Modelling and solving algorithm for two-stage scheduling of construction component manufacturing with machining and welding process

This paper focuses on a two-stage machining and welding scheduling problem based on an investigation at a structural metal manufacturing plant, aiming to minimise the total makespan. Several parts processed at Stage one according to classical job-shop scheduling are grouped into a single construction component at the second welding stage. Fabrication of the construction component cannot begin until all comprising parts have been completed at Stage one. This paper establishes a novel mathematic model to minimise the total makespan by mainly considering the dominance relationship between the construction component and the corresponding parts. In order to solve this two-stage problem, we propose an improved harmony search algorithm. A local search method is applied to the best vector at each iteration, so that a more optimal vector can be subsequently realised. The average value, minimum value, relative percentage deviation and standard deviation are discussed in the experimental section, and the proposed local best harmony search algorithm outperforms the genetic algorithm, immune algorithm and harmony search algorithm without local search. Moreover, six optimal solutions are given as Gantt charts, which vividly illustrate that the mathematical model established in this paper can facilitate the development of a better scheduling scheme.     

A scatter search approach with dispatching rules for a joint decision of cell formation and parts scheduling in batches

A joint decision of cell formation and parts scheduling is addressed for a cellular manufacturing system where each type of machine and part may have multiple numbers and parts must require processing and transferring in batches. The joint decision problem is not only to assign batches and associated machine groups to cells, but also to sequence the processing of batches on each machine in order to minimise the total tardiness penalty cost. A nonlinear mixed integer programming mathematical model is proposed to formulate the problem. The proposed model, within nonlinear terms and integer variables, is difficult to solve efficiently for real size problems. To solve the model for practical purposes, a scatter search approach with dispatching rules is proposed, which considers two different combination methods and two improvement methods to further expand the conceptual framework and implementation of the scatter search so as to better fit the addressed problem. This scatter search approach interactively uses a combined dispatching rule to solve a scheduling sub-problem corresponding to each integer solution visited in the search process. A computational study is performed on a set of test problems with various dimensions, and computational results demonstrate the effectiveness of the proposed approach.     

Production scheduling optimization algorithm for the hot rolling processes

The hot rolling production scheduling problem is an extremely difficult and time-consuming process, so it is quite difficult to achieve an optimal solution with traditional optimization methods owing to the high computational complexity. To ensure the feasibility of solutions and improve the efficiency of the scheduling, this paper proposes a vehicle routing problem (VRP) to model the problem and develops an easily implemented hybrid approach (QPSO-SA) to solve the problem. In the hybrid approach, quantum particle swarm optimization (QPSO) combines local search and global search to search the optimal results and simulated annealing (SA) employs certain probability to avoid getting into a local optimum. The computational results from actual production data have shown that the proposed model and algorithm are feasible and effective for the hot rolling scheduling problem.     

A multi-objective optimisation model to integrating flexible process planning and scheduling based on hybrid multi-objective simulated annealing

Process planning and production scheduling play important roles in manufacturing systems. In this paper we present a mixed integer linear programming (MILP) scheduling model, that is to say a slot-based multi-objective multi-product, that readily accounts for sequence-dependent preparation times (transition and set up times or machine changeover time). The proposed scheduling model becomes computationally expensive to solve for long time horizons. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimisation problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for this, the hybrid multi-objective simulated annealing algorithm (MOHSA) is proposed by fully utilising the capability of the exploration search and fast convergence. Two numerical experiments have been performed to demonstrate the effectiveness and robustness of the proposed algorithm.     

Multiple-variable neighbourhood search for the single-machine total weighted tardiness problem

The single-machine total weighted tardiness (SMTWT) problem is a typical discrete combinatorial optimization problem in the scheduling literature. This problem has been proved to be NP hard and thus provides a challenging area for metaheuristics, especially the variable neighbourhood search algorithm. In this article, a multiple variable neighbourhood search (m-VNS) algorithm with multiple neighbourhood structures is proposed to solve the problem. Special mechanisms named matching and strengthening operations are employed in the algorithm, which has an auto-revising local search procedure to explore the solution space beyond local optimality. Two aspects, searching direction and searching depth, are considered, and neighbourhood structures are systematically exchanged. Experimental results show that the proposed m-VNS algorithm outperforms all the compared algorithms in solving the SMTWT problem.     

Job ordering and management of wearing tools

This article considers a scheduling problem arising in flexible manufacturing systems. It is assumed that a computer numerical control machine processes a set of jobs with a set of wearing tools. The tool magazine of the machine has a given capacity and each job requires some subset of tools. The goal is to minimize the average completion time of the jobs by choosing their processing order and the tool management decisions intelligently. Previous studies concerning this problem have either omitted the tool wearing or assumed only one tool type. This study gives a mathematical formulation for the problem when the tool lifetimes are deterministic. It is shown that problems of a practical size cannot be solved to optimality within a reasonable time. Therefore genetic algorithms and local search methods are considered to resolve the problem. When the solutions of these new algorithms are compared against the optimal solutions and lower bounds, they are nearly optimal.     

