Tools › Operations Research › Optimization › Transportation and Assignment › Example
Winston Section 7.6: the Widgetco transshipment problem
| Tool | Transportation and Assignment |
| Source | Winston, W. L. (2004). Operations Research: Applications and Algorithms, 4th ed. Brooks/Cole, Belmont, CA. Section 7.6. |
| Level | Undergraduate |
Problem
Widgetco makes widgets in Memphis (150 a day) and Denver (200) for customers in Los Angeles and Boston (130 each), shipping directly or through New York and Chicago. Convert the network to a transportation table with a buffer at the transshipment points and find the minimum-cost shipping plan.
Inputs to Enter
- Problem select: Transshipment, Widgetco (Winston)
- Nodes: Memphis source 150, Denver source 200, New York and Chicago transshipment, Los Angeles sink 130, Boston sink 130
- Arc costs: Memphis → NY 8, Chicago 13, LA 25, Boston 28; Denver → NY 15, Chicago 12, LA 26, Boston 25; NY → Chicago 6, LA 16, Boston 17; Chicago → NY 6, LA 14, Boston 16
Answers
- Buffer s = 350 (total supply); 4 × 4 table with a dummy column of 90 for the unused supply
- Optimal cost $6,370: Memphis → New York 130, New York → Los Angeles 130, Denver → Boston 130 direct; Memphis 20 and Denver 70 unused
- Alternative optimum flagged (Memphis → New York → Boston at 25 ties Denver → Boston at 25)
Notes
Choose the Widgetco entry in the problem select; the node list and arc list load together. The optimum is also confirmed by the Linear Programming tool's simplex.