The amount of lumber produced and consumed by three states is shown in the following table. Intrastate shipment distances are 200 miles and interstate distances are 800 miles (between states 1 and 2), 1,000 miles (between states 1 and 3), and 400 miles (between states 2 and 3). Assuming an impedance function of the form 1/d, estimate the tonnage of lumber that will travel between the three states:
Tons of Lumber Produced and Consumed Per Year (Tons)
What will be an ideal response?
The general form for the gravity model is
For example, the number of trips from zone 1 to zone 2, T12, is
Thus the initial trip table is
Because computed attractions do not match given attractions, attractions are
adjusted using Equation 12.4:
For example, attractions for the second iteration for zone 2 can be found as =
(10,000)(10,000)/8,923 = 11,207. Similarly, the new attractions for zones 1 and 3
are found to be 719 and 7,339, respectively.
After five iterations, the final flows are found as shown below.
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