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Heuristics for an assembly flow-shop with non-identical assembly machines and sequence dependent setup times to minimize sum of holding and delay costs
... A variable neighbourhood search is also developed to solve the problem. Navaei et al. (2014) also study the same problem with Mozdgir et al. (2013) but to minimise the total holding and delay costs. They mathematically formulate the problem, yet a nonlinear model. ...
... After studying the literature, there is only one mathematical programming model which is in form of a mixed nonlinear programming model (Navaei et al., 2014). Since the effective mathematical models of scheduling problems are linear (Reisi-Nafchi and Moslehi, 2015;Tavakkoli-Moghaddam et al., 2010), it can be easily concluded that the available model is ineffective. ...
... For larger instances, there are two recent metaheuristics in the literature, VNS proposed by Mozdgir et al. (2013) and ICA proposed by Navaei et al. (2014). Their results show that more effective algorithm can be developed to solve this problem. ...
... A variable neighbourhood search is also developed to solve the problem. Navaei et al. (2014) also study the same problem with Mozdgir et al. (2013) but to minimise the total holding and delay costs. They mathematically formulate the problem, yet a nonlinear model. ...
... After studying the literature, there is only one mathematical programming model which is in form of a mixed nonlinear programming model (Navaei et al., 2014). Since the effective mathematical models of scheduling problems are linear (Reisi-Nafchi and Moslehi, 2015;Tavakkoli-Moghaddam et al., 2010), it can be easily concluded that the available model is ineffective. ...
... For larger instances, there are two recent metaheuristics in the literature, VNS proposed by Mozdgir et al. (2013) and ICA proposed by Navaei et al. (2014). Their results show that more effective algorithm can be developed to solve this problem. ...
... The authors considered the model divided into two submodels and used the hybrid genetic algorithm (HGA) as a solution method. Navaei et al. (2014) presented a study for a problem defined as a two-stage assembly flow shop scheduling problem (TSAFSP) and considered setup times in both stages. The authors presented mixed-integer nonlinear programming (MINLP) and various heuristics and combinations between them, such as simulated annealing (SA) and an imperialist competitive algorithm (ICA). ...
... The authors presented mixed-integer nonlinear programming (MINLP) and various heuristics and combinations between them, such as simulated annealing (SA) and an imperialist competitive algorithm (ICA). This study by Navaei et al. (2014) is an offshoot of another study conducted in the same ...
... For the objective makespan, Navaei, et al. (Navaei, Ghomi, Jolai, Shiraqai, & Hidaji, 2013) addressed multiple non-identical machines in the assembly stage and developed a MILP model and a hybrid simulated annealing algorithm (SA) to minimize the makespan. Based on this above research, Navaei, et al. (Navaei, Ghomi, Jolai, & Mozdgir, 2014) further considered sequence-dependent setup times into assembly flow shop with no-identical assembly machines. To solve this strong NP-hard problem, they extended the original model, and also developed four meta-heuristics including two versions of SA and two versions of the imperialist competitive algorithm (ICA). ...
... Mozdgir, et al. (Mozdgir, Ghomi, Jolai, & Navaei, 2013) addressed non-identical assembly machines and setup times and developed a hybrid variable neighborhood search (VNS) algorithm to minimize the total completion time and makespan. Navaei, et al. (Navaei et al., 2014) aimed to minimize the sum of delay and holding cost of two-stage non-identical assembly flow shop with setup times, and developed four meta-heuristics including two versions of SA and two versions of the imperialist competitive algorithm. Kazemi, Mazdeh and Rostami (Kazemi, Mazdeh, & Rostami, 2017) investigated a batched delivery system in two-stage multi-machine assembly flow shop scheduling. ...
In this paper, preventive maintenance (PM) activities are incorporated into two-stage assembly flow shop scheduling where m1 dedicated machines in fabrication stage and m2 machines in assembly stage. Each machine is given a new feature maintenance level, whose initial value is determined based on the Weibull probability distribution. To ensure the machines’ reliability and production continuity, we need to find a fit product sequence along with PM execution time points. Hence this paper tries to tackle this new integration problem by a mixed integer linear programming model, two heuristics MCMTPM and NEHPM, and a PM-based iterated greedy algorithm (IGPM). IGPM is embedded with a problem-specific solution evaluation and two types of local search methods. The final experimental results show that compared with the other 9 state-of-the-art methods, the proposed IGPM embedded with NEHPM and reference local search generates the best results in all benchmark instances.
... Yoon, Lee, and Sung (2007) proved the reversibility of AF(m,1), that is, job sequence in the assembly system has the same makespan as that of its reverse sequence in the disassembly system. Navaei et al. (2014) studied AF(m 1 , m 2 ) with single assembly level products that are assembled on non-identical machines with sequence-dependent set-up times. They also proposed SA enhanced with a heuristic algorithm that assigns operations to the assembly machines. ...
... 3.2. Most of the studies consider identical machines in the second stage and there is no study regarding nonidentical assembly machines except Navaei et al. (2013Navaei et al. ( , 2014. Besides, there is no study that considers flexible machines in both machining and assembly stages at the same time. ...
The past few years have witnessed a resurgence of interest in assembly flow shop scheduling as evidenced by increasing number of published articles in this field. A basic assembly flow shop consists of two types of stages: fabrication or machining stage and assembly stage. Machining and assembly stages are composed of either one or a set of machines that are working in parallel. Final products have hierarchical assembly structure with several components and assembly operation(s). The components need to be processed in the machining stage(s) and then assembled based on hierarchical assembly structure. The goal is to find the sequence of jobs that optimises certain objectives. Assembly flow shop scheduling problem has several interesting derivatives and applications in various manufacturing and service industries. This paper provides a consolidated survey of assembly flow shop models with their solution methodology. Finally, the paper concludes by presenting some problems receiving less attention and proposes several salient research opportunities.
