Exact and approximation algorithms for makespan minimization on unrelated parallel machines
نویسندگان
چکیده
منابع مشابه
Exact and Approximation Algorithms for Makespan Minimization on Unrelated Parallel Machines
The NP-hard problem addressed in this paper is well known in the scheduling literature as Rl( C,,,. We propose lower bounds based on Lagrangian relaxations and additive techniques. We then introduce new cuts which eliminate infeasible disjunctions on the cost function value, and prove that the bounds obtained through such cuts dominate the previous bounds. These results are used to obtain exact...
متن کاملApproximation Algorithms for Subclasses of the Makespan Problem on Unrelated Parallel Machines with Restricted Processing Times
Let there be m parallel machines and n jobs, where a job j can be scheduled on machine i to take pi, j ∈ Z+ time units. The makespan Cmax is the completion time of a machine that finishes last. The goal is to produce a schedule with all n jobs that has minimum makespan. This is the makespan problem on unrelated parallel machines, denoted as R||Cmax. Assume p,q ∈ Z+ are constants, let A(p,q) = {...
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We consider the problem of scheduling n jobs to minimize the makespan on m unrelated machines, where job j requires time pij if processed on machine i. A classic algorithm of Lenstra et al. [5] yields the best known approximation ratio of 2 for the problem. Improving this bound has been a prominent open problem for over two decades. In this paper we obtain a tighter bound for a wide subclass of...
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In this paper, we study the unrelated parallel machine problem for minimizing the makespan, which is NP-hard. We used Simulated Annealing (SA) and Tabu Search (TS) with Neighborhood Search (NS) based on the structure of the problem. We also used a modified SA algorithm, which gives better results than the traditional SA and developed an effective heuristic for the problem: Squeaky Wheel Optimiz...
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This paper presents an empirical comparison of polynomial-time approximation algorithms and local search heuristics for the problem of minimizing total weighted completion time on unrelated parallel machines. Algorithms with a worst-case performance guarantee are based on rounding a fractional solution to an LP-rela....<ation or to a convex quadratic programming relaxation. We also investigate ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(96)00087-x