Scheduling unrelated parallel machines with optional machines and jobs selection

[EN] In this paper we study two generalizations of the well known unrelated parallel machines scheduling problem under makespan (Cmax) minimization. First, a situation in which not every available parallel machine should be used and it is desirable to employ only a subset of the parallel machines. This is referred to as Not All Machines or NAM in short. This environment applies frequently in production shops where capacity exceeds demand or when production capacity can be lent to third companies. Also, NAM can be used to increase production capacity and it is not clear how many additional machines should be acquired. The second studied generalization has been referred to as Not All Jobs or NAJ. Here, there is no obligation to process all available jobs. We propose Mixed Integer Programming mathematical formulations for both NAM and NAJ, and it is shown that the latter can be effectively solved with modern commercial solvers. We also present three algorithms to solve the NAM problem. These algorithms are compared with the proposed MIP formulation when solved with IBM ILOG CPLEX 12.1. Comprehensive computational and statistical experiments prove that our proposed algorithms significantly improve the results given by the solver. © 2011 Elsevier Ltd. All rights reserved.The authors would like to thank the anonymous referees for their careful and detailed comments which have helped to improve this manuscript considerably. 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, under the project ‘‘OSC’’ with references IMIDIC/2008/137, IMIDIC/2009/198 and IMIDIC/2010/175 and the Polytechnic University of Valencia, under the project ‘‘PPAR— Production Programming in Highly Constrained Environments: New Algorithms and Computational Advances’’ with reference 3147.Fanjul Peyró, L.; Ruiz García, R. (2012). Scheduling unrelated parallel machines with optional machines and jobs selection. Computers and Operations Research. 39(7):1745-1753. https://doi.org/10.1016/j.cor.2011.10.012S1745175339

Enriched metaheuristics for the resource constrained unrelated parallel machine scheduling problem

[EN] A Scatter Search algorithm together with an enriched Scatter Search and an enriched Iterated Greedy for the unrelated parallel machine problem with one additional resource are proposed in this paper. The optimisation objective is to minimise the maximum completion of the jobs on the machines, that is, the makespan. All the proposed methods start from the best known heuristic for the same problem. Non feasible solutions are allowed in all the methods and a Repairing Mechanism is applied to obtain a feasible solution from a resource constraint point of view. All the proposed algorithms apply different local search procedures based on insertion, swap and restricted neighbourhoods. Computational experiments are carried out using an exhaustive benchmark of instances. After analysing the results, we can conclude that the enriched methods obtain superior results, outperforming the best known solutions for the same problem.The authors are supported by the Spanish Ministry of Economy and Competitiveness, under the projects "SCHEYARD - Optimization of Scheduling Problems in Container Yards" (No. DPI201565895-R) and "OPTEMAC -Optimizacion de Procesos en Terminales Maritimas de Contenedores" (No. DPI2014-53665-P), all of them partially financed with FEDER funds. The authors are also partially supported by the EU Horizon 2020 research and innovation programme under grant agreement no. 731932 "Transforming Transport: Big Data Value in Mobility and Logistics". Interested readers can download contents from http://soa.iti.es, like the instances used and a software for generating further instances. Source codes are available upon justified request from the authors.Vallada Regalado, E.; Villa Juliá, MF.; Fanjul-Peyro, L. (2019). Enriched metaheuristics for the resource constrained unrelated parallel machine scheduling problem. Computers & Operations Research. 111:415-424. https://doi.org/10.1016/j.cor.2019.07.016S41542411

Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times

[EN] Parallel machine scheduling problems have many practical and industrial applications. In this paper we study a generalization which is the unrelated parallel machine scheduling problem with machine and job sequence setup times (UPMS) with makespan minimization criterion. We propose new mixed integer linear programs and a mathematical programming based algorithm. These new models and algorithms are tested and compared with the existing ones in an extensive and comprehensive computational campaign. The performance of two popular commercial solvers (CPLEX and Gurobi) is also compared in the experiments. Results show that the proposed methods significantly improve on existing methods and are able to obtain solutions for extremely large instances of up to 1000 jobs and eight machines with relative deviations from lower bounds below 0.8%.The authors are partially supported by the Spanish Ministry of Economy and Competitiveness, under the project SCHEYARD Optimization of Scheduling Problems in Container Yards (No.DPI2015-65895-R) financed by FEDER funds. Special thanks are due to our colleague Alfredo Marín, for fruitful discussions that helped improve this paper and to Tran and coauthors for all the help received during the reimplementation of their efficient methods. Thanks are also due to three anonymous referees for their helpful reports.Fanjul-Peyro, L.; Ruiz García, R.; Perea Rojas Marcos, F. (2019). Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times. Computers & Operations Research. 101:173-182. https://doi.org/10.1016/j.cor.2018.07.007S17318210