... Non-linear programming model Mansouri et al. (2007Mansouri et al. ( , 2009 EMA Nagano et al. (2014) m (no-wait) Cmax A hybrid evolutionary cluster search metaheuristic Nagano et al. (2015) m (no-wait) ࢣC j A new constructive heuristic Navaei et al. (2014) 2 (assembly flowshop) Sum of holding and delay costs Metaheuristics including SA Nishi et al. (2011) m ࢣw j T j Column generation algorithm Nishi and Hiranaka (2013) m ࢣw j T j Lagrangian relaxation and cut generation, dynamic programming Pargar and Zandieh (2012) m (flexible) F l (Cmax, ࢣT j ) Mathematical model, A metaheuristic approach called water flow like Qian et al. (2011) m (no-wait, r j ) ࢣC j Hybrid DE Rabiee et al. (2012) 2 (no-wait, probable rework) ࢣC j Adapted imperialist competitive algorithm Rabiee et al. (2014) 2 (flexible, no-wait, probable rework) ...
... They proposed a GA hybridized with problem knowledge-based heuristics and showed that it is efficient by computational experiments. On the other hand, Navaei et al. (2014) proposed hybrid metaheuristics, including SA, for the problem of AF2/ST sd /C max where there exist more than one machine at the second stage and where the objective is to minimize the sum of holding and delay costs. Mozdgir et al. (2013) addressed the problem of AF2/ST sd /F l (C max , ࢣC j ) such that there are a number of non-identical machine at the second stage. ...
Scheduling involving setup times/costs plays an important role in today's modern manufacturing and service environments for the delivery of reliable products on time. The setup process is not a value added factor, and hence, setup times/costs need to be explicitly considered while scheduling decisions are made in order to increase productivity, eliminate waste, improve resource utilization, and meet deadlines. However, the vast majority of existing scheduling literature, more than 90 percent, ignores this fact. The interest in scheduling problems where setup times/costs are explicitly considered began in the mid-1960s and the interest has been increasing even though not at an anticipated level. The first comprehensive review paper (Allahverdi et al., 1999) on scheduling problems with setup times/costs was in 1999 covering about 200 papers, from mid-1960s to mid-1988, while the second comprehensive review paper (Allahverdi et al., 2008) covered about 300 papers which were published from mid-1998 to mid-2006. This paper is the third comprehensive survey paper which provides an extensive review of about 500 papers that have appeared since the mid-2006 to the end of 2014, including static, dynamic, deterministic, and stochastic environments. This review paper classifies scheduling problems based on shop environments as single machine, parallel machine, flowshop, job shop, or open shop. It further classifies the problems as family and non-family as well as sequence-dependent and sequence-independent setup times/costs. Given that so many papers have been published in a relatively short period of time, different researchers have addressed the same problem independently, by even using the same methodology. Throughout the survey paper, the independently addressed problems are identified, and need for comparing these results is emphasized. Moreover, based on performance measures shop and setup times/costs environments, the less studied problems have been identified and the need to address these problems is specified. The current survey paper, along with those of Allahverdi et al. (1999, 2008), is an up to date survey of scheduling problems involving static, dynamic, deterministic, and stochastic problems for different shop environments with setup times/costs since the first research on the topic appeared in the mid-1960s.
... Because of the complexity of the assembly process of the products such as automobile engines [66], some researchers considered the flexible assembly process in the literature, i.e., the assembly operation is done with multiple machines [67][68][69]. This extension is added to the distributed scheduling problems by [70,71]. ...
... As stated by Framinan et al. [8], two-stage ASP with DPm → 1 layout, in which m dedicated parallel machines are for fabrication and one assembly machine is for assembly, has been extensively considered, and various methods including exact method, heuristic and meta-heuristic have been successfully used [10][11][12][13][14]. Meta-heuristics have become the scheduling problems [17,18,[35][36][37][38][39][40][41][42]. Regarding distributed scheduling, Marandi and Fatemi Ghomi [43] studied distributed scheduling together with a vehicle routing problem and developed an improved ICA after a mathematical model was provided. ...
The real-life assembly production often has transportation between fabrication and assembly, and the capacity of transportation machine is often considered; however, the previous works are mainly about two-stage distributed assembly scheduling problems. In this study, a distributed energy-efficient assembly scheduling problem (DEASP) with transportation capacity is investigated, in which dedicated parallel machines with symmetry under the given conditions, transportation machines and an assembly machine are used. An adaptive imperialist competitive algorithm (AICA) is proposed to minimize makespan and total energy consumption. A heuristic and an energy-saving rule are used to produce initial solutions. An adaptive assimilation with adaptive global search and an adaptive revolution are implemented, in which neighborhood structures are chosen dynamically, and revolution probability and search times are decided by using the solution quality. The features of the problem are also used effectively. Computational experiments are conducted on a number of instances. The computational results demonstrate that the new strategies of AICA are effective and efficient and AICA can provide promising results for the considered DEASP.
... Computational results reveal the effectiveness of the proposed approach. Navaei et al. (2014) proposed a two-stage flow shop problem with sequence-dependent setup times to minimize inventory carrying (finished goods inventory) and tardiness costs. Simulated annealing (SA) and imperialist competitive algorithms (ICA) were applied to address the optimization problem. ...
