#### Document Type

Paper

#### Publication Date

11-13-2016

#### Advisor(s)

Steve Condie, Illinois Mathematics and Science Academy

#### Description

In the modern business world, maximizing profits is the highest priority. Businesses, especially small ones, should try to save money whenever possible. Along with cutting wages, removing competition, and increasing advertising and production, efficiency of company sites can save money. For example, a cheap 50 ft. by 100 ft. warehouse costs $35,000, but when coupled with the costs of maintenance and wages, increasing the number of warehouses significantly increases costs.

Clearly, warehouses are expensive, making it necessary to place them in optimal locations. In this problem, we attempt to reduce the number of warehouses while shipping to the entirety of the continental US via one-day transit.

In order to solve the problem, we used transit-time maps from www.ups.com/maps since the problem specifies one-day transit ground shipping via the United Parcel Service. The Python programs we created retrieved maps as image files from ups.com and allowed us to overlay combinations of ZIP codes and analyze the pixels of the resulting images. The only thing left to do was choose the best combinations.

Since covering 100% of the continental United States is not cost efficient, we created a program that optimizes the one-day transit coverage for a given number of warehouses using genetic algorithms. This program allowed us to not only calculate the minimum number of warehouses needed for 100% coverage, but also find the best coverage given a variable number of warehouses. We in turn used the data we collected in order to find the optimal locations to build warehouses.

In order to save the most amount of money, state clothing and sales tax rates were also taken into consideration when we chose warehouse locations. We modified the original program to weigh both sales and clothing tax rates and find optimal warehouse locations.

#### Recommended Citation

Kumar, Suchet '19; Vadakumchery, Tommy '19; Kim, Nathan '19; and Cao, Bert '19, "2016: HiMCM International Mathematics Modeling Contest: National Outstanding Paper" (2016). *Distinguished Student Work*. 5.

https://digitalcommons.imsa.edu/math_sw/5

## Comments

The team was awarded National Outstanding Paper at the HiMCM International Mathematics Modeling Contest.

Of the 840 teams entered, only 9 teams achieved this designation.