Suppose that traffic congestion has rendered the distance-based impedance function unsuitable for Problem 12-16. A detailed survey yields present-day commodity flows shown below. In the future, state #1 lumber production will increase to 18,000 and state #2 lumber consumption will increase to 21,000. Estimate the lumber flows between the three states.

Question

What will be an ideal response?

Answer 1

Because impedances are not available and an older OD matrix is available,

the Fratar method is appropriate. In the application of Eq. 12.5, note that the

growth factor Gi refers to lumber produced and the growth factor Gj refers to

lumber consumed. Note also that tij is a true from/to matrix (e.g., lumber tons

from zone i to zone j will not equal tons from zone j to zone i).

The growth factors are as follows:



Equation 12.5 may be applied using the tonnage of lumber from zone 1 to zone 2

as an example:



Ten iterations of the Fratar method gives the following trip interchange matrix: