Help with Optimization and Decision Support Modeling for Business project

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OSCM571_ProjectExample_FinalModel.xlsx
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Season & Player Data

Season Data - SportsRadar.com Application Programming Interface
Home_ID Home_Team Home_FGM Home_FGA Home_FGP Home_3PM Home_3PA Home_3PP Home_2PM Home_2PA Home_2PP Home_Blocked_Att Home_FTM Home_FTA Home_FTP Home_OR Home_DR Home_R Home_A Home_T Home_Stl Home_Blocks Home_ATR Home_PF Home_FBPts Home_SCPts Home_POT Home_FFoul Home_TFoul Home_PaintPts
9b166a3f-e64b-4825-bb6b-92c6f0418263 Arizona 30.44 61.38 0.4959270121 7.76 21.94 0.353691887 22.68 39.44 0.5750507099 2.79 15.91 21.56 0.7379406308 10.44 28.35 38.79 19.9 13.18 6.71 5.71 1.5098634294 16.47 15.03 12.35 15.12 0.03 0.2058823529 42.65
Per minute 0.1522 0.3069 0.0024796351 0.0388 0.1097 0.0017684594 0.1134 0.1972 0.0028752535 0.01395 0.07955 0.1078 0.0036897032 0.0522 0.14175 0.19395 0.0995 0.0659 0.03355 0.02855 0.0075493171 0.08235 0.07515 0.06175 0.0756 0.00015 0.0010294118 0.21325
Advanced Stats - Not Used in Model PLAYER TOTALS
Player Games Games Started Minutes Played Player Efficiency Rating True Shooting % Effective Field Goal % 3 Point Attempt Rate Free Throw Attempt Rate Points Produced Offensive Rebound % Defensive Rebound % Total Rebound Percentage% Assist % Steal % Block % Turnover % Usage Percentage % Offensive Win Share Defensive Win Shares Win Shares Win Shares per 40 minutes FG FGA FG% 2P 2PA 2P% 3P 3PA 3P% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS Box Plus/Minus
Adama Bal 23 0 104 12.1 0.608 0.63 0.63 0.074 32 2.3 7.4 5.1 15.4 1.6 0.9 20 15.9 0.1 0.2 0.3 0.12 13 27 0.481 5 10 0.5 8 17 0.471 0 2 0 2 8 10 10 3 1 7 10 34 3.6
Azuolas Tubelis 36 35 885 24.4 0.578 0.554 0.105 0.399 476 9.5 16.8 13.6 17.3 2.4 2.7 15.1 27.3 2.6 2 4.6 0.21 196 363 0.54 186 325 0.572 10 38 0.263 97 145 0.669 70 154 224 81 39 25 77 69 499 8
Bennedict Mathurin 37 37 1201 21.1 0.576 0.536 0.465 0.368 600 5.1 12.6 9.3 13.8 1.6 0.8 10.4 25.1 4 2.2 6.2 0.205 218 484 0.45 135 259 0.521 83 225 0.369 136 178 0.764 51 157 208 94 36 10 66 68 655 8
Christian Koloko 37 37 941 28 0.661 0.635 0.01 0.472 437 12.1 18 15.4 9.8 1.6 10.3 14.3 20.7 3.4 2.4 5.9 0.25 183 288 0.635 183 285 0.642 0 3 0 100 136 0.735 95 175 270 51 28 102 59 103 466 10.5
Dalen Terry 37 37 1029 16.9 0.584 0.563 0.336 0.231 343 5 12.8 9.3 22.1 2.5 1.1 16.7 14.1 2.4 2.1 4.5 0.176 115 229 0.502 87 152 0.572 28 77 0.364 39 53 0.736 43 136 179 145 46 12 51 84 297 8
Grant Weitman 16 0 26 -1 0.333 0.333 0.667 0 2 4.6 7.4 6.2 0 0 0 25 7.3 0 0 0 0.016 1 3 0.333 1 1 1 0 2 0 0 0 1 2 3 0 0 0 1 3 2 -5.8
Jordan Mains 15 0 30 16.6 0.508 0.429 0.429 0.857 11 16 25.8 21.4 0 3.7 0 16.9 18.7 0 0.1 0.1 0.172 3 7 0.429 3 4 0.75 0 3 0 4 6 0.667 4 8 12 0 2 0 2 4 10 0.6
Justin Kier 37 6 743 13.8 0.564 0.53 0.483 0.234 253 1.9 13.4 8.3 17.7 1.8 0.1 18.3 17.4 1.2 1.4 2.6 0.14 89 201 0.443 54 104 0.519 35 97 0.361 39 47 0.83 12 103 115 83 24 1 50 48 252 4.6
