.25 0.65 0.40 0.55 0.20 0.65
10. Computers Unlimited sells microcomputers to universities and colleges on the east coast, and ships them from three distribution warehouses. The firm is able to supply the following numbers of microcomputers to the universities by the beginning of the academic year.
Distribution Warehouse Supply (microcomputers)
1. Richmond 420
2. Atlanta 610
3. Washington, D.C 340
Four universities have ordered microcomputers that must be delivered and installed by the beginning of the academic year:
University Demand (microcomputers)
A.Tech 520
B. A and M 250
C. State 400
D. Central 380
The shipping and installation costs per microcomputer from each distributor to each university are as follows:
FROM/TO A B C D
1 22 17 30 18
2 15 35 20 25
3 28 21 16 14
11. A large manufacturing company is closing three of its existing plants and intends to transfer some of its more skilled employees to three plants that will remain open. The number of employees available for transfer from each closing plant is as follows:
Closing Plant Transferable Employees
1 60
2 105
3 70
The following number of employees can be accomodated at the three plants remaining open:
Open Plants Employees Demanded
A 45
B 90
C 35
Each transferred employee will increase product output per day at each plant as follows:
FROM/TO A B C
1 5 8 6
2 10 9 12
3 7 6 8
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