Tools › Operations Research › Optimization › Transportation and Assignment › Example
Hillier and Lieberman Section 9.1: the P&T Company transportation problem
| Tool | Transportation and Assignment |
| Source | Hillier, F. S., and Lieberman, G. J. (2015). Introduction to Operations Research, 10th ed. McGraw-Hill, New York. Section 9.1, Table 9.2. |
| Level | Undergraduate |
Problem
Three canneries with outputs of 75, 125 and 100 truckloads supply four warehouses needing 80, 65, 70 and 85 truckloads at the shipping costs of Table 9.2. Find an initial basic feasible solution by the northwest-corner rule and by Vogel's approximation method, then the minimum-cost shipping plan by the transportation simplex method.
Inputs to Enter
- Problem select: Transportation, P&T Company (the default)
- Supplies 75, 125, 100; demands 80, 65, 70, 85 (balanced, 300)
- Costs per truckload: Cannery 1 464, 513, 654, 867; Cannery 2 352, 416, 690, 791; Cannery 3 995, 682, 388, 685
Answers
- Northwest-corner start: x11 75, x21 5, x22 65, x23 55, x33 15, x34 85, Z = 165,595
- Vogel's start: first allocation x33 = 70 on the penalty 294 of Cannery 3; Z = 152,535, already optimal
- Optimum Z = 152,535 with x12 20, x14 55, x21 80, x22 45, x33 70, x34 30; unique (no zero reduced cost), not degenerate; cost decreases every MODI iteration from the northwest-corner start
Notes
The tool's default problem is this example; press Submit to reproduce it. The same optimum is confirmed by the Linear Programming tool's simplex in the test script.