Mathematical Modeling with LPL : Explain and run a Model
Problem Statement
Modeling Description
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model golfers "The Social Golfer Problem"; parameter m:=4; n:=4; k:=5; -- parameter m:=8; n:=4; k:=7; -- parameter m:=5; n:=3; k:=8; set w := 1..k "weeks"; i,j := 1..m*n "golfers"; g := 1..m "groups (per week)"; binary variable x{w,i,g}; constraint A{w,i}: sum{g} x = 1; B{w,g}: sum{i} x = n; C{i,j|i<j}: atmost(1){g,w} (x[w,i,g] and x[w,j,g]); --C{i,j|i<j}: sum{g,w} (x[w,i,g] and x[w,j,g]) = 1; D{i}: x[1,i,i%m]; E{i}: x[2,i,Ceil(i/n)]; solve; Write('The group of players is as follows:\n\n'); Write(' %-14s\n',{w}('Week '&w)); Write{g}('Group %s %-14s\n',g, {w}Strreplace(Format('(%s)',{i|x}(i&',')),',)',')')); end
Problem Statement
Modeling Description
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The solution is as follows:
The LOG-File output of LPL is as follows: