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.

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 Parallel machines scheduling with time-dependent deterioration, using meta-heuristic algorithms

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Jaber Kalaki Juybari ◽  
Somayyeh Kalaki Juybari ◽  
Reza Hasanzadeh
Keyword(s):  
Large Scale ◽  
Processing Time ◽  
Parallel Machines ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Time Dependent ◽  
Mixed Integer ◽  
Small Scale ◽  
Simulating Annealing ◽  
Parallel Machines Scheduling

AbstractIn this paper, we consider the identical parallel machines scheduling problem with exponential time-dependent deterioration. The meaning of time-dependent deterioration is that the processing time of a job is not a constant and depends on the scheduled activities. In other words, when a job is processed later, it needs more processing time compared to the jobs processed earlier. The main purpose is to minimize the makespan. To reach this aim, we developed a mixed integer programming formulation for the problem. We solved problem in small scale using GAMS software, while due to the fact that in larger scales the aforesaid case is a complex and intricate optimized problem which is NP-hard, it is not possible to solve it by standard calculating techniques (in logical calculating times); we applied the meta-heuristic genetic algorithm, simulating annealing and artificial immune system, and their performance has been evaluated. In the end, we showed that solving the problem in small scale, with the meta-heuristic algorithms (GA, SA, and AIS) equals the optimal solution (GAMS), And on a large scale, at a time of approximately equal solution, meta-heuristic algorithm simulating annealing, provides a more optimal solution.

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.

scholarly journals Variable Neighborhood Search for Parallel Machines Scheduling Problem with Step Deteriorating Jobs

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Wenming Cheng ◽  
Peng Guo ◽  
Zeqiang Zhang ◽  
Ming Zeng ◽  
Jian Liang
Keyword(s):  
Variable Neighborhood Search ◽  
Parallel Machines ◽  
Programming Model ◽  
Search Algorithm ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Mixed Integer ◽  
Computational Time ◽  
Neighborhood Search ◽  
Scheduling Problem

In many real scheduling environments, a job processed later needs longer time than the same job when it starts earlier. This phenomenon is known as scheduling with deteriorating jobs to many industrial applications. In this paper, we study a scheduling problem of minimizing the total completion time on identical parallel machines where the processing time of a job is a step function of its starting time and a deteriorating date that is individual to all jobs. Firstly, a mixed integer programming model is presented for the problem. And then, a modified weight-combination search algorithm and a variable neighborhood search are employed to yield optimal or near-optimal schedule. To evaluate the performance of the proposed algorithms, computational experiments are performed on randomly generated test instances. Finally, computational results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time even for large-sized problems.

scholarly journals Minimizing total tardiness for the order scheduling problem with sequence-dependent setup times using hybrid matheuristics

2022 ◽  
Vol 13 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Massimo Pinto Antonioli ◽  
Carlos Diego Rodrigues ◽  
Bruno de Athayde Prata
Keyword(s):  
Setup Times ◽  
Total Tardiness ◽  
Mixed Integer ◽  
Order Scheduling ◽  
Due Date ◽  
Customer Order ◽  
Large Size ◽  
Milp Model ◽  
Dependent Setup Times ◽  
Customer Order Scheduling

This paper aims at presenting a customer order scheduling environment in which the setup times are explicit and depend on the production sequence. The considered objective function is the total tardiness minimization. Since the variant under study is NP-hard, we propose a mixed-integer linear programming (MILP) model, an adaptation of the Order-Scheduling Modified Due-Date heuristic (OMDD) (referred to as Order-Scheduling Modified Due-Date Setup (OMMD-S)), an adaptation of the Framinan and Perez-Gonzalez heuristic (FP) (hereinafter referred to as Framinan and Perez-Gonzalez Setup (FP-S)), a matheuristic with Same Permutation in All Machines (SPAM), and the hybrid matheuristic SPAM-SJPO based on Job-Position Oscillation (JPO). The algorithms under comparison have been compared on an extensive benchmark of randomly generated test instances, considering two performance measures: Relative Deviation Index (RDI) and Success Rate (SR). For the small-size evaluated instances, the SPAM is the most efficient algorithm, presenting the better values of RDI and SR. For the large-size evaluated instances, the hybrid matheuristic SPAM-JPO and MILP model are the most efficient methods.

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