In order to make use of the load-distance technique, I need to take you back to high school geometry. No, you won't have to use the Pythagorean theorem, but instead the straight line distance formula. If you don't remember, it is the square root of the sum of the difference between the x values of two sites, squared, plus the difference between the y values of two sites, squared. Here's the formula on screen, actually (see video). In order to use the load-distance technique, we'll be using this formula a lot. Also, that means we'll be placing the whole region to be examined on a giant Cartesian plane. It doesn't matter where you start, as long as the relative distances are the same, and you keep everything positive. As a tip, however, I'll advise you to use miles as each unit. It just makes things easier to understand. In other words, don't go shifting the grid after we begin!
Finding the Distance of Sites
So your widget factory has two potential locations, represented on the graph at points (20, 30) and (40, 10). What? What graph? In order to use the load-distance technique, we have to overlay the map of the area onto a coordinate graph. We'll refer to these as A and B. Meanwhile, you have two major suppliers. It's a little known fact that widgets are produced from gizmos and gadgets, but now you know. The gizmo source is located at (30, 30), while the gadget source is located at (5, 20). We will refer to these as 1 and 2. Also, note that just because the first factory and the gizmo source both have y coordinates of 30 that they are not located at the same place. Now, we get to find the distance between each potential factory site and each supplier location. We'll do the first two together, then for the sake of time, I'll give you the last two.
For the distance from factory A to supplier 1, first subtract the x value of the supplier from that of the factory. That's 20-30, or negative 10. Squared, that's 100. We'd add that to the difference of the y value of each, but since 30 - 30 is zero, we only need to find the square root of 100. That comes out to 10. That's the distance from factory A to supplier 1.
For the distance from factory A to supplier 2, first subtract the x value of the supplier from that of the factory. Once again, that's 20 - 5, or 15, then squared, which gives us 225. We do have to subtract 20 from 30, so 30 - 20 is 10, when squared gives us 100. Add 225 and 100 together, and you get 325. Take the square root, and you end up with 18.03.
To save you from the math, the next two values come out to the distance from factory B to supplier 1 is 22.36, and the distance from factory B to supplier 2 is 36.40. On the surface of it, factory A looks like the better choice, but let's factor in the relative weight of the loads.
Finding the Load-Distance
To factor in the relative weight of the loads, we have to find out how many loads each supplier delivers. For the sake of ease, let's say that supplier 1 delivers 200 loads, while supplier 2 delivers 100 loads. To find the load distance, which takes both distance and number of loads into account, we have to use this formula (see video).
Now that can look intimidating, but all it is asking us to do is multiply each supplier's distance from a given factory by the number of loads it puts out, and then add the sums together. Got those distances handy? Good. For factory A, that means that the distance from supplier 1 is 10, times the 200 loads that it gives. That means that we have 2,000 right there. Now, add that to the distance from supplier 2 (which was 18.03) times the 100 loads it gives, meaning you're adding 2,000 to 1,803. You end up with load distance score of 3,803 for factory A.
Now, let's look at factory B. First, the loads times distance for supplier 1 is 22.36 times 200, or 4,472. The loads times distance for supplier 2 is 3,640. Add the two together, and you get 8,072 as the load distance score for factory B.
Now, remember that shorter distances are better for business, as it means lower transportation costs. Since 3,803 is lower than 8,072, that means that factory site A is the better choice.
Lesson Summary
In this lesson we learned how to use the load-distance technique to compare distances to suppliers relative to the number of shipments needed from them. We used the straight line distance formula to find the distance from each supplier to each factory. Remember that the straight line distance formula is the square root of the sum of the difference between the x values of two sites, squared, plus the difference between the y values of two sites, squared. Then, we multiplied the distances by the number of loads, adding each value up to determine the load distance score of each factory. A lower score means a better, and cheaper, factory site.
