scholarly journals Agent Scheduling in Unrelated Parallel Machines with Sequence- and Agent–Machine–Dependent Setup Time Problem

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2955
Author(s):  
Jesús Isaac Vázquez-Serrano ◽  
Leopoldo Eduardo Cárdenas-Barrón ◽  
Rodrigo E. Peimbert-García
Keyword(s):  
Parallel Machines ◽  
Critical Role ◽  
Setup Time ◽  
Mixed Integer ◽  
Unrelated Parallel Machines ◽  
Manufacturing Companies ◽  
Time Problem ◽  
Medium Level ◽  
Agent Scheduling ◽  
Dependent Setup Times

Assignation-sequencing models have played a critical role in the competitiveness of manufacturing companies since the mid-1950s. The historic and constant evolution of these models, from simple assignations to complex constrained formulations, shows the need for, and increased interest in, more robust models. Thus, this paper presents a model to schedule agents in unrelated parallel machines that includes sequence and agent–machine-dependent setup times (ASUPM), considers an agent-to-machine relationship, and seeks to minimize the maximum makespan criteria. By depicting a more realistic scenario and to address this NP-hard problem, six mixed-integer linear formulations are proposed, and due to its ease of diversification and construct solutions, two multi-start heuristics, composed of seven algorithms, are divided into two categories: Construction of initial solution (designed algorithm) and improvement by intra (tabu search) and inter perturbation (insertions and interchanges). Three different solvers are used and compared, and heuristics algorithms are tested using randomly generated instances. It was found that models that linearizing the objective function by both job completion time and machine time is faster and related to the heuristics, and presents an outstanding level of performance in a small number of instances, since it can find the optimal value for almost every instance, has very good behavior in a medium level of instances, and decent performance in a large number of instances, where the relative deviations tend to increase concerning the small and medium instances. Additionally, two real-world applications of the problem are presented: scheduling in the automotive industry and healthcare.

scholarly journals MIP Models and Hybrid Algorithms for Simultaneous Job Splitting and Scheduling on Unrelated Parallel Machines

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Duygu Yilmaz Eroglu ◽  
H. Cenk Ozmutlu
Keyword(s):  
Genetic Algorithms ◽  
Local Search ◽  
Parallel Machines ◽  
Search Algorithm ◽  
Mixed Integer ◽  
Unrelated Parallel Machines ◽  
Job Splitting ◽  
Mip Models ◽  
Dependent Setup Times ◽  
Genetic Local Search

We developed mixed integer programming (MIP) models and hybrid genetic-local search algorithms for the scheduling problem of unrelated parallel machines with job sequence and machine-dependent setup times and with job splitting property. The first contribution of this paper is to introduce novel algorithms which make splitting and scheduling simultaneously with variable number of subjobs. We proposed simple chromosome structure which is constituted by random key numbers in hybrid genetic-local search algorithm (GAspLA). Random key numbers are used frequently in genetic algorithms, but it creates additional difficulty when hybrid factors in local search are implemented. We developed algorithms that satisfy the adaptation of results of local search into the genetic algorithms with minimum relocation operation of genes’ random key numbers. This is the second contribution of the paper. The third contribution of this paper is three developed new MIP models which are making splitting and scheduling simultaneously. The fourth contribution of this paper is implementation of the GAspLAMIP. This implementation let us verify the optimality of GAspLA for the studied combinations. The proposed methods are tested on a set of problems taken from the literature and the results validate the effectiveness of the proposed algorithms.

Uniform Parallel Machines Scheduling with Setup Time, Learning Effect, Machine Idle Time, and Processing Set Restrictions to Minimize Earliness/Tardiness Costs

2021 ◽  
pp. 107-133
Author(s):  
Javad Rezaeian ◽  
Keyvan Shokoufi ◽  
Reza Alizadeh Foroutan
Keyword(s):  
Parallel Machines ◽  
Simulated Annealing Algorithm ◽  
Heuristic Algorithms ◽  
Setup Time ◽  
Mixed Integer ◽  
Computational Time ◽  
Just In Time ◽  
Large Size ◽  
Parallel Machines Scheduling ◽  
Dependent Setup Times

Inspired by a real industrial case, this study deals with the problem of scheduling jobs on uniform parallel machines with past-sequence-dependent setup times to minimize the total earliness and tardiness costs. The paper contributes to the existing literature of uniform parallel machines problems by the novel idea of considering position-based learning effects along with processing set restrictions. The presented problem is formulated as a Mixed Integer linear programming (MILP) model. Then, an exact method is introduced to calculate the accurate objective function in the just-in-time (JIT) environments for a given sequence of jobs. Furthermore, three meta-heuristic approaches, (1) a genetic algorithm (GA), (2) a simulated annealing algorithm (SA), and (3) a particle swarm optimization algorithm (PSO) are proposed to solve large size problems in reasonable computational time. Finally, computational results of the proposed meta-heuristic algorithms are evaluated through extensive experiments and tested using ANOVA followed by t-tests to identify the most effective meta-heuristic.

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

2008 ◽  
Vol 35 (4) ◽  
pp. 1250-1264 ◽  
Author(s):  
Pedro Leite Rocha ◽  
Martín Gómez Ravetti ◽  
Geraldo Robson Mateus ◽  
Panos M. Pardalos
Keyword(s):  
Parallel Machines ◽  
Exact Algorithms ◽  
Setup Times ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines ◽  
Dependent Setup Times

scholarly journals Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Bailin Wang ◽  
Haifeng Wang
Keyword(s):  
Parallel Machines ◽  
Mixed Integer ◽  
List Scheduling ◽  
Unrelated Parallel Machines ◽  
Order Acceptance ◽  
Trade Off ◽  
Pareto Ranking ◽  
Machine Eligibility ◽  
Net Profit ◽  
Order Acceptance And Scheduling

This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms.

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