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39 lines
1.3 KiB
Modula-2
39 lines
1.3 KiB
Modula-2
/*
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A warehouse has to store n boxes in a rack with m shelves.
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The first m1 shelves have length L1, while the remaining have length L2.
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Each box j = 1..n has length l_j and a frequency of usage f_j.
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Write a linear programming model that helps the warehouse to decide how to store the boxes,
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so that the sum of the frequencies of the boxes stored in the first m1 shelves is maximized.
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(N.B. It is not known if all the boxes can be stored.)
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*/
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# Set casse
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param nCasse >= 1;
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set CASSE := 1..nCasse;
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# Set scaffali
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param nScaffali >= 1;
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set SCAFFALI := 1..nScaffali;
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# Parametri cassa
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param dimensione{c in CASSE} >= 0;
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param frequenza{c in CASSE} >= 0;
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# Parametri scaffali
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param spazioA >= 0;
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param spazioB >= 0;
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param cutoff >= 1, <= nScaffali + 1; # Tutti gli scaffali maggiori o uguali a questo numero saranno considerati nel set B
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param spazio{s in SCAFFALI} := if s >= cutoff then spazioB else spazioA;
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set SCAFFALI_A := 1..cutoff;
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set SCAFFALI_B := cutoff + 1 ..nScaffali;
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# Vincoli
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var suScaffale{c in CASSE, s in SCAFFALI} binary;
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c1{c in CASSE}: sum{s in SCAFFALI} suScaffale[c, s] == 1;
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c2{s in SCAFFALI}: sum{c in CASSE} dimensione[c] * suScaffale[c, s] <= spazio[s];
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# Funzione obiettivo
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maximize z: sum{c in CASSE, s in SCAFFALI_A} suScaffale[c, s] * frequenza[c];
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solve;
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end;
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