Bad-scenario-set robust scheduling for a job shop to hedge against processing time uncertainty

This paper proposed two robust scheduling formulations in real manufacturing systems based on the concept of bad scenario set to hedge against processing time uncertainty, which is described by discrete scenarios. Two proposed robust scheduling formulations are applied to an uncertain job-shop scheduling problem with the makespan as the performance criterion. The united-scenario neighbourhood (UN) structure is constructed based on bad scenario set for the scenario job-shop scheduling problem. A tabu search (TS) algorithm with the UN structure is developed to solve the proposed robust scheduling problem. An extensive experiment was conducted. The computational results show that the first robust scheduling formulation could be preferred to the second one for the discussed problem. It is also verified that the obtained robust solutions could hedge against the processing time uncertainty through decreasing the number of bad scenarios and the degree of performance degradation on bad scenarios. Moreover, the computational results demonstrate that the developed TS algorithm is competitive for the proposed robust scheduling formulations.     

基于瓶颈的制造单元两阶段群组调度程序与仿真

为解决具有瓶颈的制造单元调度问题,提出了一种以瓶颈为基础的两阶段群组调度方法.该方法充分运用瓶颈机器,使所有零件的最大完成时间最小化.为评估调度方法的绩效,文章建立了两阶段群组调度程序的5机制造单元仿真模型.仿真实验结果证明,本方法不仅平均总完工时间最短,而且是绩效表现最稳定的调度方法.     

A fuzzy approach for sequencing interrelated activities in a DSM

Production and manufacturing systems often involve a myriad of interrelated activities. How these activities are organised and scheduled has a significant effect on the success of a system. Recently, the Design Structure Matrix (DSM) has been regarded as an effective tool for modelling and scheduling interrelated activities. Based on fuzzy set theory, this study explicitly addresses the uncertain activity dependencies in our formulation and develops a mathematical model for sequencing interrelated activities in a DSM. Because of the complexity of the model, a new approach, which embeds an exact algorithm within a framework of a local search heuristic, is presented for solving large problem instances. Testing results demonstrate that relatively good solutions can be easily obtained by our approach, thereby providing managers with an effective tool for scheduling a large number of interrelated activities with uncertain dependencies.     

基于文化基因算法的开放车间调度问题研究

针对开放车间调度问题,运用了文化基因算法进行优化求解。在文化基因算法的框架中,既有种群中的全局搜索,又包含针对问题自身特点的局部搜索,为解决开放车间调度问题提供了一种新的算法。按照文化基因算法的思想和特点,将爬山法作为局部搜索策略加入到全局搜索策略所用到的遗传算法中,通过对开放车间调度问题的邻域结构进行研究,加入爬山搜索法进行优化求解。基于40个标准算例,通过与下界值的比较,验证了所提算法在解决具有较大搜索空间的调度问题时,其拥有更出色的算法性能。     

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.     

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.     

Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm

The integration of process planning and scheduling is considered as a critical component in manufacturing systems. In this paper, a multi-objective approach is used to solve the planning and scheduling problem. Three different objectives considered in this work are minimisation of makespan, machining cost and idle time of machines. To solve this integration problem, we propose an improved controlled elitist non-dominated sorting genetic algorithm (NSGA) to take into account the computational intractability of the problem. An illustrative example and five test cases have been taken to demonstrate the capability of the proposed model. The results confirm that the proposed multi-objective optimisation model gives optimal and robust solutions. A comparative study between proposed algorithm, controlled elitist NSGA and NSGA-II show that proposed algorithm significantly reduces scheduling objectives like makespan, cost and idle time, and is computationally more efficient.     

A review of the research methodology for the re-entrant scheduling problem

This paper considers the re-entrant scheduling problem, wherein the most remarkable character is that the jobs enter the processing lines more than once. The objective is to provide a comprehensive review which gives the researchers and practitioners an overview of the applicability of techniques in re-entrant scheduling. Few published reviews dealt with this particular kind of problem and only some research regards the re-entrant character as a hypotaxis of their main problems. This paper is the first paper that gives a full picture of the re-entrant scheduling problem. Considered as a NP-hard problem, a growing number of researchers have employed various methods to solve this complex problem. A survey has been conducted from the recently published literature on the re-entrant problem. This paper has summarised the problem and the relative research methodologies have been studied. Mathematical methods and meta-heuristics, especially Petri net, dispatching rules and genetic algorithm, emerge as the most frequently used methods in recent years, which are presented in detail. Moreover, future research implications have been identified and are suggested. It may help to bring in more awareness of the problem and new techniques to solve it.     

