Locating DCs for Toy Stores $($Adapted from exercise $8\mathrm{.}1$ in Synder & Shen, $2020)$ A

toy store chain operates $8$ retail stores in Texas. The company currently ships all products from a

central distribution center $($DC$)$ to the stores, but it is considering closing the central DC and instead

operating multiple regional DCs that serve the retail stores. It will use the CFLP to determine where

to locate DCs$.$ Planners at the company have identified $5$ potential cities in which regional DCs may

be located. The file toy$-$stores.xlsx lists the longitude and latitude for all of the locations $($stores and

DCs$),$ as well as the annual demand $($measured in pallets$)$ at each store and the fixed annual location

cost at each potential DC location. Using optimization software of your choice, implement the CFLP

model and solve it using the data provided. Assume that transportation from DCs to stores costs $$1$

per mile, as measured by the great circle distance between the two locations. Report the optimal cities

to locate DCs in$,$ the assignment of stores to the opened DCs$,$ and the optimal

City Lon Lat Demand $($pallets$)$

Amarillo $101\mathrm{.}818835\mathrm{.}20355893$

Austin $97\mathrm{.}7506630\mathrm{.}3049318502$

Dallas $96\mathrm{.}7674732\mathrm{.}7931536936$

Houston $95\mathrm{.}3873329\mathrm{.}7680563937$

Irving $96\mathrm{.}9693432\mathrm{.}857696235$

Laredo $99\mathrm{.}486627\mathrm{.}53432916$

Pasadena $95\mathrm{.}1520229\mathrm{.}66064149$

San Antonio $98\mathrm{.}5053629\mathrm{.}4576532464$

City Lon Lat Fixed Cost Capacity

Amarillo $101\mathrm{.}818835\mathrm{.}20355207472040000$

Austin $97\mathrm{.}7506630\mathrm{.}304933444378050000$

El Paso $106\mathrm{.}437531\mathrm{.}849254161972033000$

Houston $95\mathrm{.}3873329\mathrm{.}768057411680100000$

Laredo $99\mathrm{.}486627\mathrm{.}53432587614027000$