This paper addresses the joint optimization model of production scheduling, work-in-process (WIP) inventory control and group preventive maintenance (PM) planning in a multi-machine system with multi-components. The objective is to obtain optimum production sequence, PM intervals and grouping of components, which minimize the total expected cost per unit time of the system. A new meta-heuristic named Jaya algorithm and two popular algorithms viz. simulated annealing (SA) and particle swarm optimization (PSO) are applied to optimize the objective function. Initially, the optimum group of components is obtained based on the integer multiples of individual PM intervals. Secondly, the job permutation sequence incorporating group PM intervals is identified with the largest order value (LOV) rule. The shift in optimum PM intervals is realized with an advanced-postpone balancing approach. Computational results reveal that the proposed integrated model along with group PM yields up to 25% cost reductions when compared to the integrated model with individual maintenance as well as 37% savings while no integration is performed. Furthermore, the performance of algorithms is evaluated with large-sized problems. The obtained results show that Jaya and SA yielded comparable results, however, PSO is least productive. Thus, the proposed approach yields better economic performance and brings more improvised solutions as compared to the conventional methods of integrated scheduling and maintenance optimization problems.
... Furthermore, studies have likewise been investigated on other objectives such as costs and orders lead time. Navaei et al. (2014) addressed two-stage assembly flow shop scheduling with non-identical assembly machines at the second stage and setup times to minimize a sum of holding and delay costs. Blocher and Chhajed (2007) aimed to minimize customer order lead time of the two-stage assembly supply chain. ...
In this paper, flexible preventive maintenance (PM) activities are incorporated into two-stage assembly flow shop scheduling where m dedicated machines in the fabrication stage and one machine in the assembly stage. The operational status of each machine is described by a continuous variable, maintenance level. The maintenance level value is inversely proportional to the processing time. Once a PM activity is performed, this value will return to the initial value. Different from the PM at fixed predefined time intervals, flexible PM can be carried out at any time point, but the maintenance levels are not less than 0. Hence, a MILP model with maintenance level constraints is formulated to minimize the total completion time and maintenance time. Regarding the methods, a latest PM decision strategy is proposed to determine the execution time of PM activities. This new strategy is embedded into 15 constructive heuristics and 7 meta-heuristics (three variants of iterated local search, three variants of Q-learning-based ant colony system with local search and a Q-learning-based hyper-heuristics) to address this new problem. The final experimental analysis demonstrates the significance of the integrated model and the effectiveness of the proposed constructive heuristics and meta-heuristics.
... Variable Neighborhood Search (VNS) 12 . Hybrid Particle Swarm Optimization and Simulated Annealing(HPSOSA) 13 . Hybrid Genetic Algorithm and Tabu Search (HGATS) 14 . ...
در این مقاله مسئلهی زمانبندی تولید کارگاهی انعطافپذیر با یک مرحلهی مونتاژ و زمان آمادهسازی وابسته به توالی با هدف کمینهسازی زمان تکمیل محصولات مورد بررسی قرار میگیرد. این مسئله، مدلی از سیستمهای تولیدی است که در آن هر محصول از مونتاژ مجموعهیی از قطعات مختلف تولید میشود. در ابتدا، یک مدل برنامهریزی خطی عدد صحیح مختلط توسعه داده شده است. اعتبارسنجی مدل ریاضی پیشنهادی با استفاده از نرمافزار گمز و بهازای مسائل کوچک و متوسط انجام شده است. سپس با توجه به اینکه مسئلهی مورد بررسی NP-hard است، الگوریتم بهینهسازی ازدحام ذرات و دو الگوریتم فراابتکاری ترکیبی برای حل مسائل در ابعاد متوسط و بزرگ پیشنهاده است. نتایج عددی الگوریتمهای پیشنهادی با الگوریتم ترکیبی لی و گائو مقایسه شده است. نتایج محاسباتی نشان میدهد که در ابعاد متوسط و بزرگ مسئله، الگوریتم ترکیبی بهینهسازی ازدحام ذرات و جستوجوی همسایگی متغیر نسبت به سایر الگوریتمها عملکرد بهتری دارد.
... They presented an efficient hybrid genetic algorithm. Navaei et al. (2014) proposed hybrid metaheuristics for the two-stage assembly flowshop scheduling problem with multi machines at the second stage. They also considered sequence-dependent set-up times and the objective is to minimise the sum of holding and delay costs. ...
This paper addresses a two-stage assembly flowshop scheduling problem with the objective of minimising maximum tardiness where set-up times are considered as separate from processing times. The performance measure of maximum tardiness is important for some scheduling environments, and hence, it should be taken into account while making scheduling decisions for such environments. Given that the problem is strongly NP-hard, different algorithms have been proposed in the literature. The algorithm of Self-Adaptive Differential Evolution (SDE) performs as the best for the problem in the literature. We propose a new hybrid simulated annealing and insertion algorithm (SMI). The insertion step, in the SMI algorithm, strengthens the exploration step of the simulated annealing algorithm at the beginning and reinforces the exploitation step of the simulated annealing algorithm towards the end. Furthermore, we develop several dominance relations for the problem which are incorporated in the proposed SMI algorithm. We compare the performance of the proposed SMI algorithm with that of the best existing algorithm, SDE. The computational experiments indicate that the proposed SMI algorithm performs significantly better than the existing SDE algorithm. More specifically, under the same CPU time, the proposed SMI algorithm, on average, reduces the error of the best existing SDE algorithm over 90%, which indicates the superiority of the proposed SMI algorithm.
... Solano-Charris et al. (2009) studied the same problem and chose the objective of minimizing both makespan and total completion time and proposed an ant colony optimization method. Navaei et al. (2014) for the first time, chose the objective function of minimizing sum of holding and delay costs in the assembly flow-shop with non-identical assembly machines and sequence dependent setup times. They developed four hybrid meta-heuristics based simulated annealing (SA) and the imperialist competitive algorithm (ICA). ...
