A Fully Polynomial Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

Authors:
Mikhail Y. Kovalyov;Wieslaw Kubiak
Affiliations:
Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus;Faculty of Business Administration, Memorial University of Newfoundland, St. John‘s, NF, Canada, A1B 3X5
Venue:
Journal of Heuristics
Year:
1998

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Abstract

A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n^5L^4/\epsilon^3) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and ε is required relative error. The idea behind the scheme is rather general and it can be used to developfully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.