Each year, there are many complaints about how the NCAA Mens Basketball Committee seeds and schedules teams in the 68-team single elimination tournament to determine the National Champion. (Although there were not many complaints about the tournament in 2020!). It is inevitable that somebody is unhappy. We will approach a portion of the task by using our modeling skills to generate an alternative schedule that may or may not differ from the actual especially given that this year, the entire tournament takes place in one location. You have been asked to create the first phase of a LP model that will assign teams to regions using 2021 data. You will be using the 24 teams that are the #1 thru #6 seeds, and all 4 regions. Regions are in quotes because instead of being affiliated with a physical location, there are going to be affiliated with a #1 seed in our case, we will have the Gonzaga Region (West), the Baylor region (South), the Illinois Region (Midwest) and the Michigan Region (East). The criterion used by your model for scheduling teams will be minimizing the sum of distance between the team location and the region location. The region location used is the campus location of the assigned #1 seed. Distance data is provided on a separate spreadsheet.

Historically, models developed have shown ways that the selection committee could have made better decisions in assigning teams to regions. We really dont have an analogous schedule to compare it against (as the committee is using only the dubiously created s-curves), but we will have fun with it anyway. Requirements for assigning teams to regions:1) Each of the four regions will have exactly one #1 seed assigned, exactly one #2 seed assigned, exactly one #3 assigned, exactly one #4 assigned, exactly one #5 assigned and exactly one #6 assigned. The #1 seed assigned is given, and drives the entire selection process. 2) Teams from the same conference cannot be assigned to the same region (unless there are more than 4 teams from the same conference). Conferences are shown on the data file. (Note that the conference affiliations of the #1 seeds DO MATTER.) Conference affiliations are simply an attribute of the team (think Knapsack problem). There are 6 BIG12 teams and 5 BIG10 teams. Assign them using the following two rules: Every region must have at least 1 BIG12 (BIG 10) team, but no region can have more than 2 BIG12 (BIG10) teams. Hint: If there is only 1 team from a conference, you obviously dont have to worry about constraining them. This is true for Houston and for SDSU. 3) There are 10 teams that have a Q factor they are either marquee teams or teams that have captured the interest of the basketball fanbase because of some unique aspect of the team (Many of the Q teams have won national titles, and then there are the small underdog schools like Gonzaga and my own Creighton BlueJays). Schedule teams to regions such that each region has at least 2 teams with a Q rating. Dont worry about the value. And we do consider the Q factor (if they exist) of the #1 seeds. THE MODEL - Implement an appropriate linear programming model that assigns the 24 (or really 20, since the #1 seeds are preassigned) teams to Regions, minimizing the sum of overall distances subject to the items listed above (seeds, conference requirements, and Q factor). Suggestion: Attack modularly. Summarize the team assignments in a table. It shouldnt be too hard to translate the model solution to team names.

"0" 5 2 CONF SEED WCC B12 B10 B10 1 1 1 1 Gonzaga Baylor Illinois Michigan 2500 1120 320 180 "Q" CONF Seed 2 B10 2 B10 2 785 415 575 SEC 2 2025 2360 2460 645 685 700 AAC 2 230 1075 1330 B12 3 1875 510 525 755 1 SEC 3 2415 425 810 975 N B12 3 2385 195 1165 1390 B12 3 565 185 1200 280 2 745 190 Ohio State lowa Alabama Houston KU Arkansas Texas West Virginia OSU Purdue Virginia Florida State Villanova Creighton Colorado Tennessee Texas Tech BYU 1025 275 950 4 4 4 4 5 1 645 1185 5 3 B12 B10 ACC ACC BEAST BEAST P12 SEC B12 WCC MTNW P12 2480 2075 2360 2670 3135 2945 1825 1370 2575 1805 720 5 1305 1180 1605 715 845 740 375 770 480 1020 5 5 6 6 200 1195 590 745 1305 555 1260 1600 2325 2540 445 925 1325 1145 6 SDSU 1275 2105 1300 1200 6 USC 1445 2190 "0" 5 2 CONF SEED WCC B12 B10 B10 1 1 1 1 Gonzaga Baylor Illinois Michigan 2500 1120 320 180 "Q" CONF Seed 2 B10 2 B10 2 785 415 575 SEC 2 2025 2360 2460 645 685 700 AAC 2 230 1075 1330 B12 3 1875 510 525 755 1 SEC 3 2415 425 810 975 N B12 3 2385 195 1165 1390 B12 3 565 185 1200 280 2 745 190 Ohio State lowa Alabama Houston KU Arkansas Texas West Virginia OSU Purdue Virginia Florida State Villanova Creighton Colorado Tennessee Texas Tech BYU 1025 275 950 4 4 4 4 5 1 645 1185 5 3 B12 B10 ACC ACC BEAST BEAST P12 SEC B12 WCC MTNW P12 2480 2075 2360 2670 3135 2945 1825 1370 2575 1805 720 5 1305 1180 1605 715 845 740 375 770 480 1020 5 5 6 6 200 1195 590 745 1305 555 1260 1600 2325 2540 445 925 1325 1145 6 SDSU 1275 2105 1300 1200 6 USC 1445 2190