Kerr Kriisa 33 31 975 11.7 0.516 0.488 0.829 0.171 357 2.1 6.6 4.6 24.6 1.1 0.3 18.8 18.6 1.6 1.3 2.9 0.119 100 287 0.348 20 49 0.408 80 238 0.336 40 49 0.816 17 67 84 155 19 3 72 59 320 3.7
Oumar Ballo 37 0 564 24.1 0.649 0.622 0 0.655 239 12.4 18 15.5 6.3 1.3 7.4 14.5 19.1 1.8 1.3 3.2 0.224 92 148 0.622 92 148 0.622 0 0 68 97 0.701 58 105 163 21 13 44 33 60 252 7.7
Pelle Larsson 37 2 767 14.4 0.617 0.569 0.506 0.417 265 4.7 12.2 8.9 13.5 2 1 20.9 16.9 1.5 1.5 2.9 0.153 86 180 0.478 53 89 0.596 33 91 0.363 61 75 0.813 30 97 127 66 28 8 57 93 266 5
Shane Nowell 19 0 66 5.5 0.396 0.361 0.278 0.111 16 0 21.9 12.2 13.8 3.3 2.9 29.7 19.4 -0.1 0.2 0.1 0.036 6 18 0.333 5 13 0.385 1 5 0.2 2 2 1 0 15 15 6 4 2 8 9 15 -3
Tautvilas Tubelis 14 0 24 -10.2 0.268 0.286 0.429 0.143 3 0 0 0 0 0 0 28.6 20.7 -0.1 0 -0.1 -0.151 2 7 0.286 2 4 0.5 0 3 0 0 1 0 0 0 0 0 0 0 3 1 4 -16.8
STAT PER MINUTE PLAYED THESE STATS ARE ON A PER GAME BASIS
Player Games Games Started Minutes Played FG FGA FG% 2P 2PA 2P% 3P 3PA 3P% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS Box Plus/Minus Offensive Box Plus/Minus Defensive Box Plus/Minus
Adama Bal 23 0 104 0.125 0.2596153846 0.004625 0.0480769231 0.0961538462 0.0048076923 0.0769230769 0.1634615385 0.0045288462 0 0.0192307692 0 0.0192307692 0.0769230769 0.0961538462 0.0961538462 0.0288461538 0.0096153846 0.0673076923 0.0961538462 0.3269230769 3.6 1.6 2
Azuolas Tubelis 36 35 885 0.2214689266 0.4101694915 0.0006101695 0.2101694915 0.3672316384 0.0006463277 0.011299435 0.0429378531 0.0002971751 0.1096045198 0.1638418079 0.0007559322 0.0790960452 0.1740112994 0.2531073446 0.0915254237 0.0440677966 0.0282485876 0.0870056497 0.0779661017 0.5638418079 8 4.8 3.2
Bennedict Mathurin 37 37 1201 0.1815154038 0.4029975021 0.0003746878 0.1124063281 0.215653622 0.0004338052 0.0691090758 0.1873438801 0.000307244 0.1132389675 0.1482098251 0.0006361366 0.0424646128 0.1307243963 0.1731890092 0.0782681099 0.0299750208 0.0083263947 0.0549542048 0.0566194838 0.545378851 8 6.1 1.9
Christian Koloko 37 37 941 0.1944739639 0.3060573858 0.000674814 0.1944739639 0.302869288 0.0006822529 0 0.0031880978 0 0.1062699256 0.1445270988 0.000781084 0.1009564293 0.1859723698 0.2869287991 0.0541976621 0.0297555792 0.1083953241 0.0626992561 0.1094580234 0.4952178533 10.5 5.2 5.3
Dalen Terry 37 37 1029 0.1117589893 0.2225461613 0.0004878523 0.084548105 0.1477162293 0.0005558795 0.0272108844 0.074829932 0.0003537415 0.0379008746 0.0515063168 0.0007152575 0.0417881438 0.1321671526 0.1739552964 0.1409135083 0.0447035957 0.0116618076 0.0495626822 0.0816326531 0.2886297376 8 3.5 4.5
Grant Weitman 16 0 26 0.0384615385 0.1153846154 0.0128076923 0.0384615385 0.0384615385 0.0384615385 0 0.0769230769 0 0 0 0 0.0384615385 0.0769230769 0.1153846154 0 0 0 0.0384615385 0.1153846154 0.0769230769 -5.8 -6.1 0.3
