You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
77 lines
2.0 KiB
77 lines
2.0 KiB
/* ASSIGN, Assignment Problem */
|
|
|
|
/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
|
|
|
|
/* The assignment problem is one of the fundamental combinatorial
|
|
optimization problems.
|
|
|
|
In its most general form, the problem is as follows:
|
|
|
|
There are a number of agents and a number of tasks. Any agent can be
|
|
assigned to perform any task, incurring some cost that may vary
|
|
depending on the agent-task assignment. It is required to perform all
|
|
tasks by assigning exactly one agent to each task in such a way that
|
|
the total cost of the assignment is minimized.
|
|
|
|
(From Wikipedia, the free encyclopedia.) */
|
|
|
|
param m, integer, > 0;
|
|
/* number of agents */
|
|
|
|
param n, integer, > 0;
|
|
/* number of tasks */
|
|
|
|
set I := 1..m;
|
|
/* set of agents */
|
|
|
|
set J := 1..n;
|
|
/* set of tasks */
|
|
|
|
param c{i in I, j in J}, >= 0;
|
|
/* cost of allocating task j to agent i */
|
|
|
|
var x{i in I, j in J}, >= 0;
|
|
/* x[i,j] = 1 means task j is assigned to agent i
|
|
note that variables x[i,j] are binary, however, there is no need to
|
|
declare them so due to the totally unimodular constraint matrix */
|
|
|
|
s.t. phi{i in I}: sum{j in J} x[i,j] <= 1;
|
|
/* each agent can perform at most one task */
|
|
|
|
s.t. psi{j in J}: sum{i in I} x[i,j] = 1;
|
|
/* each task must be assigned exactly to one agent */
|
|
|
|
minimize obj: sum{i in I, j in J} c[i,j] * x[i,j];
|
|
/* the objective is to find a cheapest assignment */
|
|
|
|
solve;
|
|
|
|
printf "\n";
|
|
printf "Agent Task Cost\n";
|
|
printf{i in I} "%5d %5d %10g\n", i, sum{j in J} j * x[i,j],
|
|
sum{j in J} c[i,j] * x[i,j];
|
|
printf "----------------------\n";
|
|
printf " Total: %10g\n", sum{i in I, j in J} c[i,j] * x[i,j];
|
|
printf "\n";
|
|
|
|
data;
|
|
|
|
/* These data correspond to an example from [Christofides]. */
|
|
|
|
/* Optimal solution is 76 */
|
|
|
|
param m := 8;
|
|
|
|
param n := 8;
|
|
|
|
param c : 1 2 3 4 5 6 7 8 :=
|
|
1 13 21 20 12 8 26 22 11
|
|
2 12 36 25 41 40 11 4 8
|
|
3 35 32 13 36 26 21 13 37
|
|
4 34 54 7 8 12 22 11 40
|
|
5 21 6 45 18 24 34 12 48
|
|
6 42 19 39 15 14 16 28 46
|
|
7 16 34 38 3 34 40 22 24
|
|
8 26 20 5 17 45 31 37 43 ;
|
|
|
|
end;
|