The American Baseball League consists of 14 professional baseball teams organized into 3 divisions: The West Division with Seattle, Oakland, California and Texas; the Central Division with Kansas City, Minnesota, Chicago, Milwaukee, and Cleveland; and the East Division with Detroit, Toronto, Baltimore, New York, and Boston.
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 of 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. BOS MIN MIN MIN MIN Home Team Series Date SEA OAK CAL TEX KC MIN CHI MKE DET CLE TOR BALNY Mon CAL BOS SEA TORONY CHI 1 Tues CAL BOS SEA TOR. NY KC CHE Wed CAL BOS SEA TOR. NY KCS CHI Thuri. DET MKEKC CHT TOR 2 Fri DET NY MKE KC CHI TOR Sat DET NY MKE KC CHI TOR Sun DET NY(2) MKE CHI TOR Mon. MKE NY BOS MIN Tues. MKE DET NY CHI" BOS CLE MIN Wed. MKE DET NY" CHI BOS CLE MIN Thurs MKE DET NY CHI CLE Fri NY MKE DET BAL CLE" KC BOS 1 Sat NY MKE DET BAL CLE. KC BOS Sun NY MKE DET BAL CLE KC BOS Mon TEX CLE BOS 5 Toes TEX BOSCLE CAL SEA BAL OAK Wed TEX BOS CLE" CAL SEA" BAL OAK Thurs TEX" BOS CAL SEA BAL OAK Denotes night game or early evening start. (2)Denotes doubleheader (Two games in one day. 3 Home Team Series SEA OAK CAL TEX KC MIN CHI MKE DET CLE TOR BAL NYBOS CAD BOS SEA DET NY MKE KC TOR NY KC CHP MKE DET NYCH BOS TOR NY MKE DET BAL CLEE MIN CLES KC BOS TEX BOSCLE CAL SEA BAL For the fourth series, umpire crew l is assigned to the Boston at Toronto series MINI MKE DET TOR NY KC 1825 CHI 2007 1694 2124 1939 2079 MIN 1399 1589 1536 853 2421 2586 1498 Crew From SEA(7) OAK(3) CAL(2) TEX(6) MIN(5) CHI(4) TOR(1) 1845 2125 2035 1756 1979 2475 2286 2175 1186 780 798 843 982 1363 506 394 403 1383 0 334 297 528 1028 740 334 0 74 235 430 968 897 497 583 206 0 366 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 of 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. BOS MIN MIN MIN MIN Home Team Series Date SEA OAK CAL TEX KC MIN CHI MKE DET CLE TOR BALNY Mon CAL BOS SEA TORONY CHI 1 Tues CAL BOS SEA TOR. NY KC CHE Wed CAL BOS SEA TOR. NY KCS CHI Thuri. DET MKEKC CHT TOR 2 Fri DET NY MKE KC CHI TOR Sat DET NY MKE KC CHI TOR Sun DET NY(2) MKE CHI TOR Mon. MKE NY BOS MIN Tues. MKE DET NY CHI" BOS CLE MIN Wed. MKE DET NY" CHI BOS CLE MIN Thurs MKE DET NY CHI CLE Fri NY MKE DET BAL CLE" KC BOS 1 Sat NY MKE DET BAL CLE. KC BOS Sun NY MKE DET BAL CLE KC BOS Mon TEX CLE BOS 5 Toes TEX BOSCLE CAL SEA BAL OAK Wed TEX BOS CLE" CAL SEA" BAL OAK Thurs TEX" BOS CAL SEA BAL OAK Denotes night game or early evening start. (2)Denotes doubleheader (Two games in one day. 3 Home Team Series SEA OAK CAL TEX KC MIN CHI MKE DET CLE TOR BAL NYBOS CAD BOS SEA DET NY MKE KC TOR NY KC CHP MKE DET NYCH BOS TOR NY MKE DET BAL CLEE MIN CLES KC BOS TEX BOSCLE CAL SEA BAL For the fourth series, umpire crew l is assigned to the Boston at Toronto series MINI MKE DET TOR NY KC 1825 CHI 2007 1694 2124 1939 2079 MIN 1399 1589 1536 853 2421 2586 1498 Crew From SEA(7) OAK(3) CAL(2) TEX(6) MIN(5) CHI(4) TOR(1) 1845 2125 2035 1756 1979 2475 2286 2175 1186 780 798 843 982 1363 506 394 403 1383 0 334 297 528 1028 740 334 0 74 235 430 968 897 497 583 206 0 366