Jordan Mains 15 0 30 0.1 0.2333333333 0.0143 0.1 0.1333333333 0.025 0 0.1 0 0.1333333333 0.2 0.0222333333 0.1333333333 0.2666666667 0.4 0 0.0666666667 0 0.0666666667 0.1333333333 0.3333333333 0.6 -1.4 1.9
Justin Kier 37 6 743 0.1197846568 0.2705248991 0.0005962315 0.0726783311 0.1399730821 0.0006985195 0.0471063257 0.130551817 0.0004858681 0.0524899058 0.0632570659 0.0011170929 0.0161507402 0.1386271871 0.1547779273 0.1117092867 0.0323014805 0.001345895 0.067294751 0.064602961 0.3391655451 4.6 1.9 2.7
Kerr Kriisa 33 31 975 0.1025641026 0.2943589744 0.0003569231 0.0205128205 0.0502564103 0.0004184615 0.0820512821 0.2441025641 0.0003446154 0.041025641 0.0502564103 0.0008369231 0.0174358974 0.0687179487 0.0861538462 0.158974359 0.0194871795 0.0030769231 0.0738461538 0.0605128205 0.3282051282 3.7 2.7 0.9
Oumar Ballo 37 0 564 0.1631205674 0.2624113475 0.0011028369 0.1631205674 0.2624113475 0.0011028369 0 0 0 0.1205673759 0.1719858156 0.0012429078 0.1028368794 0.1861702128 0.2890070922 0.0372340426 0.0230496454 0.0780141844 0.0585106383 0.1063829787 0.4468085106 7.7 4 3.8
Pelle Larsson 37 2 767 0.112125163 0.2346805737 0.0006232073 0.0691003911 0.1160365059 0.0007770535 0.0430247718 0.1186440678 0.0004732725 0.0795306389 0.0977835724 0.0010599739 0.0391134289 0.1264667536 0.1655801825 0.0860495437 0.036505867 0.0104302477 0.074315515 0.1212516297 0.3468057366 5 1.7 3.3
Shane Nowell 19 0 66 0.0909090909 0.2727272727 0.0050454545 0.0757575758 0.196969697 0.0058333333 0.0151515152 0.0757575758 0.003030303 0.0303030303 0.0303030303 0.0151515152 0 0.2272727273 0.2272727273 0.0909090909 0.0606060606 0.0303030303 0.1212121212 0.1363636364 0.2272727273 -3 -7.4 4.4
Tautvilas Tubelis 14 0 24 0.0833333333 0.2916666667 0.0119166667 0.0833333333 0.1666666667 0.0208333333 0 0.125 0 0 0.0416666667 0 0 0 0 0 0 0 0.125 0.0416666667 0.1666666667 -16.8 -12 -4.8
Data From 2021-22 Arizona Wildcats Roster and Stats | College Basketball at Sports-Reference.com
STAT PER MINUTE PLAYED Without Formulas - Ref Error was being thrown
Player Games Games Started Minutes Played FG FGA FG% 2P 2PA 2P% 3P 3PA 3P% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS Box Plus/Minus Offensive Box Plus/Minus Defensive Box Plus/Minus
Adama Bal 23 0 104 0.125 0.2596153846 0.004625 0.0480769231 0.0961538462 0.0048076923 0.0769230769 0.1634615385 0.0045288462 0 0.0192307692 0 0.0192307692 0.0769230769 0.0961538462 0.0961538462 0.0288461538 0.0096153846 0.0673076923 0.0961538462 0.3269230769 3.6 1.6 2
Azuolas Tubelis 36 35 885 0.2214689266 0.4101694915 0.0006101695 0.2101694915 0.3672316384 0.0006463277 0.011299435 0.0429378531 0.0002971751 0.1096045198 0.1638418079 0.0007559322 0.0790960452 0.1740112994 0.2531073446 0.0915254237 0.0440677966 0.0282485876 0.0870056497 0.0779661017 0.5638418079 8 4.8 3.2
Bennedict Mathurin 37 37 1201 0.1815154038 0.4029975021 0.0003746878 0.1124063281 0.215653622 0.0004338052 0.0691090758 0.1873438801 0.000307244 0.1132389675 0.1482098251 0.0006361366 0.0424646128 0.1307243963 0.1731890092 0.0782681099 0.0299750208 0.0083263947 0.0549542048 0.0566194838 0.545378851 8 6.1 1.9
