Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Heuristics for scheduling unrelated parallel machines
Computers and Operations Research
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Exact and approximation algorithms for makespan minimization on unrelated parallel machines
Discrete Applied Mathematics
Computers and Operations Research
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms for Scheduling Tasks on Unrelated Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling Tasks on Unrelated Machines: Large Neighborhood Improvement Procedures
Journal of Heuristics
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Unrelated parallel machine scheduling using local search
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
A multiobjective optimization approach to solve a parallel machines scheduling problem
Advances in Artificial Intelligence
Scheduling unrelated parallel machines with optional machines and jobs selection
Computers and Operations Research
An iterated greedy algorithm for the large-scale unrelated parallel machines scheduling problem
Computers and Operations Research
Minimizing resource consumption on uniform parallel machines with a bound on makespan
Computers and Operations Research
Computers and Operations Research
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In this paper we study the unrelated parallel machines problem where n independent jobs must be assigned to one out of m parallel machines and the processing time of each job differs from machine to machine. We deal with the objective of the minimisation of the maximum completion time of the jobs, usually referred to as makespan or C"m"a"x. This is a type of assignment problem that has been frequently studied in the scientific literature due to its many potential applications. We propose a set of metaheuristics based on a size-reduction of the original assignment problem that produce solutions of very good quality in a short amount of time. The underlying idea is to consider only a few of the best possible machine assignments for the jobs and not all of them. The results are simple, yet powerful methods. We test the proposed algorithms with a large benchmark of instances and compare them with current state-of-the-art methods. In most cases, the proposed size-reduction algorithms produce results that are statistically proven to be better by a significant margin.