MAT540 Homework Week 10 Page 1 of 2 MAT540 Week 10 Homework Chapter 6 1. Consider the following transportation problem: From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125 Demand 70 100 80 Formulate this problem as a linear programming model and solve it by the using the computer. 2. Consider the following transportation problem: From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150 110 140 100 Demand Solve it by using the computer. 3. World foods, Inc. imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table: MAT540 Homework Week 10 Page 2 of 2 To (Cost) From 4. Norfolk 5. Supply New York 6. Savannah 1. Hamburg 320 280 555 75 2. Marseilles 410 470 365 85 3. Liverpool 550 355 525 40 The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the demands (1000 lb.) at the distribution centers are as follows: Distribution Center Warehouse 7. Dallas 8. St. Louis 9. Chicago 4. Norfolk 80 78 85 5. New York 100 120 95 6. Savannah 65 75 90 Demand 85 70 65 Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs. 4. The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the sales persons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table: Salesperson Region (days) A B C D E 1 20 10 12 10 22 2 14 10 18 11 15 3 12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23 Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time. 1. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $6 11 4 To (cost) 2 $5 8 10 3 $5 9 7 1 0.00 0.00 70.00 70.00 = 70 To 2 100.00 0.00 0.00 100.00 = 100 3 50.00 0.00 30.00 80.00 = 80 $1,240.00 Constraint 150 0 100 Supply <= <= <= 150 85 125 Note: Blue cells are your decision variables s 2. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $8 6 9 To (cost) 2 $14 17 24 3 $8 7 10 1 0.00 0.00 110.00 110.00 = 110 To 2 120.00 20.00 0.00 140.00 = 140 3 0.00 60.00 40.00 100.00 = 100 3830 Constraint 120 80 150 Supply = = = 120 80 150 Note: Blue cells are your decision variables s 3. World Foods, Inc. From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah 4. Norfolk $320 410 550 To (cost) 5. New York $280 470 355 6. Savannah $555 365 525 Distribution Center 7. Dallas 8. St. Louis 9. Chicago $80 $78 $85 100 120 95 65 75 90 To (cost) DV From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah Constraints Demand 4. Norfolk 5. New York 6. Savannah 0.00 0.00 0.00 75.00 0.00 40.00 0.00 85.00 0.00 75.00 85.00 40.00 Supply from sources Constraints = = = 75 85 40 Distribution Center 7. Dallas 8. St. Louis 9. Chicago Constraints 0.00 50.00 35.00 85 <= 85 0.00 0.00 50.00 50 <= 70 0.00 65.00 0.00 65 <= 65 0.00 0.00 0.00 Net Flow (distribution center) = = = 0.00 0.00 0.00 220 Objective Minimize Cost $83,425 200 4. Omega pharmaceutical firm Region (days) Sales-person 1 2 3 4 5 DV Sales-person 1 2 3 4 5 Constraints Region assigned Objective Minimize Time A B C D E 20 14 12 16 12 10 10 13 12 15 12 18 19 14 19 10 11 11 22 26 22 15 14 16 23 A B C D E Assignment = = = = = = 1 = 1 = 1 = 1 = 1 1 1 1 1 1 1. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $6 11 4 To (cost) 2 $5 8 10 1 0.00 0.00 70.00 70.00 = 70 To 2 100.00 0.00 0.00 100.00 = 100 $1,240.00 3 $5 9 7 3 50.00 0.00 30.00 80.00 = 80 Constraint 150 0 100 Supply <= <= <= 150 85 125 Note: Blue cells are your decision variables s 2. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $8 6 9 To (cost) 2 $14 17 24 1 0.00 0.00 110.00 110.00 = 110 To 2 120.00 20.00 0.00 140.00 = 140 3830 3 $8 7 10 3 0.00 60.00 40.00 100.00 = 100 Constraint 120 80 150 Supply = = = 120 80 150 Note: Blue cells are your decision variables s 3. World Foods, Inc. From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah 4. Norfolk $320 410 550 To (cost) 5. New York $280 470 355 6. Savannah $555 365 525 Distribution Center 7. Dallas 8. St. Louis 9. Chicago $80 $78 $85 100 120 95 65 75 90 To (cost) DV From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah Constraints Demand 4. Norfolk 5. New York 6. Savannah 0.00 0.00 0.00 