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==Definition==
In the following, we have ''n'' kinds of items, <math>x_1</math> through <math>x_n</math> and ''m'' kinds of bins <math>b_1</math> through <math>b_m</math>. Each bin <math>b_i</math> is associated with a budget <math>w_i</math>. For a bin <math>b_i</math>, each item <math>x_j</math> has a profit <math>p_{ij}</math> and a weight <math>w_{ij}</math>. A solution is a subset of items ''U'' and an assignment from ''U'' to the bins. A feasible solution is a solution in which for each bin <math>b_i</math> the
Mathematically the generalized assignment problem can be formulated as:
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