This paper investigates the two-stage assembly flow shop scheduling problem with a batched delivery system where there are m independent machines at the first stage doing the components of a job and multiple identical assembly machines at the second stage, each of which can assemble the components and complete the job. The objective is to schedule the jobs, to form them into batches so as to minimize the sum of tardiness plus delivery costs. To the best of our knowledge, the assembly flow shop scheduling problem with this objective function has not been addressed so far. A mathematical model for this problem is presented. However, due to the fact that this model happens to be a mixed integer nonlinear programming model and cannot guarantee to reach the solution at reasonable time we developed the imperialist competitive algorithm (ICA) and a hybrid algorithm (HICA) by incorporating the dominance relations. Computational results show that HICA performs better than ICA with respect to the value of the objective function, However the runtime of the ICA is less than HICA.
... Computational experiments revealed that the hybrid VNS heuristic performed much better than GAMS with respect to the percentage errors and run times. Navaei, Fatemi Ghomi, Jolai, and Mozdgir (2014) addressed a two-stage assembly flow-shop scheduling problem with non-identical assembly machines at the second stage to minimize a sum of holding and delay costs, and sequence dependent setup times were considered for both stages. They developed four hybrid meta-heuristics to solve the addressed problem. ...
Numerous operational constraints within both industry and service sectors mandate the concurrent scheduling of tasks. This need is particularly evident in the assembly of products within manufacturing processes. This paper concentrates on minimizing makespan in the two-stage assembly flow shop problem. Our contributions include the introduction of novel dominance rules, a proposal for a heuristic method, and the development of a branch and bound algorithm. Additionally, we conduct an empirical analysis of makespan distribution for small-size instances. Through extensive experimentation, our study demonstrates the efficiency of the introduced dominance rules and the strong performance of the developed branch and bound algorithm.
Distributed three-stage assembly scheduling problem extensively exists in the real-life assembly production process and is seldom considered. The integration of reinforcement learning with meta-heuristic can effectively improve the performance of meta-heuristic and effectively solve the problem; however, the integration is seldom used to cope with the problem. In this study, distributed three-stage assembly scheduling problem with DPm→1 layout and maintenance at three stages is considered and a mathematical model is provided. A new artificial bee colony with Q-learning (QABC) is proposed to minimize maximum tardiness. An effective Q-learning algorithm is implemented to dynamically select search operator, which consists of 12 states based on population quality evaluation, 8 actions defined by global search and neighborhood search, a new reward and an effective action selection. Two employed bee swarms are formed, an adaptive communication and an adaptive competition process between them are adopted to intensify exploration ability and improve search efficiency. QABC and its four comparative algorithms are tested on 80 instances. The computational results demonstrate that the new strategies of QABC really improve its search performance and QABC is a competitive algorithm for the considered problem.
Assembly flow shop scheduling problem with DPm → 1 layout has important applications in various manufacturing systems and has been extensively considered in single factory; however, this problem with fuzzy processing time is seldom studied in multiple factories. In this paper, fuzzy distributed assembly flow shop scheduling problem (FDAFSP) is considered, in which each factory has DPm → 1 layout, and an imperialist competitive algorithm with empire cooperation (ECICA) is developed to minimize fuzzy makespan. In ECICA, an adaptive empire cooperation between the strongest empire and the weakest empire is implemented by exchanging computing resources and search ability, historical evolution data are used and a new imperialist competition is adopted. Numerical experiments are conducted on various instances and ECICA is compared with the existing methods to test its performance. Computational results demonstrate that ECICA has promising advantages on solving FDAFSP.
Two-stage assembly flow shop scheduling problem with D P m → 1 layout has been extensively considered in single factory; however, distributed two-stage assembly flow shop scheduling problem (DTAFSP) with D P m → 1 layout in each factory is not studied fully; moreover, teaching-learning-based optimisation is seldom used to solve DTAFSP. In this paper, a cooperated teaching-learning-based optimisation (CTLBO) is proposed to minimise makespan. Multiple classes are constructed. The whole search procedure consists of two stages and each stage possesses two teacher's phases and a learner phase. Class cooperation between the best class and the worst one is implemented by exchanging search times and search ability at the second stage and seldom adopted in the existing works. Extensive experiments are conducted and CTLBO is compared with the existing methods to test its performances. Computational results demonstrate that CTLBO has very competitive performances on solving the considered DTAFSP.
Production scheduling is one of the most critical issues in manufacturing and production systems and has markedly positive impact on the performances of manufacturing. In the past decades, various scheduling problems have been extensively solved by multi-population meta-heuristics, which are artificial bee colony (ABC), imperialist competitive algorithm (ICA) and shuffled frog-leaping algorithm (SFLA); however, the related works of multi-population meta-heuristics to scheduling are hardly reviewed. In this paper, we provide an extensive recall on solving production scheduling based on ABC, ICA or SFLA. A new classification on scheduling problems is first given, then three algorithms are described and their applications to scheduling are summarized in a systematic way; finally, the main conclusions are drawn and some future research directions are presented.
Flow shop scheduling is a type of scheduling where sequence follows for each job on a set of machines for processing. In practice, jobs in flow shops can arrive at irregular times, and the no-wait constraint allows the changes in the job order to flexibly manage such irregularity. The flexible flow shop scheduling problems with no-wait have mainly addressed for flow optimization on the shop floor in manufacturing, processing, and allied industries. The scope of this paper is to identify the literature available on permutation and non-permutation flow shop scheduling with no-wait constraint. This paper organizes scheduling problems based on performance measures of variability and shop environments. The extended summary of two/three-machine and m-machine problems has been compiled, including their objectives, algorithms, parametric considerations, and their findings. A systematic appearance of both conceptual and analytical results summarizes various advances of the no-wait constraint. The paper includes independently investigated problems and suggestions for future research directions.
Purpose
In real manufacturing systems, schedules are often disrupted with uncertainty factors such as random machine breakdown, random process time, random job arrivals or job cancellations. This paper aims to investigate robust scheduling for a two-stage assembly flow shop scheduling with random machine breakdowns and considers two objectives makespan and robustness simultaneously.
Design/methodology/approach
Owing to its structural and algorithmic complexity, the authors proposed imperialist competitive algorithm (ICA), genetic algorithm (GA) and hybridized with simulation techniques for handling these complexities. For better efficiency of the proposed algorithms, the authors used artificial neural network (ANN) to predict the parameters of the proposed algorithms in uncertain condition. Also Taguchi method is applied for analyzing the effect of the parameters of the problem on each other and quality of solutions.
Findings
Finally, experimental study and analysis of variance (ANOVA) is done to investigate the effect of different proposed measures on the performance of the obtained results. ANOVA's results indicate the job and weight of makespan factors have a significant impact on the robustness of the proposed meta-heuristics algorithms. Also, it is obvious that the most effective parameter on the robustness for GA and ICA is job.
Originality/value
Robustness is calculated by the expected value of the relative difference between the deterministic and actual makespan.
This article proposes hybrid branch and bound algorithms to minimise the makespan for the two-stage assembly scheduling problem with separated setup times. In the studied problem, there are multiple machines at the first stage, each of which produces a component of a job. When all components are available, a single assembly machine at the second stage completes the job. Existing algorithms are based on the state space search and hence suffer from the state space explosion problem. In order to reduce the search space, lower and upper bounds for a partial schedule are proposed. Also, a heuristic function and a dominance rule are developed to guide the search process. Moreover, accelerated factors are introduced to increase the speed of the search. Experimental results indicate that our algorithms outperform an existing method, and can find the optimal or near-optimal schedules in a short time for all tested problems with up to ten thousand jobs and nine first-stage machines.
Two-stage assembly flow shops are integral part of several manufacturing systems such as computer and engine manufacturing lines. This paper explores three objectives of makespan, total tardiness, and total completion times for two-stage assembly flow shop with release time. To the best of our knowledge, these performance measures have not been addressed simultaneously in assembly flow shops. We derive polynomial optimal solutions for special cases of this problem with a single objective and then develop heuristics with promising starting solutions for the multi-objective case. Due to NP-hardness of the problem, we apply a customized reference-based Non-dominated Sorting Genetic Algorithm (NSGA-III) and Multi-Objective Particle Swarm Optimization (MOPSO) as solution procedures. Finally, we present extensive computational analysis to compare the performance of employed heuristic and metaheuristics on randomly generated instances. Results show that both NSGA-III and MOPSO generate competitive solutions for the presented problem. However, NSGA-III generates significantly better results than MOPSO based on one of the three performance metrics.
Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult.
In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.
To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.
MCDA methods become increasingly popular in energy decision-making due to their capability to deal with complex decision processes, in face of multiple and conflicting evaluation criteria (of technical, economic, environmental and social nature), different stakeholders with different views and preferences, several sources of uncertainty and distinct time frames. Literature reviews with specific focuses on the use of MCDA in energy problems have been reported. Hobbs and Meier (2000) provide a wide review of MCDM methods and energy-environment applications. Greening and Bernow (2004) describe a modeling framework incorporating developments in integrated assessment of energy and environmental issues, and suggest a strategy for developing a set of coordinated policies from varying levels of information about policy attributes and DM’s preferences. Pohekar and Ramachandran (2004) review the application of various MCDM methods in the framework of sustainable energy planning. Løken (2007) provide an overview of some of the most relevant MCDA methods proposed in the literature. Mirakyan and Guio (2013) present a review of methods and tools for integrated energy planning in cities and territories, concluding that the purpose of MCDA methodologies is not just required to define the “right” energy plan but rather to support the understanding of the multi-criteria complex situation that supports interactive planning and learning, helping people to systematically consider, articulate and apply value judgments.
The poblems most often dealt with with MCDA approaches are:
- Comparison of power generation technologies, involving the appraisal of available primary energy sources and technological options, considering conventional technologies and/or renewable energy technologies.
- Formulation and development of energy plans and policies, involving the choices faced by energy planners at the national, regional or local level seeking to identify the most desired one among alternative scenarios, taking into account the public debate on energy policy, energy conservation strategies and energy resource allocation issues.
- Selection of energy projects, namely concerning renewable energy investments for electricity generation.
- Location decisions, namely focussing on the siting of new wind farms and hydro and thermal power plants, also complemented with choices regarding operational parameters.
- Energy efficiency studies, mainly devoted to the evaluation of energy efficiency measures and programs either in technology replacement or building refurbishment.
In this paper, a two-stage assembly scheduling problem is considered with the objective of minimizing the total weighted flowtime. A lower bounding procedure and a dominance criterion are developed and incorporated into a branch and bound procedure. A heuristic procedure is also used to derive an initial upper bound. Computational results of the algorithm are presented. The two-stage assembly scheduling problem is a generalization of the two-machine flowshop problem, which has received attention in the literature recently. In the first stage, there are m - 1 machines assigned to produce m - 1 different types of component, which is required for each job. In the second stage, an assembly machine is used to assemble the components. Each machine can process only one job at any time. The objective is to minimize the sum of weighted completion times (total weighted flowtime) of all jobs. We develop a branch and bound algorithm to solve the problem. Lower bounds and a dominance criterion are incorporated in the algorithm to improve its efficieny. We also conduct computational experiments, which show that the algorithm can solve moderate sized problems in reasonable amount of time. The algorithm could be used to provide a benchmark for the evaluation of heuristics for larger sized problems. This problem appears in many real world situations. Examples are plenty in papers published by prominent researchers.
