A category of traffic assignment problems seeks to find the lowest possible costs for a fixed amount of traffic. The above example illustrates the assignment of 35 units between locations A and F at a minimum cost.
- Step 1. Identify all possible paths between locations with a transport demand (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 the link with 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 the remaining capacity of each path link.
- Step 3. Repeat by increasing the 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 on each link by its unit cost. In this case, the minimum cost to assign 35 units of traffic between A and F is 130, which is on average 3.7 per unit.