Christian Koloko 37 37 941 0.1944739639 0.3060573858 0.000674814 0.1944739639 0.302869288 0.0006822529 0 0.0031880978 0 0.1062699256 0.1445270988 0.000781084 0.1009564293 0.1859723698 0.2869287991 0.0541976621 0.0297555792 0.1083953241 0.0626992561 0.1094580234 0.4952178533 10.5 5.2 5.3
Dalen Terry 37 37 1029 0.1117589893 0.2225461613 0.0004878523 0.084548105 0.1477162293 0.0005558795 0.0272108844 0.074829932 0.0003537415 0.0379008746 0.0515063168 0.0007152575 0.0417881438 0.1321671526 0.1739552964 0.1409135083 0.0447035957 0.0116618076 0.0495626822 0.0816326531 0.2886297376 8 3.5 4.5
Grant Weitman 16 0 26 0.0384615385 0.1153846154 0.0128076923 0.0384615385 0.0384615385 0.0384615385 0 0.0769230769 0 0 0 0 0.0384615385 0.0769230769 0.1153846154 0 0 0 0.0384615385 0.1153846154 0.0769230769 -5.8 -6.1 0.3
Jordan Mains 15 0 30 0.1 0.2333333333 0.0143 0.1 0.1333333333 0.025 0 0.1 0 0.1333333333 0.2 0.0222333333 0.1333333333 0.2666666667 0.4 0 0.0666666667 0 0.0666666667 0.1333333333 0.3333333333 0.6 -1.4 1.9
Justin Kier 37 6 743 0.1197846568 0.2705248991 0.0005962315 0.0726783311 0.1399730821 0.0006985195 0.0471063257 0.130551817 0.0004858681 0.0524899058 0.0632570659 0.0011170929 0.0161507402 0.1386271871 0.1547779273 0.1117092867 0.0323014805 0.001345895 0.067294751 0.064602961 0.3391655451 4.6 1.9 2.7
Kerr Kriisa 33 31 975 0.1025641026 0.2943589744 0.0003569231 0.0205128205 0.0502564103 0.0004184615 0.0820512821 0.2441025641 0.0003446154 0.041025641 0.0502564103 0.0008369231 0.0174358974 0.0687179487 0.0861538462 0.158974359 0.0194871795 0.0030769231 0.0738461538 0.0605128205 0.3282051282 3.7 2.7 0.9
Oumar Ballo 37 0 564 0.1631205674 0.2624113475 0.0011028369 0.1631205674 0.2624113475 0.0011028369 0 0 0 0.1205673759 0.1719858156 0.0012429078 0.1028368794 0.1861702128 0.2890070922 0.0372340426 0.0230496454 0.0780141844 0.0585106383 0.1063829787 0.4468085106 7.7 4 3.8
Pelle Larsson 37 2 767 0.112125163 0.2346805737 0.0006232073 0.0691003911 0.1160365059 0.0007770535 0.0430247718 0.1186440678 0.0004732725 0.0795306389 0.0977835724 0.0010599739 0.0391134289 0.1264667536 0.1655801825 0.0860495437 0.036505867 0.0104302477 0.074315515 0.1212516297 0.3468057366 5 1.7 3.3
Shane Nowell 19 0 66 0.0909090909 0.2727272727 0.0050454545 0.0757575758 0.196969697 0.0058333333 0.0151515152 0.0757575758 0.003030303 0.0303030303 0.0303030303 0.0151515152 0 0.2272727273 0.2272727273 0.0909090909 0.0606060606 0.0303030303 0.1212121212 0.1363636364 0.2272727273 -3 -7.4 4.4
Tautvilas Tubelis 14 0 24 0.0833333333 0.2916666667 0.0119166667 0.0833333333 0.1666666667 0.0208333333 0 0.125 0 0 0.0416666667 0 0 0 0 0 0 0 0.125 0.0416666667 0.1666666667 -16.8 -12 -4.8
Data From 2021-22 Arizona Wildcats Roster and Stats | College Basketball at Sports-Reference.com
Per Minute
Adama Bal 0.7961538462 0.7961538462 0.7961538462