75.00 0.00 40.00 0.00 85.00 0.00 75.00 85.00 40.00 Supply from sources Constraints = = = 75 85 40 Distribution Center 7. Dallas 8. St. Louis 9. Chicago Constraints 0.00 50.00 35.00 85 <= 85 0.00 0.00 50.00 50 <= 70 0.00 65.00 0.00 65 <= 65 0.00 0.00 0.00 Net Flow (distribution center) = = = 0.00 0.00 0.00 220 Objective Minimize Cost $83,425 200 4. Omega pharmaceutical firm Sales-person 1 2 3 4 5 Region (days) C 12 18 19 14 19 D 10 11 11 22 26 E 22 15 14 16 23 Sales-person A B C D E Assignment 0 0 0 0 1 1 = 1 0 1 0 0 0 1 = 1 0 0 0 1 0 1 = 1 1 0 0 0 0 1 = 1 0 0 1 0 0 1 = 1 1 1 1 1 1 Region assigned Objective B 10 10 13 12 15 1 2 3 4 5 Constraints DV A 20 14 12 16 12 Minimize Time 60 = = = = = 1 1 1 1 1 3. World Foods, Inc. From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah 4. Norfolk $320 410 550 To (cost) 5. New York $280 470 355 6. Savannah $555 365 525 Distribution Center 7. Dallas 8. St. Louis 9. Chicago $80 $78 $85 100 120 95 65 75 90 To (cost) DV From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah Constraints Demand 4. Norfolk 5. New York 6. Savannah 0.00 0.00 0.00 75.00 0.00 40.00 0.00 85.00 0.00 75.00 85.00 40.00 Supply from sources Constraints = = = 75 85 40 Distribution Center 7. Dallas 8. St. Louis 9. Chicago Constraints 0.00 50.00 35.00 85 = 85 0.00 0.00 50.00 50 <= 70 0.00 65.00 0.00 65 = 65 0.00 115.00 85.00 Net Flow (distribution center) = = = 0.00 115.00 85.00 220 Objective Minimize Cost $83,425 200 1. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $6 11 4 To (cost) 2 $5 8 10 1 0.00 0.00 70.00 70.00 = 70 To 2 100.00 0.00 0.00 100.00 = 100 $1,240.00 3 $5 9 7 3 50.00 0.00 30.00 80.00 = 80 Constraint 150 0 100 Supply <= <= <= 150 85 125 Note: Blue cells are your decision variables s 2. transportation problem From A B C DV From A B C Constraint Demand Objective Minimize Cost 1 $8 6 9 To (cost) 2 $14 17 24 1 0.00 0.00 110.00 110.00 = 110 To 2 120.00 20.00 0.00 140.00 = 140 3830 3 $8 7 10 3 0.00 60.00 40.00 100.00 = 100 Constraint 120 80 150 Supply = = = 120 80 150 Note: Blue cells are your decision variables s 3. World Foods, Inc. From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah 4. Norfolk $320 410 550 To (cost) 5. New York $280 470 355 6. Savannah $555 365 525 Distribution Center 7. Dallas 8. St. Louis 9. Chicago $80 $78 $85 100 120 95 65 75 90 To (cost) DV From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah Constraints Demand 4. Norfolk 5. New York 6. Savannah 0.00 0.00 0.00 75.00 0.00 40.00 0.00 85.00 0.00 75.00 85.00 40.00 Supply from sources Constraints = = = 75 85 40 Distribution Center 7. Dallas 8. St. Louis 9. Chicago Constraints 0.00 50.00 35.00 85 <= 85 0.00 0.00 50.00 50 <= 70 0.00 65.00 0.00 65 <= 65 0.00 0.00 0.00 Net Flow (distribution center) = = = 0.00 0.00 0.00 220 Objective Minimize Cost $83,425 200 4. Omega pharmaceutical firm Sales-person 1 2 3 4 5 Region (days) C 12 18 19 14 19 D 10 11 11 22 26 E 22 15 14 16 23 Sales-person A B C D E Assignment 0 0 0 0 1 1 = 1 0 1 0 0 0 1 = 1 0 0 0 1 0 1 = 1 1 0 0 0 0 1 = 1 0 0 1 0 0 1 = 1 1 1 1 1 1 Region assigned Objective B 10 10 13 12 15 1 2 3 4 5 Constraints DV A 20 14 12 16 12 Minimize Time 60 = = = = = 1 1 1 1 1 3. World Foods, Inc. From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah 4. Norfolk $320 410 550 To (cost) 5. New York $280 470 355 6. Savannah $555 365 525 Distribution Center 7. Dallas 8. St. Louis 9. Chicago $80 $78 $85 100 120 95 65 75 90 To (cost) DV From 1. Hamburg 2. Marseilles 3. Liverpool Warehouse 4. Norfolk 5. New York 6. Savannah Constraints Demand 4. Norfolk 5. New York 6. Savannah 0.00 0.00 0.00 75.00 0.00 40.00 0.00 85.00 0.00 75.00 85.00 40.00 Supply from sources Constraints = = = 75 85 40 Distribution Center 7. Dallas 8. St. Louis 9. Chicago Constraints 0.00 50.00 35.00 85 = 85 0.00 0.00 50.00 50 <= 70 0.00 65.00 0.00 65 = 65 0.00 115.00 85.00 Net Flow (distribution center) = = = 0.00 115.00 85.00 220 Objective Minimize Cost $83,425 200