Note: We should use the Microsoft Excel Solver to solve this case study after assigning the Umpire Crews to the series based on the different data in the tables including the distances on third table.

In addition to assigning schedules for each team, the American League must determine the best way to assign the umpire crews to various games played throughout the league. Umpire crews are assigned to specific home-team cities for the 2-, 3- and 4-game series in that city but are not assigned on an individual game basis double headers count as one game in assigning the crews. There are seven different crews. Several considerations are important in making the umpire crew assignments. Because of the amount of travel required, airline costs can be substantial. From a cost point of view, assignments with minimum travel distances are desirable. However, there should be a balance such that each crew works approximately the same number of games with each team in each city. These two goals are in conflict. There are also several other requirements: 1. A crew cannot travel from city A to city B if the last game in city A is a night game and the first game in city B is an afternoon game on the next day. 2. A crew cannot travel from a West Coast location (Seattle, Oakland, California) to Chicago or any Eastern Division City without a day off. 3. Because of flight scheduling difficulties, a crew traveling into or out of Toronto must have a day off unless coming from or going to New York, Boston, Detroit or Cleveland. 4. Any crew traveling from a night game in Seattle, Oakland, or California cannot be assigned to Kansas City or Texas for a game on the next day. 5. No crew should be assigned to the same team for more than 2 series in a row. Umpire crews have already been assigned for the first 4 series of the 5-series schedule (see table). The number next to each team identification indicates the umpire crew assigned for that pairing The second table shows the distances from the cities where the 4th series is being played to the cities where the 5th series is being played. There are some other issues league management would like considered: over the past nine series, crew 4 has umpired three series with Kansas City and three with Milwaukee. Crew 5 has not been assigned to any games with New York, Toronto, or Detroit over the past month. Managerial Report: Prepare a written (typed) recommendation to league management concerning the assignment of umpire crews to the fifth series that will minimize the distance traveled. Include supporting documents: Solver solution and sensitivity analysis. Comment on any significant effects that would occur due to shadow prices and reduced costs. Home Team CHI MKE CAL KC MIN CLE TOR NY BOS OAK CAL* CAL* CAL SEA SEA SEA TOR* TOR* TOR* DET NY* NY* NY TEX BOS* BOS* BOS KC* KC KC* KC KC* KC CHI CHI* CHI CHI BAL CHI* CHI* CHI TOR* TOR* TOR NY* NY NY(2) MIN* MIN" MIN* MIN* TOR MIN* Schedule Series Day SEA Mon. 1 Tue Wed Thu DET* Fri DET 2 Sat DET Sun DET Mon MKE* Tue MKE* 3 Wed MKE* Thu MKE Fri NY* 4 4 Sat NY* Sun NY* Mon Tue 5 Wed Thu * Denotes night games MKE MKE MKE MKE NY NY* NY* NY DET DET* BOS* BOS* BOS* MIN* MIN* DET* DET* DET MKE MKE MKE CHI* CHI" CHI* BAL BAL* BAL CLE* CLE* CLE CLE CLE CLE* BOS BOS BOS BOS* BAL* BAL* BAL* KC* KC* KC CLE* CLE* CLE* DET TEX* TEX* TEX TEX* BOSS BOS BOS CAL* CAL* CAL SEA SEA* SEA* OAK* OAK* OAK* (2) Doubleheader Umpire Crew Assignments for the First Four Series SEA CAL KC CLE Home Team CHI MKE TOR TOR NY Series 1 BOS MIN SEA DET NY KCE OAK CALS NY DET? TEX BOS KCS CHIC BAL CHI TOR MIN 2 CHIC MIN 3 DET MKE? NY MKE NY? DET BOS 4 MKE BAL CLE BOS KC CLE BOS BAL 5 TEX CLE CAL SEA OAK Example: BOS For the 4th series, umpire crew 1 is assigned to the Boston at Toronto series. Ciri NY TOR 2124 Cost Matrix For Umpire Crew Assignments (Series 5) Crew From KC MIN CHI MKE SEA(7) 1825 1399 2007 1694 OAK(3) 1498 1589 2125 1845 CAL(2) 1363 1536 2035 1756 TEX(6) 506 853 798 843 MIN(5) 394 0 334 297 CHI(4) 403 334 0 74 TOR(1) 968 897 497 583 DET 1939 2079 1979 982 2286 2175 1186 780 430 0 2421 2586 2475 1383 1028 740 366 528 235 206