2. The coach of an age group swim team needs to assign swimmers to a 200-yard me

Question

2. The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are Stroke Chris David Tony Carl 37.7 33.3 Ken Backstroke Breaststroke 43.4 Butterfly Freestyle 32.9 33.1 28.5 26.4 33.8 42.2 38.9 29.6 37.0 34.7 30.4 28.5 35.4 41.8 33.6 31.1 29.2 The coach wishes to determine how to assign four swimmers to the four different strokes to minimize the sum of the corresponding best times. (a) Formulate this problem as an assignment problem. (b) Obtain an optimal solution by using Julia.

Explanation / Answer

Ans....
LP Formulation :
Let us define xij = 1 if stroke i is allocated to swimmer j
xij = 0 otherwise
and Cij is the best time swimmer j for stroke i
Our objective is to minimize the total best time
Min cijxij
subjected to xij == 1 for each stroke i belongs to {Backstroke,Breaststroke,Butterfly,Freestyle}
xij == 1 for each swimmer j belongs to {Carl, Chris, David, Tony, Ken}
xij = 0 or 1 for all i and j
Optimal Solution for this probelm is Carl - Backstroke
Chris - Breaststroke
David - Butterfly
Tony - Freestyle

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