Azuolas Tubelis 0.3254237288 0.3254237288 0.3254237288
Bennedict Mathurin 0.2464612823 0.2464612823 0.2464612823
Christian Koloko 0.412858661 0.412858661 0.412858661
Dalen Terry 0.2876579203 0.2876579203 0.2876579203
Grant Weitman -3.5692307692 -3.5692307692 -3.5692307692
Jordan Mains 0.3 0.3 0.3
Justin Kier 0.2290713324 0.2290713324 0.2290713324
Kerr Kriisa 0.1252307692 0.1252307692 0.1252307692
Oumar Ballo 0.505141844 0.505141844 0.505141844
Pelle Larsson 0.2411994785 0.2411994785 0.2411994785
Shane Nowell -0.8636363636 -0.8636363636 -0.8636363636
Tautvilas Tubelis -9.8 -9.8 -9.8

IntegerSolution

Problem Data: See Previous Sheet
Objective Function: Maximize team +/- by deciding how many minutes each player plays in a given game
Decision Variables: X_i How Many Minutes Player i Should Play
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis
+/- 0.7961538462 0.3254237288 0.2464612823 0.412858661 0.2876579203 -3.5692307692 0.3 0.2290713324 0.1252307692 0.505141844 0.2411994785 -0.8636363636 -9.8
PLAYER STATS BY MINUTE PLAYED Total Needed Amount to Beat Season Averages
FGM 0.13 0.22 0.18 0.19 0.11 0.04 0.10 0.12 0.10 0.16 0.11 0.09 0.08 31.22 >= 30.44
3PM 0.08 0.01 0.07 0.00 0.03 0.00 0.00 0.05 0.08 0.00 0.04 0.02 0.00 7.77 >= 7.76
2PM 0.05 0.21 0.11 0.19 0.08 0.04 0.10 0.07 0.02 0.16 0.07 0.08 0.08 23.46 >= 22.68
FTM 0.00 0.11 0.11 0.11 0.04 0.00 0.13 0.05 0.04 0.12 0.08 0.03 0.00 16.03 >= 15.91
OR 0.02 0.08 0.04 0.10 0.04 0.04 0.13 0.02 0.02 0.10 0.04 0.00 0.00 10.81 >= 10.44
DR 0.08 0.17 0.13 0.19 0.13 0.08 0.27 0.14 0.07 0.19 0.13 0.23 0.00 28.38 >= 28.35
R 0.10 0.25 0.17 0.29 0.17 0.12 0.40 0.15 0.09 0.29 0.17 0.23 0.00 39.18 >= 38.79
A 0.10 0.09 0.08 0.05 0.14 0.00 0.00 0.11 0.16 0.04 0.09 0.09 0.00 19.91 >= 19.90
Stl 0.03 0.04 0.03 0.03 0.04 0.00 0.07 0.03 0.02 0.02 0.04 0.06 0.00 6.74 >= 6.71
Blocks 0.01 0.03 0.01 0.11 0.01 0.00 0.00 0.00 0.00 0.08 0.01 0.03 0.00 5.72 >= 5.71
Pts 0.33 0.56 0.55 0.50 0.29 0.08 0.33 0.34 0.33 0.45 0.35 0.23 0.17 86.24 >= 84.00
T 0.07 0.09 0.05 0.06 0.05 0.04 0.07 0.07 0.07 0.06 0.07 0.12 0.13 13.18 <= 13.18
PF 0.10 0.08 0.06 0.11 0.08 0.12 0.13 0.06 0.06 0.11 0.12 0.14 0.04 15.61 <= 16.47
Minute Restrictions Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Minute Restriction Minute Restriction to Prevent Injuries and Fatigue
4 4 <= 36.00
31 31 <= 36.00
36 36 <= 36.00
36 36 <= 36.00
27 27 <= 36.00
0 0 <= 36.00
6 6 <= 36.00
25 25 <= 36.00
33 33 <= 36.00
2 2 <= 36.00
0 0 <= 36.00
0 0 <= 36.00
0 0 <= 36.00
Total Game Minutes
200 = 200.00
Front-Court Minute Restriction Forwards & Centers
31 36 6 2 0 75 <= 80.00
Back-Court Minute Restriction Guards
4 36 27 0 25 33 0 0 125 >= 120.00
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Total +/- Per Minute of Game
Minutes Played 4 31 36 36 27 0 6 25 33 2 0 0 0 57.44 =SUMPRODUCT(B50:N50,B8:N8)

LinearSolution

Problem Data: See Previous Sheet
Objective Function: Maximize team +/- by deciding how many minutes each player plays in a given game