A hybrid nested partitions algorithm for scheduling flexible resource in flow shop problem

Production scheduling with flexible resources is critical and challenging in many modern manufacturing firms. This paper applies the nested partitions (NP) framework to solve the flexible resource flow shop scheduling (FRFS) problem using an efficient hybrid NP algorithm. By considering the domain knowledge, the ordinal optimisation principle and the NEH heuristics are integrated into the partitioning scheme to search the feasible region. An efficient resource-allocation procedure is built into the sampling scheme for the FRFS problem. A large number of benchmark examples with flexible resources are tested. The test results show that the hybrid NP algorithm is more efficient than either generic NP or heuristics alone. The algorithm developed in this study is capable of selecting the most promising region for a manufacturing system with a high degree of accuracy. The algorithm is efficient and scalable for large-scale problems.     

Multi-criteria optimisation-based dynamic scheduling for controlling FMS

This study deals with controlling flexible manufacturing systems (FMS) operating in volatile production environments. Most studies that address this issue use some sort of adaptive scheduling that enables the FMS to cope with the randomness and variability efficiently. The methods presented in the literature are usually based on heuristics and use simple dispatching rules. They do not consider changing the decision criteria dynamically as the system conditions change. In contrast to previous studies, the present study focuses on developing a control mechanism for dynamic scheduling that is based on incremental optimisation. This means that each time a scheduling decision is made, the local optimisation problem is solved such that the next jobs to be processed on machines are selected. The objective function (dominant decision criterion) for this optimisation problem is selected dynamically based on production order requirements, actual shop-floor status and system priorities. The proposed multi-criteria optimisation-based dynamic scheduling methodology was evaluated and compared with some known scheduling rules/policies. The results obtained demonstrate the superiority of the suggested methodology as well as its capability to cope with a multi-criteria environment.     

Re-entrant flow shop scheduling problem with time windows using hybrid genetic algorithm based on auto-tuning strategy

The re-entrant flow shop scheduling problem considering time windows constraint is one of the most important problems in hard-disc drive (HDD) manufacturing systems. In order to maximise the system throughput, the problem of minimising the makespan with zero loss is considered. In this paper, evolutionary techniques are proposed to solve the complex re-entrant scheduling problem with time windows constraint in manufacturing HDD devices with lot size. This problem can be formulated as a deterministic Fm?|?fmls, rcrc, temp?|?C_max problem. A hybrid genetic algorithm was used for constructing chromosomes by checking and repairing time window constraints, and improving chromosomes by a left-shift heuristic as a local search algorithm. An adaptive hybrid genetic algorithm was eventually developed to solve this problem by using fuzzy logic control in order to enhance the search ability of the genetic algorithm. Finally, numerical experiments were carried out to demonstrate the efficiency of the developed approaches.     

Tabu search for the job-shop scheduling problem with multi-purpose machines

In this paper we study the following generalization of the job-shop scheduling problem. Each operation can be performed by one machine out of a set of machines given for this operation. The processing time does not depend on the machine which has been chosen for processing the operation. This problem arises in the area of flexible manufacturing. As a generalization of the jobshop problem it belongs to the hardest problems in combinatorial optimization. We show that an application of tabu search techniques to this problem yields excellent results for benchmark problems.Supported by Deutsche Forschungsgemeinschaft, Project JoP-TAG     

Dynamic scheduling for complex engineer-to-order products

The current paper considers dynamic production scheduling for manufacturing systems producing products with deep and complex product structures and complicated process routings. It is assumed that manufacturing and assembly processing times are deterministic. Dynamic scheduling problems may be either incremental (where the schedule for incoming orders does not affect the schedule for existing orders) or regenerative (where a new schedule is produced for both new and existing orders). In both situations, a common objective is to minimize total costs (the sum of work-in-progress holding costs, product earliness and tardiness costs). In this research, heuristic and evolutionary-strategy-based methods have been developed to solve incremental and regenerative scheduling problems. Case studies using industrial data from a company that produces complex products in low volume demonstrate the effectiveness of the methods. Evolution strategy (ES) provides better results than the heuristic method, but this is at the expense of significantly longer computation times. It was found that performing regenerative planning is better than incremental planning when there is high interaction between the new orders and the existing orders.     

基于Lévy Flight的混合GA在柔性作业车间调度问题中的性能分析

近年来,柔性作业车间调度问题(FJSP)由于其NP难特性与在制造系统中的广泛应用被大量关注。为提高该类问题求解效率,本文在标准Lévy flight的基础上提出了一种新的离散Lévy flight搜索策略,并将该策略与遗传算法框架结合,形成一种离散Lévy flight策略的混合遗传算法。该混合算法通过使用离散Lévy flight搜索策略对每代精英种群进行变步长搜索,提高了算法的局部搜索能力,增强了种群多样性。本文通过将CS、GA和TLBO等经典算法作为对比算法,对不同规模的54个FJSP算例进行实验,证明了所提出的算法具备更好的收敛效果与稳定性,适合于求解大规模FJSP。