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Introduction to Operations Research: Case Problem: Scheduling a Golf League Captain Mohamed Abd El Fattah, the head professional at Wadi Degla Sporting Club, must develop a schedule of matches for the couples’ golf league that begins its season at 4:00 p.m. tomorrow. Eighteen couples signed up for the league, and each couple must play every other couple over the course of the 17-week season. Mohamed thought it would be fairly easy to develop a schedule, but after working on it for a couple of hours, he has been unable to come up with a schedule. Because Mohamed must have a schedule ready by tomorrow afternoon, he asked you to help him. A possible complication is that one of the couples told Mohamed that they may have to cancel for the season. They told Mohamed they will let him know by 1:00 p.m. tomorrow whether they will be able to play this season. Managerial Report Prepare a report for Mohamed Abd El Fattah. Your report should include, at a minimum, the following items: 1. A schedule that will enable each of the 18 couples to play every other couple over the 17-week season. 2. A contingency schedule that can be used if the couple that contacted Mohamed decides to cancel for the season. Solution 1. A schedule that will enable each of the 18 couples to play every other couple over the 17-week season. No of couples = 18 Each of the 18 couples has to play with the other 17 couples. This means each couple plays 17 match in the season, so each couple must play one match every week. Total no of matches given by combination 18 C 2 18 C 2 = 18 ! ( 18 2 ) ! 2 ! = 153 match As they are 18 couples they will play 9 matches per week. Let (x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 , x 9 , x 10 , x 11 , x 12 , x 13 , x 14 , x 15 , x 16 , x 17 , x 18 ) name of couples The schedule Week 1 X 1 4 vs X 1 5 X 1 3 vs X 1 8 X 1 7 vs X 2 X 3 vs X 1 2 X 6 vs X 7 X 1 vs X 1 6 X 4 vs X 1 0 X 8 vs X 1 1 X 9 vs X 5 Week 2 X 5 vs X 7 X 1 1 vs X 1 4 X 1 2 vs X 1 3 X 1 7 vs X 8 X 1 5 vs X 1 X 1 6 vs X 9 X 2 vs X 4 X 1 8 vs X 6 X 1 0 vs X 3 Week 3 X 9 vs X 1 5 X 1 4 vs X 1 7 X 3 vs X 2 X 7 vs X 1 6 X 1 vs X 1 1 X 8 vs X 4 X 6 vs X 5 X 1 3 vs X 1 0 X 1 8 vs X 1 2 Week 4 X 1 2 vs X 6 X 3 vs X 8 X 1 7 vs X 1 X 1 6 vs X 5 X 1 5 vs X 7 X 1 1 vs X 9 X 1 0 vs X 1 8 X 4 vs X 1 4 X 2 vs X 1 3 Week 5 X 1 8 vs X 2 X 7 vs X 1 1 X 1 vs X 4 X 5 vs X 1 5 X 8 vs X 1 3 X 1 4 vs X 3 X 6 vs X 1 6 X 1 2 vs X 1 0 X 9 vs X 1 7 Week 6 X 1 1 vs X 5 X 2 vs X 1 2 X 4 vs X 9 X 3 vs X 1 X 1 0 vs X 6 X 1 7 vs X 7 X 1 5 vs X 1 6 X 1 8 vs X 8 X 1 3 vs X 1 4
2. A contingency schedule that can be used if the couple that contacted Mohamed decides to cancel for the season. No of couples = 17 Each of the 17 couples has to play with the other 16 couples. This means each couple plays 16 match in the season, so each couple must play one match every week. And will have one free couple during the 17 weeks. Total no of matches given by combination 17 C 2 17 C 2 = 17 !

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