Decision Variables: X_i How Many Minutes Player i Should Play
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis
+/- 0.7961538462 0.3254237288 0.2464612823 0.412858661 0.2876579203 -3.5692307692 0.3 0.2290713324 0.1252307692 0.505141844 0.2411994785 -0.8636363636 -9.8
PLAYER STATS BY MINUTE PLAYED Total Needed Amount to Beat Season Averages
FGM 0.13 0.22 0.18 0.19 0.11 0.04 0.10 0.12 0.10 0.16 0.11 0.09 0.08 31.36 >= 30.44
3PM 0.08 0.01 0.07 0.00 0.03 0.00 0.00 0.05 0.08 0.00 0.04 0.02 0.00 7.76 >= 7.76
2PM 0.05 0.21 0.11 0.19 0.08 0.04 0.10 0.07 0.02 0.16 0.07 0.08 0.08 23.60 >= 22.68
FTM 0.00 0.11 0.11 0.11 0.04 0.00 0.13 0.05 0.04 0.12 0.08 0.03 0.00 15.91 >= 15.91
OR 0.02 0.08 0.04 0.10 0.04 0.04 0.13 0.02 0.02 0.10 0.04 0.00 0.00 10.67 >= 10.44
DR 0.08 0.17 0.13 0.19 0.13 0.08 0.27 0.14 0.07 0.19 0.13 0.23 0.00 28.35 >= 28.35
R 0.10 0.25 0.17 0.29 0.17 0.12 0.40 0.15 0.09 0.29 0.17 0.23 0.00 39.02 >= 38.79
A 0.10 0.09 0.08 0.05 0.14 0.00 0.00 0.11 0.16 0.04 0.09 0.09 0.00 19.90 >= 19.90
Stl 0.03 0.04 0.03 0.03 0.04 0.00 0.07 0.03 0.02 0.02 0.04 0.06 0.00 6.74 >= 6.71
Blocks 0.01 0.03 0.01 0.11 0.01 0.00 0.00 0.00 0.00 0.08 0.01 0.03 0.00 5.71 >= 5.71
Pts 0.33 0.56 0.55 0.50 0.29 0.08 0.33 0.34 0.33 0.45 0.35 0.23 0.17 86.39 >= 84.00
T 0.07 0.09 0.05 0.06 0.05 0.04 0.07 0.07 0.07 0.06 0.07 0.12 0.13 13.18 <= 13.18
PF 0.10 0.08 0.06 0.11 0.08 0.12 0.13 0.06 0.06 0.11 0.12 0.14 0.04 15.57 <= 16.47
Minute Restrictions Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Minute Restriction Minute Restriction to Prevent Injuries and Fatigue
5.3473450922 5.3473450922 <= 36.00
31.7512950907 31.7512950907 <= 36.00
36 36 <= 36.00
36 36 <= 36.00
26.8722423362 26.8722423362 <= 36.00
0 0 <= 36.00
4.8511710245 4.8511710245 <= 36.00
27.5397728398 27.5397728398 <= 36.00
30.1452005237 30.1452005237 <= 36.00
1.492973093 1.492973093 <= 36.00
0 0 <= 36.00
0 0 <= 36.00
0 0 <= 36.00
Total Game Minutes
200 = 200.00
Front-Court Minute Restriction Forwards & Centers
31.7512950907 36 4.8511710245 1.492973093 0 74.0954392081 <= 80.00
Back-Court Minute Restriction Guards
5.3473450922 36 26.8722423362 0 27.5397728398 30.1452005237 0 0 125.9045607919 >= 120.00
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Total +/- Per Minute of Game
Minutes Played 5.35 31.75 36.00 36.00 26.87 0.00 4.85 27.54 30.15 1.49 0.00 0.00 0.00 58.35 =SUMPRODUCT(B50:N50,B8:N8)

Linear Sensitivity Report

Microsoft Excel 16.0 Sensitivity Report
Worksheet: [OSCM_Prototype w range name and non Integer.xlsx]LinearSolution
Report Created: 4/18/2022 10:22:27 AM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$50 Minutes Played Adama Bal 5.3473450922 0 0.7961538462 0.2436421185 0.3014186598
$C$50 Minutes Played Azuolas Tubelis 31.7512950907 0 0.3254237288 0.4693202249 0.0587753269
$D$50 Minutes Played Bennedict Mathurin 36 0 0.2464612823 1E+30 0.0988870662
$E$50 Minutes Played Christian Koloko 36 0 0.412858661 1E+30 0.3081391083
