Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Balanced optimization problems
Operations Research Letters
Minimum deviation and balanced optimization: A unified approach
Operations Research Letters
Operations Research Letters
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We assume that I is a given finite set and for each i@eI a cost C"i is defined. Further, let F be a family of subsets of I such that each subset has the same cardinality. The Minimum Deviation Problem (MDP) considered in this paper is MinimiseS@eF@?j@eSmaxi@eS(C"i)-C"j. We show that the MDP can be solved in O(|I|f(|I|)) time provided the Minsum problem MinimiseS@eF@?j@eS(-C"j) can be solved in O(f(|I|)) time. We also show that the Minimum Deviation Assignment Problem of order n can be solved in O(n^4) time as compared with O(n^5) which is obtained by using the above result. Minimum Deviation Linear Programs are also considered and the use of parametric analysis is proposed to solve such problems.