This paper introduces a new two-stage assembly scheduling problem. There are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule jobs on the machines so that the makespan is minimized. We show that the search for an optimal solution may be restricted to permutation schedules. The problem is proved to be NP-hard in the strong sense even when m=2. A schedule associated with an arbitrary permutation of jobs is shown to provide a worst-case ratio bound of two, and a heuristic with a worst-case ratio bound of 2-1/m is presented. The compact vector summation technique is applied for finding approximation solution with worst-case absolute performance guarantees.
In this paper, we address the two-stage assembly flowshop scheduling problem with a weighted sum of makespan and mean completion
time criteria, known as bicriteria. Since the problem is NP-hard, we propose heuristics to solve the problem. Specifically,
we propose three heuristics; simulated annealing (SA), ant colony optimization (ACO), and self-adaptive differential evolution
(SDE). We have conducted computational experiments to compare the performance of the proposed heuristics. It is statistically
shown that both SA and SDE perform better than ACO. Moreover, the experiments reveal that SA, in general, performs better
than SDE, while SA consumes less CPU time than both SDE and ACO. Therefore, SA is shown to be the best heuristic for the problem.
In this paper, we consider a three-stage assembly flowshop scheduling problem with bi-objectives, namely the mean flow time
and maximum tardiness. This problem can be considered as a production system model consisting of three stages: (1) different
production operations are done in parallel, concurrently and independently, (2) the manufactured parts are collected and transferred
to the next stage, and (3) these parts are assembled into final products. In this paper, sequence-dependent setup times and
transfer times are also considered as two important presumptions in order to make the problem more realistic. We present a
novel mathematical model for a production system with a new lower bound for the given problem. Obtaining an optimal solution
for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization
tools is extremely difficult. Thus, we propose two meta-heuristics, namely simulated annealing and tabu search, to solve a
number of test problems generated at random. Finally, the computational results are illustrated and compared in order to show
the efficiency of the foregoing meta-heuristics.
KeywordsAssembly flowshop scheduling-Mean flow time-Maximum tardiness-Sequence-dependent setup times-Simulated annealing-Tabu search
This paper considers the m-machine no-wait flowshop problem with the objective of minimizing the maximum lateness where setup times are considered as
separate from processing times and treated as sequence-independent. A dominance relation is developed for the case of three
machines and several heuristics and four new effective and efficient genetic algorithms are proposed. The genetic algorithms
make use of advanced concepts like steady-state and elitist generational scheme as well as new fast-selection operators. Extensive
experimentation is conducted to evaluate the performance of the dominance rule, the proposed heuristics, and the genetic algorithms.
The computational and statistical analyses by means of experimental designs show that the genetic algorithms provide better
results than the existing literature under the same conditions. Additionally, the proposed dominance rule shows great potential
for instances where the processing and setup times are tightly distributed.
We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.
In a recent paper we introduced the queue-and-idleness-ratio (QIR) family of routing rules for many- server service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, QIR produces an important state-space collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That state-space collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of QIR stochastically minimizes convex holding costs in a finite-horizon setting when the service rates are restricted to be pool-dependent. Under additional regularity conditions, the special version of QIR reduces to a simple policy: Linear costs produce a priority-type rule, in which the least-cost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a many-server analogue of the generalized-c" (Gc") rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.
In this paper, genetic algorithm (GA) and simulated annealing (SA) with improved bottom left (BL) algorithm were applied to two-dimensional non-guillotine rectangular packing problems. The performance and efficiency of these algorithms on several test problems [Hopper, E., Turton, B.C.H., 2000. An empirical investigation of meta-heuristic and heuristic algorithms for two-dimensional packing problem. European Journal of Operational Research 128 (1), 34–57] were compared. These test problems consist of 17 and 29 individual rectangular pieces to place in main object limited with a size of 200×200 units. Both solution approaches were compared, based on the trim losses of the test problems. Also, the influences of the GA parameters (population sizes, mutation rates, crossover techniques) and of the SA parameters (cooling schedules, neighborhood moves, the number of inner loop, different temperature values) on the solution of these problems were examined. For considering all solutions of the test problems, the hybrid GA produces much better results than the hybrid SA.
Clustering techniques have received attention in many fields of study such as engineering, medicine, biology and data mining. The aim of clustering is to collect data points. The K-means algorithm is one of the most common techniques used for clustering. However, the results of K-means depend on the initial state and converge to local optima. In order to overcome local optima obstacles, a lot of studies have been done in clustering. This paper presents an efficient hybrid evolutionary optimization algorithm based on combining Modify Imperialist Competitive Algorithm (MICA) and K-means (K), which is called K-MICA, for optimum clustering N objects into K clusters. The new Hybrid K-ICA algorithm is tested on several data sets and its performance is compared with those of MICA, ACO, PSO, Simulated Annealing (SA), Genetic Algorithm (GA), Tabu Search (TS), Honey Bee Mating Optimization (HBMO) and K-means. The simulation results show that the proposed evolutionary optimization algorithm is robust and suitable for handling data clustering.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
The paper considers a flowshop scheduling problem of a manufacturing cell that contains families of jobs whose setup times are dependent on the manufacturing sequence of the families. Two objectives, namely the makespan and total flow time, have been considered simultaneously in this work. Since minimisation of each of these two objectives is an Np-Hard problem, a Multi-Objective Genetic Algorithm (MOGA) has been proposed to deal with the bi-criteria optimisation problem. The performance of the proposed MOGA is compared with the makespan and total flow time lower bounds. The proposed MOGA obtained solutions that only deviate by an average of 1% from the lower bounds. Future research will develop more efficient lower bounds for the total flow time and also compare the proposed method with other multiobjective meta-heuristics. [Received on 6 February 2007; Revised 6 June 2007; Accepted 16 June 2007]
e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the common due date, and scheduling job delivery, we consider the option of performing a rate-modifying activity on the machine. The processing time of a job scheduled after the rate-modifying activity decreases depending on a job-dependent factor. Finished jobs are delivered in batches. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find a common due date for all the jobs, a location of the rate-modifying activity, and a delivery date for each job to minimize the sum of earliness, tardiness, holding, due date, and delivery cost. We provide some properties of the optimal schedule for the problem and present polynomial algorithms for some special cases.
