# LOG201: Your best friend Sarah knows that you learned how to calculate, for a given group of cities with their Cartesian coordinates: Supply Chain Management Home Work, SUSS

Question 3

Your best friend Sarah knows that you learned how to calculate, for a given group of cities with their Cartesian coordinates, a location for a distribution center that would minimize the distance. Thus, she asks you to calculate the coordinates for a distribution center, so that she can minimize its distance to ten cities in Mexico.”

You found a map of Mexico online, and after asking Sarah for a list of the ten major cities in Mexico, you decide to use an improvised grid to assign horizontal and vertical coordinates to the cities. These coordinates, shown in the table below, use as the origin a point in the top left corner of the map. You tried to make these units as close to kilometers as possible. However, you prefer to think of them as relative coordinates on an arbitrary Euclidean grid.

“No”, she says, “but let’s assume they all have equal weight, a weight of 1 for example”.

Part 2

Curious about Sarah’s request, you ask her what she is working on. She shares with you that together with her co-workers she is volunteering for an organization that will soon distribute notebooks to every school-aged child throughout Mexico. You suggest that solving this problem with equal weights is not good enough, since some cities surely have more schoolchildren than others. A quick online search provides you with approximate values for the populations of the different areas where the cities are located. Using these population values, you propose to your friend to use weight values, as listed in the table below.

Using these weights, solve this as a continuous, demand-weighted distance-minimizing, location (or Weber) problem.

Part 3

You decide to estimate the distance of distributing the notebooks from a DC in one of a set of selected cities to the school children in another city. Given that you only need a quick and dirty estimate, you assume a Euclidean space and a circuity factor of 1.25, which gives you the distances in the table below (where cities are identified using the first three letters in their name). Regardless of which city the DC is located in, there will also be transportation from the DC to the school children within that same city. For distances inside each city, you assume 5 distance units, except for Mexico City, for which you use 10 distance units since it is a larger city.

The distances between the cities are given in your arbitrary grid units, which may or may not be kilometers.

After thinking about it for a while, your friend tells you that they may want to open two DCs. She wants these DCs to be located in two of the five candidate cities (Chihuahua, Mexico City, Monterrey, Puebla, and San Luis Potosi), but they should not be located in the same city. The plan would be to distribute all the hundreds of thousands of notebooks through these two DCs, using trucks. Let’s assume that the cost of opening and operating such a DC in any of these cities would be about the same and that the cost of outbound transportation from the DC to the cities is about the same on a per unit per mile basis.

In which two cities would you recommend that they open these two DCs, in order to minimize the outbound transportation costs? Select the answer options that apply. Use the same demand weights as in Part 2. (Hint: If you are puzzled by the fact that we are asking for this without providing any costs for DCS or trucks, you should start playing with different values and see how the model behaves.)

Part 4

After some market research on carriers in Mexico, you calculate an average transportation cost of \$1 per distance unit per 1031 notebooks (e.g. you would pay \$100 to move 1031 notebooks to 100 distance units). You also estimate that the fixed cost of operating each distribution center in one of these cities is \$464,000 dollars per year. The yearly demands in the cities are approximated by the weights used in the previous parts.

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