You decide to estimate the distance of distributing the backpacks 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 an 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. City Weights
Chihuahua 896368
Ciudad Victoria 311696
Durango 502392
Mexico City 19765592
Monterrey 4375360
Morelia 759880
Oaxaca 629200
Puebla 2835272
San Luis Potosi 1007688
Villahermosa 619520
Chi Ciu Dur Mex Mon Mor Oax Pue San Vil
Chi 5 719 503 1158 590 1069 1458 1250 913 1575
Mex 1158 475 698 10 643 188 310 127 253 545
Mon 590 203 376 643 5 626 911 706 393 990
Pue 1250 519 808 127 706 313 208 5 338 417
San 913 249 482 253 393 258 545 338 5 704
After thinking about it for a while, your roommate 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, 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 backpacks 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 the 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.
You make some phone calls to carriers in Mexico, and you calculate an average transportation cost of $1 per distance unit per 968 backpacks (e. g. you would pay $100 to move 968 backpacks 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 previous parts.
Assuming that these values are correct and applicable throughout the country, how many distribution centers would you recommend opening?
Where would you recommend that they open these DCs, in order to minimize the total cost (fixed + transportation)?
A) Chihuahua
B) Mexico City
C) Monterrey
D) Puebla
E) San Luis Potosi