$F$50 Minutes Played Dalen Terry 26.8722423362 0 0.2876579203 0.0443848878 0.1580406434
$G$50 Minutes Played Grant Weitman 0 -6.9250110757 -3.5692307692 6.9250110757 1E+30
$H$50 Minutes Played Jordan Mains 4.8511710245 0 0.3 0.0574747641 0.1585129921
$I$50 Minutes Played Justin Kier 27.5397728398 0 0.2290713324 0.0472186962 0.0175154496
$J$50 Minutes Played Kerr Kriisa 30.1452005237 0 0.1252307692 0.0345940582 0.1485569666
$K$50 Minutes Played Oumar Ballo 1.492973093 0 0.505141844 0.1577737647 0.3378824776
$L$50 Minutes Played Pelle Larsson 0 -0.4394924799 0.2411994785 0.4394924799 1E+30
$M$50 Minutes Played Shane Nowell 0 -0.4578370512 -0.8636363636 0.4578370512 1E+30
$N$50 Minutes Played Tautvilas Tubelis 0 -14.4737325203 -9.8 14.4737325203 1E+30
Current Obj Value 58.3486591051
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease Max RHS Change Est New +/- Actual New +/- Improvement
$O$26 Bal Minute Restriction 5.3473450922 0 36 1E+30 30.6526549078
$O$27 A Tubelis Minute Restriction 31.7512950907 0 36 1E+30 4.2487049093
$O$28 Mathurin Minute Restriction 36 0.0988870662 36 1.192274917 2.0482079377 37.19 58.47 0.12
$O$29 Koloko Minute Restriction 36 0.3081391083 36 0.7644339169 0.363886976 36.76 58.35 58.58 0.24
$O$30 Terry Minute Restriction 26.8722423362 0 36 1E+30 9.1277576638
$O$31 Weitman Minute Restriction 0 0 36 1E+30 36
$O$32 Mains Minute Restriction 4.8511710245 0 36 1E+30 31.1488289755
$O$33 Kier Minute Restriction 27.5397728398 0 36 1E+30 8.4602271602
$O$34 Kriisa Minute Restriction 30.1452005237 0 36 1E+30 5.8547994763
$O$35 Ballo Minute Restriction 1.492973093 0 36 1E+30 34.507026907
$O$36 Larsson Minute Restriction 0 0 36 1E+30 36
$O$37 Nowell Minute Restriction 0 0 36 1E+30 36
$O$38 T Tubelis Minute Restriction 0 0 36 1E+30 36
$O$44 FrontCourtMinPlayed 74.0954392081 0 80 1E+30 5.9045607919
$O$22 T Total 13.18 1.5955380701 13.18 0.0551024804 0.1680625412 13.24 58.44 0.09
$O$23 PF Total 15.5711068986 0 16.47 1E+30 0.8988931014
$O$11 FGM Total 31.3584846547 0 30.44 0.9184846547 1E+30
$O$12 3PM Total 7.76 -18.8844196196 7.76 0.0146669551 0.0610922972 7.70 58.63 59.50 1.15
$O$13 2PM Total 23.5984846547 0 22.68 0.9184846547 1E+30
$O$14 FTM Total 15.91 -1.4281490926 15.91 0.1504296829 0.048474321 15.86 58.56 58.42 0.07
$O$15 OR Total 10.6710859155 0 10.44 0.2310859155 1E+30
$O$16 DR Total 28.35 -15.3383984522 28.35 0.0198247373 0.0858589225 28.26 58.65 59.67 1.32
$O$17 R Total 39.0210859155 0 38.79 0.2310859155 1E+30
$O$18 A Total 19.9 -11.1993783133 19.9 0.0423256091 0.2380713251 19.66 58.82 61.01 2.67
$O$19 Stl Total 6.7398916807 0 6.71 0.0298916807 1E+30
$O$20 Blocks Total 5.71 -7.9186259885 5.71 0.0172424963 0.0561093785 5.65 58.49 58.79 0.44
$O$21 Pts Total 86.3869693094 0 84 2.3869693094 1E+30
$O$47 BackCourtMinPlayed 125.9045607919 0 120 5.9045607919 1E+30
$O$41 TotalTeamMinPlayed 200 4.4742902616 200 0.3954376279 0.0707175934 Max 3PM, DR, and A changes 62.56
