Modeling and Computer solutions as well. (Transportations; Transshipment; Assignment) Linear Programming
P1
| 1. transportation problem | ||||||||||
| From | To (cost) | |||||||||
| 1 | 2 | 3 | ||||||||
| A | $6 | $5 | $5 | |||||||
| B | 11 | 8 | 9 | |||||||
| C | 4 | 10 | 7 | |||||||
| DV | From | To | Supply | Note: Blue cells are your decision variables | ||||||
| 1 | 2 | 3 | Constraint | |||||||
| A | 0 | <= | 150 | |||||||
| B | 0 | <= | 85 | |||||||
| C | 0 | <= | 125 | |||||||
| Constraint | 0.00 | 0.00 | 0.00 | |||||||
| = | = | = | ||||||||
| Demand | 70 | 100 | 80 | |||||||
| Objective | Minimize Cost | $0.00 |
P2
| 2. transportation problem | ||||||||||
| From | To (cost) | |||||||||
| 1 | 2 | 3 | ||||||||
| A | $8 | $14 | $8 | |||||||
| B | 6 | 17 | 7 | |||||||
| C | 9 | 24 | 10 | |||||||
| DV | From | To | Supply | Note: Blue cells are your decision variables | ||||||
| 1 | 2 | 3 | Constraint | |||||||
| A | 0 | = | 120 | |||||||
| B | 0 | = | 80 | |||||||
| C | 0 | = | 150 | |||||||
| Constraint | 0.00 | 0.00 | 0.00 | |||||||
| = | = | = | ||||||||
| Demand | 110 | 140 | 100 | |||||||
| Objective | Minimize Cost | 0 |
P3
| 3. World Foods, Inc. | ||||||||||
| From | To (cost) | |||||||||
| 4. Norfolk | 5. New York | 6. Savannah | ||||||||
| 1. Hamburg | $320 | $280 | $555 | |||||||
| 2. Marseilles | 410 | 470 | 365 | |||||||
| 3. Liverpool | 550 | 355 | 525 | |||||||
| Warehouse | Distribution Center | |||||||||
| 7. Dallas | 8. St. Louis | 9. Chicago | ||||||||
| 4. Norfolk | $80 | $78 | $85 | |||||||
| 5. New York | 100 | 120 | 95 | |||||||
| 6. Savannah | 65 | 75 | 90 | |||||||
| DV | From | To (cost) | Supply from sources | |||||||
| 4. Norfolk | 5. New York | 6. Savannah | Constraints | |||||||
| 1. Hamburg | 0.00 | = | 75 | |||||||
| 2. Marseilles | 0.00 | = | 85 | |||||||
| 3. Liverpool | 0.00 | = | 40 | |||||||
| Warehouse | Distribution Center | |||||||||
| 7. Dallas | 8. St. Louis | 9. Chicago | Constraints | Net Flow (distribution center) | ||||||
| 4. Norfolk | 0.00 | = | 0.00 | |||||||
| 5. New York | 0.00 | = | 0.00 | |||||||
| 6. Savannah | 0.00 | = | 0.00 | |||||||
| Constraints | 0 | 0 | 0 | |||||||
| <= | <= | <= | ||||||||
| Demand | 85 | 70 | 65 | |||||||
| 220 | 200 | |||||||||
| Objective | Minimize Cost | $0 |
P4
| 4. Omega pharmaceutical firm | ||||||||||
| Region (days) | ||||||||||
| Sales-person | 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 | |||||
| DV | Sales-person | A | B | C | D | E | Assignment | |||
| 1 | = | 1 | ||||||||
| 2 | = | 1 | ||||||||
| 3 | = | 1 | ||||||||
| 4 | = | 1 | ||||||||
| 5 | = | 1 | ||||||||
| Constraints | ||||||||||
| = | = | = | = | = | ||||||
| Region assigned | 1 | 1 | 1 | 1 | 1 | |||||
| Objective | Minimize Time |