Illustrative Example Gravity Model

In the risk pooling Example 5.8, ABC Tools examined three network options, from completely deconsolidated to fully consolidated, based on inventory in the supply chain. Suppose ABC Tools decides to go with the option of one central warehouse suppl5dng all three customer regions. Then, the next question is where the central location should be such that it minimizes the distribution cost. 

The supply at the plant, the demands at the retailers, their coordinate locations in miles and their freight rates are given in Table 5.12. 

The problem is to determine the location of the single DC that will minimize the total distribution cost. Use an accuracy of 5% for termination of the algorithm. 

Using these values, we calculate the distances for the existing facilities using Equation 5.53 as di = 29.23, d2 = 31.78, d = 41.35 and d = 46.41. The total distribution cost is given by 

Using the aforementioned distances in Equations 5.56 and 5.57, we update the values of x and y. These calculations can be easily done on a spreadsheet as shown in Table 5.13. 

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In Chapter 21 on box models no distinction was made between a compound being present as a dissolved species or sorbed to solid surfaces (e.g., suspended particles, sediment-water interface). In Boxes 18.5 and 19.1, and also in Illustrative Example 19.6, we learned that several of the transport and transformation processes may selectively act on either the dissolved or the sorbed form of a constituent. For instance, a molecule sitting on the surface of a sedimentaiy particle at the lake bottom does not feel the effect of turbulent flow in the lake water, while the dissolved chemical species is passively moved around by the currents. In contrast, a molecule sorbed to a suspended particle (e.g., an algal cell) can sink through the water column because of gravity, unlike its dissolved counterpart. 

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