Heuristic Method for Costs Minimization A category of traffic assignment problems seek to find the
lowest possible costs for a fixed amount of traffic. The above
example illustrate the assignment of 35 units between locations
A and F at a minimum cost.

Step 1. Identify all possible paths between locations having a transport
demand (all paths between A and F). Order these paths by their cost,
from the lowest to the highest.

Step 2. Take the lowest cost path and assign all the traffic that
the link having the lowest capacity can support (A-B-E-F). Subtract
this number from the capacity of every link on the path. This subtraction
cannot be lower than 0 its result is the remaining
capacity of each link of the path.

Step 3. Repeat by increasing order of path cost until all the demand
is assigned. If all the demand can not be assigned, the
problem cannot be solved.

Step 4. Once all the demand has been assigned, calculate the
total cost by multiplying the traffic used on each link by its
respective unit cost. In this case, the minimum costs to assign
35 units of traffic between A and F is 130, which is on average
3.7 per unit.