A commander has a flow problem involving points on the battlefield. The points are numbered 1 though m, and the distance is given for every pair of points dij. The distances are symmetric and unit cost is proportional to distance.

Equivalent models with 0 lower bounds can replace models with lower bounds on flow. Fig. 28 shows a general arc with the parameters lower bound, upper bound, cost and gain. An equivalent representation of the arc with zero lower bounds is also shown. The transformation requires modification of the external flows at both ends of the arc. When arcs have equal upper and lower bounds, the effected arc may be eliminated because its upper bound on flow will be zero.

Figure 28. Elimination of Lower Bounds