Size-reduction heuristics for the unrelated parallel machines scheduling problem

[EN] 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 Cmax. This is a type of assignment problem that has been frequently studied in the scienti¿c 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 signi¿cant margin. & 2010 Elsevier Ltd. All rights reservedThis work is partially funded by the Spanish Ministry of Science and Innovation, under the project ‘‘SMPA—Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances’’ with references number DPI2008-03511/DPI. The authors should also thank the IMPIVA—Institute for the Small and Medium Valencian Enterprise, for the project OSC with reference IMIDIC/2008/137 and the Polytechnic University of Valencia, for the project PPAR with reference 3147.Fanjul Peyró, L.; Ruiz García, R. (2011). Size-reduction heuristics for the unrelated parallel machines scheduling problem. Computers and Operations Research. 38(1):301-309. https://doi.org/10.1016/j.cor.2010.05.005S30130938

A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search

The parallel machine scheduling problem with unrelated machines is studied where the objective is to minimize the maximum makespan. In this paper, new local search algorithms are proposed where the neighborhood search of a solution uses the 'efficiency' of the machines for each job. It is shown that this method yields better solutions and shorter running times than the more general local search heuristics

High-Performance Computing for Scheduling Decision Support: A Parallel Depth-First Search Heuristic

Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a need for developing solution heuristics. For scheduling problems with setup times on unrelated parallel machines, there is limited research on solution methods and to the best of our knowledge, parallel computer architectures have not yet been taken advantage of. We address this gap by proposing and implementing a new solution heuristic and by testing different parallelization strategies. In our computational experiments, we show that our heuristic calculates near-optimal solutions even for large instances and that computing time can be reduced substantially by our parallelization approach

Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times

[EN] A novel scheduling problem that results from the addition of resource-assignable setups is presented in this paper. We consider an unrelated parallel machine problem with machine and job sequence-dependent setup times. The new characteristic is that the amount of setup time does not only depend on the machine and job sequence but also on the amount of resources assigned, which can vary between a minimum and a maximum. The aim is to give solution to real problems arising in several industries where frequent setup operations in production lines have to be carried out. These operations are indeed setups whose length can be reduced or extended according to the amount of resources assigned to them. The objective function considered is a linear combination of total completion time and the total amount of resources assigned. We present a mixed integer program (MIP) model and some fast dispatching heuristics. We carry out careful and comprehensive statistical analyses to study what characteristics of the problem affect the MIP model performance. We also study the effectiveness of the different heuristics proposed. © 2011 Springer-Verlag London Limited.The authors are indebted to the referees and editor for a close examination of the paper, which has increased its quality and presentation. This work is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI. The authors should also thank the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198, and IMIDIC/2010/175.Ruiz García, R.; Andrés Romano, C. (2011). Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times. 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An exact extended formulation for the unrelated parallel machine total weighted completion time problem

The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio