Answer Report
|
 |
The minimal cost flow problem might arise in a logistics network where people and materials are being moved between various points in the world. It may be associated with the movement of locomotives between points in a railroad network to satisfy power for trains at least travel cost. Minimal cost network flow problems occur in the design and analysis of communication systems, oil pipeline systems, tanker scheduling problems, and a variety of other areas.
Sample Network Flows with Lower and Upper bonds
Total supply equals the total demand within the network. The minimal cost network flow problem may be stated as follows. Ship the available supply through the network to satisfy demand at minimal cost.
Where
- b1 = 5, b3 = 3 : supply;
- b4 = -8 : demand;
- b2 = 0 : intermediate (or transshipment);
- c12 = 1, c13 = 4, c32 = -1, c24 = 2, c34 = 6 : the unit shipping cost along the arc;
- l12 = 0, l13 = 0, l32 = 1, l24 = 0, l34 = 1 : lower bounds;
- u12 = 6, u13 = 3, u32 = 8, u24 = 4, u34 = 5 : upper bounds.
- X12, X13, X32, X24, X34 : the amount of flow on the arc to be computed;
Answer Report
|
|