With the gain factor, although 200 leave Phoenix, only 190 arrive at Chicago. The solution with loses in Fig. 6 is significantly different than those previously presented. The flows are no longer integer, the extra demand at Chicago is no longer satisfied, Austin does not produce to its full capacity, more arcs are used to provide materials lost during shipping and the profit is considerably reduced. The solution with shipping losses represented by gain factors.
Gains are very for useful modeling.
When all arc gains are 1, the model is a pure network flow model. When some gains are other than 1, the model is a generalized network flow model. Integer solutions cannot be guaranteed for the generalized model.