0.75 2/3 Assists 19.72 58.70 60.57 2.22
0.25 1/3DR 28.33 58.42

LinearSolution_Sens Test

Problem Data: See Previous Sheet
Objective Function: Maximize team +/- by deciding how many minutes each player plays in a given game
Decision Variables: X_i How Many Minutes Player i Should Play
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis
+/- 0.7961538462 0.3254237288 0.2464612823 0.412858661 0.2876579203 -3.5692307692 0.3 0.2290713324 0.1252307692 0.505141844 0.2411994785 -0.8636363636 -9.8
PLAYER STATS BY MINUTE PLAYED Total Needed Amount to Beat Season Averages
FGM 0.13 0.22 0.18 0.19 0.11 0.04 0.10 0.12 0.10 0.16 0.11 0.09 0.08 31.29 >= 30.44
3PM 0.08 0.01 0.07 0.00 0.03 0.00 0.00 0.05 0.08 0.00 0.04 0.02 0.00 7.76 >= 7.76
2PM 0.05 0.21 0.11 0.19 0.08 0.04 0.10 0.07 0.02 0.16 0.07 0.08 0.08 23.53 >= 22.68
FTM 0.00 0.11 0.11 0.11 0.04 0.00 0.13 0.05 0.04 0.12 0.08 0.03 0.00 15.91 >= 15.91
OR 0.02 0.08 0.04 0.10 0.04 0.04 0.13 0.02 0.02 0.10 0.04 0.00 0.00 11.27 >= 10.44
DR 0.08 0.17 0.13 0.19 0.13 0.08 0.27 0.14 0.07 0.19 0.13 0.23 0.00 28.35 >= 28.35
R 0.10 0.25 0.17 0.29 0.17 0.12 0.40 0.15 0.09 0.29 0.17 0.23 0.00 39.62 >= 38.79
A 0.10 0.09 0.08 0.05 0.14 0.00 0.00 0.11 0.16 0.04 0.09 0.09 0.00 19.66 >= 19.66
Stl 0.03 0.04 0.03 0.03 0.04 0.00 0.07 0.03 0.02 0.02 0.04 0.06 0.00 6.91 >= 6.71
Blocks 0.01 0.03 0.01 0.11 0.01 0.00 0.00 0.00 0.00 0.08 0.01 0.03 0.00 5.71 >= 5.71
Pts 0.33 0.56 0.55 0.50 0.29 0.08 0.33 0.34 0.33 0.45 0.35 0.23 0.17 86.26 >= 84.00
T 0.07 0.09 0.05 0.06 0.05 0.04 0.07 0.07 0.07 0.06 0.07 0.12 0.13 13.18 <= 13.18
PF 0.10 0.08 0.06 0.11 0.08 0.12 0.13 0.06 0.06 0.11 0.12 0.14 0.04 16.03 <= 16.47
Minute Restrictions Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Minute Restriction Minute Restriction to Prevent Injuries and Fatigue
Bal 10.22 10.22 <= 36.00
A Tubelis 33.21 33.21 <= 36.00
Mathurin 36.00 36.00 <= 36.00
Koloko 36.00 36.00 <= 36.00
Terry 30.30 30.30 <= 36.00
Weitman 0.00 0.00 <= 36.00
Mains 9.33 9.33 <= 36.00
Kier 11.49 11.49 <= 36.00
Kriisa 33.46 33.46 <= 36.00
Ballo 0.00 0.00 <= 36.00
Larsson 0.00 0.00 <= 36.00
Nowell 0.00 0.00 <= 36.00
T Tubelis 0.00 0.00 <= 36.00
Total Game Minutes
200.00 = 200.00
Front-Court Minute Restriction Forwards & Centers
33.21 36.00 9.33 0.00 0.00 78.54 <= 80.00
Back-Court Minute Restriction Guards
10.22 36.00 30.30 0.00 11.49 33.46 0.00 0.00 121.46 >= 120.00
Adama Bal Azuolas Tubelis Bennedict Mathurin Christian Koloko Dalen Terry Grant Weitman Jordan Mains Justin Kier Kerr Kriisa Oumar Ballo Pelle Larsson Shane Nowell Tautvilas Tubelis Total +/- Per Minute of Game
Minutes Played 10.22 33.21 36.00 36.00 30.30 0.00 9.33 11.49 33.46 0.00 0.00 0.00 0.00 61.01 =SUMPRODUCT(B50:N50,B8:N8)
Original DV Values 5.3473450922 31.7512950907 36 36 26.8722423362 0 4.8511710245 27.5397728398 30.1452005237 1.492973093 0 0 0
Increase Increase Constant Constant Increase Constant Increase Decrease Increase Decrease Constant Constant Constant