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79 lines
2.5 KiB
79 lines
2.5 KiB
/* GAP, Generalized Assignment Problem */
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/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
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/* The Generalized Assignment Problem (GAP) is to assign a set of jobs
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to a set of agents subject to the constraints that each job must be
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assigned exactly to one agent and the total resources consumed by all
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jobs assigned to an agent must not exceed the agent's capacity. */
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param m, integer, > 0;
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/* number of agents */
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param n, integer, > 0;
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/* number of jobs */
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set I := 1..m;
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/* set of agents */
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set J := 1..n;
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/* set of jobs */
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param a{i in I, j in J}, >= 0;
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/* resource consumed in allocating job j to agent i */
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param b{i in I}, >= 0;
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/* resource capacity of agent i */
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param c{i in I, j in J}, >= 0;
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/* cost of allocating job j to agent i */
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var x{i in I, j in J}, binary;
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/* x[i,j] = 1 means job j is assigned to agent i */
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s.t. one{j in J}: sum{i in I} x[i,j] = 1;
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/* job j must be assigned exactly to one agent */
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s.t. lim{i in I}: sum{j in J} a[i,j] * x[i,j] <= b[i];
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/* total amount of resources consumed by all jobs assigned to agent i
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must not exceed the agent's capacity */
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minimize obj: sum{i in I, j in J} c[i,j] * x[i,j];
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/* the objective is to find cheapest assignment (note that gap can also
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be formulated as maximization problem) */
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data;
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/* These data correspond to the instance c515-1 (gap1) from:
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I.H. Osman, "Heuristics for the Generalised Assignment Problem:
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Simulated Annealing and Tabu Search Approaches", OR Spektrum, Volume
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17, 211-225, 1995
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D. Cattrysse, M. Salomon and L.N. Van Wassenhove, "A set partitioning
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heuristic for the generalized assignment problem", European Journal
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of Operational Research, Volume 72, 167-174, 1994 */
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/* The optimal solution is 261 (minimization) or 336 (maximization) */
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param m := 5;
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param n := 15;
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param a : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 :=
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1 8 15 14 23 8 16 8 25 9 17 25 15 10 8 24
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2 15 7 23 22 11 11 12 10 17 16 7 16 10 18 22
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3 21 20 6 22 24 10 24 9 21 14 11 14 11 19 16
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4 20 11 8 14 9 5 6 19 19 7 6 6 13 9 18
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5 8 13 13 13 10 20 25 16 16 17 10 10 5 12 23 ;
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param b := 1 36, 2 34, 3 38, 4 27, 5 33;
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param c : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 :=
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1 17 21 22 18 24 15 20 18 19 18 16 22 24 24 16
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2 23 16 21 16 17 16 19 25 18 21 17 15 25 17 24
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3 16 20 16 25 24 16 17 19 19 18 20 16 17 21 24
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4 19 19 22 22 20 16 19 17 21 19 25 23 25 25 25
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5 18 19 15 15 21 25 16 16 23 15 22 17 19 22 24 ;
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end;
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