Tools › Operations Research › Optimization › Transportation and Assignment › Example
Taha Example 5.3-1: SunRay Transport by northwest corner, least cost, Vogel and the transportation simplex
| Tool | Transportation and Assignment |
| Source | Taha, H. A. (2011). Operations Research: An Introduction, 9th ed. Pearson, Upper Saddle River, NJ. Example 5.3-1. |
| Level | Undergraduate |
Problem
SunRay Transport ships grain from three silos holding 15, 25 and 10 truckloads to four mills needing 5, 15, 15 and 15. Compare the starting solutions of the northwest-corner, least-cost and Vogel methods and carry the problem to the optimum by the method of multipliers, handling the degeneracy that appears.
Inputs to Enter
- Problem select: Transportation, SunRay (Taha)
- Supplies 15, 25, 10; demands 5, 15, 15, 15
- Costs: Silo 1 10, 2, 20, 11; Silo 2 12, 7, 9, 20; Silo 3 4, 14, 16, 18
Answers
- Starting costs: northwest corner $520, least cost $475 (degenerate, x14 basic at zero), Vogel $475
- Iteration 1 from the northwest corner: x31 enters (u3 + v1 − c31 = 9), θ = 5, x11 leaves; iteration 2: Z = 475, degenerate, x14 enters
- Optimum $435 with x12 5, x14 10, x22 10, x23 15, x31 5, x34 5; degeneracy reported
Notes
Choose the SunRay entry in the problem select. The tie for the leaving variable in iteration 1 is broken as Taha does.