This paper presents a novel mixed-integer non-linear programming model for the layout design of a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands are varying during a multi-period planning horizon. As a result, the best cell configuration for one period may not be efficient for successive periods, and thus it necessitates reconfigurations. Three major and interrelated decisions are involved in the design of a CMS; namely cell formation (CF), group layout (GL) and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions in a dynamic environment. The proposed model integrating the CF and GL decisions can be used by researchers and practitioners to design GL in practical and dynamic cell formation problems. Another compromising aspect of this model is the utilization of multi-rows layout to locate machines in the cells configured with flexible shapes. Such a DCMS model with an extensive coverage of important manufacturing features has not been proposed before and incorporates several design features including alternate process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of equal area facilities and flexible reconfiguration. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, purchasing new machines, machine overhead and machine processing. Linearization procedures are used to transform the presented non-linear programming model into a linearized formulation. Two numerical examples taken from the literature are solved by the Lingo software using a branch-and-bound method to illustrate the performance of this model. An efficient simulated annealing (SA) algorithm with elaborately designed solution representation and neighborhood generation is extended to solve the proposed model because of its NP-hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison with the Lingo software. The obtained results show that the proposed SA is able to find the near-optimal solutions in computational time, approximately 100 times less than Lingo. Also, the computational results show that the proposed model to some extent overcomes common disadvantages in the existing dynamic cell formation models that have not yet considered layout problems.
This paper analyzes the n-job, two-machine flowshop sequencing problem with job processing times following exponential distributions. Three sufficient conditions are derived for determining a job sequence which minimizes a total expected linear cost function. Stronger results are obtained for several special cases.
In this paper, we address the two stage assembly flowshop scheduling problem which has m parallel machines at the first stage and an assembly machine at the second stage with a weighted sum of makespan and mean completion time criteria, known as bicriteria, which are of great importance on the industrial context. This problem is known to be intractable, and therefore the right way to proceed is through the use of heuristic techniques. To that purpose, a novel approach based on the systematic changes of the neighborhood structure within a search has been developed. Variable neighborhood search (VNS) is a recent metaheuristic, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. Extended comparisons with the SA proposed by Allahverdi showed a superior performance for the proposed approach.
This paper considers minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. After problem formulation, we present a proof to show that the general version of this problem is strongly NP-complete. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Next, a branch and bound solution scheme is suggested. Finally, three heuristics to find approximate solutions to the general problem are proposed and their error bounds are analyzed.
Purpose
This paper aims to describe colonial competitive algorithm (CCA), a novel socio‐politically inspired optimization strategy, and how it is used to solve real world engineering problems by applying it to the problem of designing a multivariable proportional‐integral‐derivative (PID) controller. Unlike other evolutionary optimization algorithms, CCA is inspired from a socio‐political process – the competition among imperialists and colonies. In this paper, CCA is used to tune the parameters of a multivariable PID controller for a typical distillation column process.
Design/methodology/approach
The controller design objective was to tune the PID controller parameters so that the integral of absolute errors, overshoots and undershoots be minimized. This multi‐objective optimization problem is converted to a mono‐objective one by adding up all the objective functions in which the absolute integral of errors is emphasized to be reduced as long as the overshoots and undershoots remain acceptable.
Findings
Simulation results show that the controller tuning approach, proposed in this paper, can be easily and successfully applied to the problem of designing MIMO controller for control processes. As a result not only was the controlled process able to significantly reduce the coupling effect, but also the response speed was significantly increased. Also a genetic algorithm (GA) and an analytical method are used to design the controller parameters and are compared with CCA. The results showed that CCA had a higher convergence rate than GA, reaching to a better solution.
Originality/value
The proposed PID controller tuning approach is interesting for the design of controllers for industrial and chemical processes, e.g. MIMO evaporator plant. Also the proposed evolutionary algorithm, CCA, can be used in diverse areas of optimization problems including, industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning.
This paper deals with the two-stage assembly flowshop scheduling problem with minimisation of weighted sum of makespan and mean completion time as the objective. The problem is NP-hard, hence we proposed a meta-heuristic named imperialist competitive algorithm (ICA) to solve it. Since appropriate design of the parameters has a significant impact on the algorithm efficiency, we calibrate the parameters of this algorithm using the Taguchi method. In comparison with the best algorithm proposed previously, the ICA indicates an improvement. The results have been confirmed statistically.
We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding), and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two different, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two different lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with different types of strongly -hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.
In this paper, a colonial competitive algorithm is applied to the problem of designing a multivariable PID controller. The goal is to design a controller to decouple the controlled process, and to track the desired inputs by outputs of the process as much as possible. The method is used to design a multi variable controller for a typical distillation column process. Also a GA and an analytical method are used to design the controller parameters. Comparison results among these methods show that the controller obtained by colonial competitive algorithm has better performance than the others.
