Unrelated Machines Scheduling With Machine Eligibility Restrictions

In this paper we present a new heuristic algorithm to minimize the makespan for scheduling jobs on unrelated parallel machines with machine eligibility restrictions ( R^ I M .1 C^^). To the best of our knowledge, the problem has not been addressed previously in the literature. The multi-phase heuristic algorithm incorporates new concepts from the multi-depot vehicle routing in the constructive heuristic. A computational study includes problems with two or four machines, up to 105 jobs, and three levels of a machine selection parameter. The heuristic algorithm solution values are compared to optimal solution values. The results show that the heuristic algorithm can yield solutions within a few percent of the optimal solutions with performance improving as the number of jobs to be scheduled increases

An ordered heuristic for the allocation of resources in unrelated parallel-machines

All rights reserved. Global competition pressures have forced manufactures to adapt their productive capabilities. In order to satisfy the ever-changing market demands many organizations adopted flexible resources capable of executing several products with different performance criteria. The unrelated parallel-machines makespan minimization problem (Rm||Cmax) is known to be NP-hard or too complex to be solved exactly. In the heuristics used for this problem, the MCT (Minimum Completion Time), which is the base for several others, allocates tasks in a random like order to the minimum completion time machine. This paper proposes an ordered approach to the MCT heuristic. MOMCT (Modified Ordered Minimum Completion Time) will order tasks in accordance to the MS index, which represents the mean difference of the completion time on each machine and the one on the minimum completion time machine. The computational study demonstrates the improved performance of MOMCT over the MCT heuristic.This work is supported by FEDER Funds through the “Programa Operacional Factores de Competitividade - COMPETE” program and by National Funds through FCT “Fundação para a Ciência e a Tecnologia” under the project: FCOMP-01-0124-FEDER-PEst-OE/EEI/UI0760/2011 and PEstOE/EEI/UI0760/2014.info:eu-repo/semantics/publishedVersio

BÜTÜNLEŞİK ÜRETİM VE DAĞITIM PROBLEMLERİ İÇİN YENİ BİR ÇÖZÜM YAKLAŞIMI:

Production and distribution activities are two basic elements in supply chain management. In literature, these problems are generally considered separately. However, it is clear that both activities have to be handled simultaneously in order to provide less system cost. Hence, enterprises are made their decisions concurrently with regard to production and distribution decisions for sustainable competitiveness. Based on this necessity, production and distribution problems have recently started to be studied together. In this paper, we first deal with production problems, reducing it to the unrelated parallel machine environment and a mathematical model is proposed. Then, we put an emphasis on the vehicle routing problem which is a strong connection with distribution decisions and develop another model. Finally, a new mathematical model formulation solving two integrated problems is developed and an illustrative example is given to validate the mathematical model.Üretim ve dağıtım faaliyetleri tedarik zinciri yönetiminde çok temel iki unsurdur. Literatürde bu iki problem genellikle birbirinden bağımsız olarak ele alınmaktadır. Ancak daha düşük sistem maliyeti için bu iki fonksiyonun bütünleşik olarak değerlendirilmesi gerektiği açıktır. Dolayısıyla kurumsal işletmeler sürdürülebilir rekabet için üretim ve dağıtım kararlarını birlikte almalıdır. Bu gereklilik üzerine son yıllarda üretim ve dağıtım problemlerinin entegre olarak ele alındığı çalışmalar artmaya başlamıştır. Bu çalışmada ilk olarak üretim problemi özdeş olmayan paralel makineler ortamına indirgenmiş ve bir matematiksel model önerilmiştir. Daha sonra dağıtım kararlarının verilmesinde araç rotalama problemi üzerinde durulmuş ve bir diğer matematiksel model geliştirilmiştir. Son olarak bu iki model temel alınarak üretim ve dağıtım problemlerini eş zamanlı çözen yeni bir model önerilmiş ve modelin geçerliliği örnek problem vasıtasıyla sağlanmıştır

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

Exact and approximation algorithms for makespan minimization on unrelated parallel machines

AbstractThe NP-hard problem addressed in this paper is well known in the scheduling literature as R∥Cmax. 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 and approximation algorithms. Computational experiments show that they outperform the most effective algorithms from the literature

Parallel machine scheduling subject to machine availability constraints

Cataloged from PDF version of article.Within a planning horizon, machines may become unavailable due to unexpected breakdowns or pre-scheduled activities. A realistic approach in constructing the production schedule should explicitly take into account such periods of unavailability. This study addresses the parallel machine-scheduling problem subject to availability constraints on each machine. The objectives of minimizing the total completion time and minimizing the maximum completion time are studied. The problems with both objectives are known to be NP-hard. We develop an exact branch-and-bound procedure and propose three heuristic algorithms for the total completion time problem. Similarly, we propose exact and approximation algorithms also for the maximum completion time problem. All proposed algorithms are tested through extensive computational experimentation, and several insights are provided based on computational results.Sevindik, KayaM.S

