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arXiv · 1303.4031

Two exact algorithms for the generalized assignment problem

Fatemeh Rajabi-Alni
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Abstract

Let A={a_1,a_2,...,a_s} and B={b_1,b_2,...,b_t} be two sets of objects with s+r=n, the generalized assignment problem assigns each element a_i in A to at least alpha_i and at most alpha '_i elements in B, and each element b_j in B to at least beta_j and at most beta '_j elements in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an O(n^4) time and O(n) space algorithm for this problem using the well known Hungarian algorithm. We also present an O(n^3) algorithm for a special case of the generalized assignment, called the limited-capacity assignment problem, where alpha_i,beta_j=1 for all i,j.

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Fatemeh Rajabi-Alni. 2013-03-17. Two exact algorithms for the generalized assignment problem. https://arxiv.org/abs/1303.4031

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