8.3-4. 8.3-4. 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 #0 yards" are Stroke $ackstroke $reaststroke $utterfly ,reestyle
Carl %&.& )%.) %%.% 2'.2
Chris %2.' %%.* 2(.# 2+.)
David %%.( )2.2 %(.' 2'.+
Tony %&.0 %).& %0.) 2(.#
Ken %#.) )*.( %%.+ %*.*
The coach wishes to determine how to assign four swimmers to the four different strokes to minimie the sum of the corresponding best times. !a" ,ormulate this problem as an assignment problem. !b" Obtain an optimal solution. Solution (a) Formulate this prolem as an assi!nment prolem Task
"ssi!ne e
Carl Chris David Tony Ken
#a$kstrok e %&.& %2.' %%.( %&.0 %#.)
#reastrok e )%.) %%.* )2.2 %).& )*.(
#utt #utter er%l %ly y
Frees Freesty tyle le
Dumm Dummy y
%%.% 2(.# %(.' %0.) %%.+
2'.2 2+.) 2'.+ 2(.# %*.*
0 0 0 0 0
) &tain an optimal solution. Subtract smallest number from each column/row
Task "ssi!ne e
1arl 1hris avid Tony en
$ackstroke %&.& %2.' %%.( %&.0 %#.)
$reastroke )%.) %%.* )2.2 %).& )*.(
$utterfly %%.% 2(.# %(.' %0.) %%.+
,reestyle 2'.2 2+.) 2'.+ 2(.# %*.*
ummy 0 0 0 0 0 1olumn 3eduction 1heck for optimality cover all ero 4 of lines 5 #
"ssi!ne e Task
1arl 1hris avid Tony
$ackstroke ).( 0 0.' ).*
$reastroke *0.% 0 '.* *.+
1 of 4
$utterfly ).( 0 *0.) *.'
,reestyle 2.( 0 %.2 2.*
ummy 0 0 0 0
en
2.#
(.&
#.*
).&
0 Subtract smallest entry from each uncovered row !0.'0"