Random Keys Genetic Algorithms Scheduling and Rescheduling Systems for Common Production Systems

The majority of scheduling research deals with problems in specific production environments with specific objective functions. However, in many cases, more than one problem type and/or objective function exists, resulting in the need for a more generic and flexible system to generate schedules. Furthermore, most of the published scheduling research focuses on creating an optimal or near optimal initial schedule during the planning phase. However, after production processes start, circumstances like machine breakdowns, urgent jobs, and other unplanned events may render the schedule suboptimal, obsolete or even infeasible resulting in a rescheduling problem, which is typically also addressed for a specific production environment, constraints, and objective functions. This dissertation introduces a generic framework consisting of models and algorithms based on Random Keys Genetic Algorithms (RKGA) to handle both the scheduling and rescheduling problems in the most common production environments and for various types of objective functions. The Scheduling system produces predictive (initial) schedules for environments including single machines, flow shops, job shops and parallel machine production systems to optimize regular objective functions such as the Makespan and the Total Tardiness as well as non-regular objective functions such as the Total Earliness and Tardiness. To deal with the rescheduling problem, and using as a basis the same RKGA, a reactive Rescheduling system capable of repairing initial schedules after the occurrence of unexpected events is introduced. The reactive Rescheduling system was designed not only to optimize regular and non-regular objective functions but also to minimize the instability, a very important aspect in rescheduling to avoid shop chaos due to disruptions. Minimizing both schedule inefficiency and instability, however, turns the problem into a multi-objective optimization problem, which is even more difficult to solve. The computational experiments for the predictive model show that it is able to produce optimal or near optimal schedules to benchmark problems for different production environments and objective functions. Additional computational experiments conducted to test the reactive Rescheduling system under two types of unexpected events, machine breakdowns and the arrival of a rush job, show that the proposed framework and algorithms are robust in handling various problem types and computationally reasonable

Greedy randomized adaptive evolutionary path relinking aplicado a problemas de máquinas paralelas não relacionadas com recursos renováveis

Orientador: Prof. Dr. José Eduardo Pécora JuniorCoorientador: Prof. Dr. Maurício Guilherme de Carvalho ResendeDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa : Curitiba, 30/07/2020Inclui referências: p. 89-94Área de concentração: Programação MatemáticaResumo: Esta dissertação aborda o problema de máquinas paralelas não relacionadas, com restrição de recursos renováveis (UPMR), para minimizar o makespan. Para este problema é proposto um Greedy Randomized Adaptive Evolutionary Path-Relinking (GRAEPR) e uma abordagem híbrida com um modelo de programação por restrição (CP). Os resultados apresentam soluções competitivas com as presentes na literatura, estabelecendo alguns novos Lower e Upper Bounds. Além disso, é apresentada uma extensão para este problema. É introduzido o problema de máquinas paralelas não relacionadas, com setup dependente e restrição de recursos renováveis (UPMSR). Para este problema é apresentado um modelo de programação inteira mista (MILP), um modelo de programação por restrição e uma uma adaptação da abordagem de Fleszar e Hindi (2018). Além disso, são modificadas as abordagens do Greedy Randomized Adaptive Evolutionary Path-Relinking e híbrida desenvolvidas para o UPMR. Um conjunto de instâncias é gerada para UPMSR e os resultados evidenciam o potencial existente na abordagem GRAEPR. Palavras-chaves: Máquinas paralelas não relacionadas. Restrição de recursos Renováveis. Programação linear inteira mista. Programação por restrição. Path-relinking.Abstract: This thesis addresses the problem of unrelated parallel machines, with restriction of renewable resources (UPMR), to minimize the makespan. For this problem, a Greedy Randomized Adaptive Evolutionary Path-Relinking (GRAEPR) and a hybrid approach with a constraint programming (CP) model is proposed. The results show competitive solutions with those found in the literature, establishing some new values for Lower and Upper Bounds. In addition, an extension is presented for this problem. We introduce the problem of unrelated parallel machines, with dependent setup and restriction of renewable resources (UPMSR). For this problem, we present a mixed integer linear programming (MILP) model, a contraint programming (CP) model, and an adaptation of the approach of Fleszar and Hindi (2018). We also modify the Greedy Randomized Adaptive Evolutionary Path-Relinking and the hybrid approach developed for the UPMR. A set of instances is generated for UPMSR and the results show the potential that exists in the GRAEPR approach. Key-words: Unrelated parallel machines. Renewable resource constraint. Mixed-integer linear programming. Constraint programming. Path-relinkin