This paper proposes an algorithm for optimization inspired by the imperialistic competition. Like other evolutionary ones, the proposed algorithm starts with an initial population. Population individuals called country are in two types: colonies and imperialists that all together form some empires. Imperialistic competition among these empires forms the basis of the proposed evolutionary algorithm. During this competition, weak empires collapse and powerful ones take possession of their colonies. Imperialistic competition hopefully converges to a state in which there exist only one empire and its colonies are in the same position and have the same cost as the imperialist. Applying the proposed algorithm to some of benchmark cost functions, shows its ability in dealing with different types of optimization problems.
This research investigates a two-stage hybrid flowshop scheduling problem in a metal-working company. The first stage consists of multiple parallel machines and the second stage has only one machine. Four characteristics of the company have substantiated the complexity of the problem. First, all machines in stage one are able to process multiple jobs simultaneously but the jobs must be sequentially set up one after another. Second, the setup time of each job is separated from its processing time and depends upon its preceding job. Third, a blocking environment exists between two stages with no intermediate buffer storage. Finally, machines are not continuously available due to the preventive maintenance and machine breakdown. Two types of machine unavailability, namely, deterministic case and stochastic case, are identified in this problem. The former occurs on stage-two machine with the start time and the end time known in advance. The latter occurs on one of the parallel machine in stage one and a real-time rescheduling will be triggered. Minimizing the makespan is considered as the objective to develop the optimal scheduling algorithm. A genetic algorithm is used to obtain a near-optimal solution. The computational results with actual data are favorable and superior over the results from existing manual schedules.
The integrated product mix-outsourcing optimization is a major problem in manufacturing enterprise. Generally, heuristic or meta-heuristic solution approaches are used to optimize such problems. Heuristic approaches for these problems include Theory of Constraints (TOC) and Standard Accounting. Sometimes heuristic approaches are inefficient especially in large problems and instead, in these cases meta-heuristic algorithms have been applied extensively. In this paper a novel meta-heuristic algorithm “Imperialist Competitive Algorithm” (ICA) is applied to solve the integrated product mix-outsourcing optimization problem. Also, the results obtained from ICA are compared with the results of TOC and Standard Accounting approaches.
This paper addresses the production scheduling problem in a multi-page invoice printing system. The system comprises three stages: the stencil preparation stage, the page printing stage and the invoice assembly stage. Since each page can be considered as a component and the invoice as the finished product, the production system for multi-page invoices can be treated as an assembly-type flowshop with parallel machines at the last two stages. Moreover, two types of sequence-dependent setup operations are considered at the second stage. The objective is to minimize the makespan for all the invoice orders. We first formulate this problem into a mixed-integer linear programming (MILP). Then a hybrid genetic algorithm (HGA) is proposed for solving it due to its NP-hardness. To evaluate the performance of the HGA heuristic, a lower bound for the makespan is developed. Numerical experiment indicates that our algorithm can solve the problem efficiently and effectively.
This study proposes a heuristic algorithm, called the multi-objective master planning algorithm (MOMPA), to solve master planning (MP) problems for a supply chain network with multiple finished products. MOMPA has three objectives: to minimize delay penalties, to minimize use of outsourcing capacity, and to minimize the costs of materials, production, processing, transportation, and inventory holding—all while respecting the capacity limitations and the demand deadlines of all those involved in a given supply chain network. MOMPA plans each demand, one by one, without backtracking, and sorts those demands using a sorting mechanism that is part of the algorithm. For each demand, the minimum production cost tree is determined within the limits of the time bucket for the demand deadline. The maximum available capacity of this tree is then computed for the “no delay” case. Following this calculation, the delay-or-not criterion is evaluated to determine whether or not further delay is necessary. MOMPA compares the results of these two procedures and allocates the appropriate capacities to the demand for all the nodes on the selected tree. If the minimum cost production tree has no available capacity, MOMPA adjusts the network and looks for a new tree. With complexity and computational analysis, MOMPA is shown to be very efficient in solving MP problems, sometimes generating the same optimal solution as the LP model.
We consider a job-shop manufacturing cell of n jobs (orders), Ji, 1⩽i⩽n, and m machines Mk, 1⩽k⩽m. Each job-operation Oiℓ (the ℓth operation of job i) has a random time duration tiℓ with the average value and the variance Viℓ. Each job Ji has its due date Di and the penalty cost Ci* for not delivering the job on time (to be paid once to the customer). An additional penalty has to be paid for each time unit of delay, i.e., when waiting for the job's delivery after the due date. If job Ji is accomplished before Di it has to be stored until the due date with the expenses per time unit.The problem is to determine optimal earliest start times Si of jobs Ji, 1⩽i⩽n, in order to minimize the average value of total penalty and storage expenses. Three basic principles are incorporated in the model:View Within ArticleA numerical example of a simulation run is presented to clarify the decision-making rule. The optimization model is verified via extensive simulation.
We consider the problem of minimizing the makespan of n jobs in an m-machine flowshop operating without buffers. Since there is no intermediate storage, a job here cannot leave a machine until the machine downstream is free. When that is the case, the job is said to be blocked. This “blocking flowshop” problem is known to be strongly NP-hard for the shop having more than two machines. In this paper, we develop a genetic algorithmic approach to solve large size restricted slowdown flowshop problems of which blocking flowshop problems are a special case. Abadi (Flowshop scheduling problems with no-wait and blocking environments: A mathematical programming approach. Ph.D Thesis, Department of Industrial Engineering, University of Toronto, Canada, 1995) has established a connection between the blocking flowshop problem and a no-wait flowshop in which jobs do not wait between operations. He uses the idea of deliberately slowing down the processing of certain operations. We utilize this concept to evaluate the makespan (fitness) of the solutions generated by genetic algorithms. Computational results indicate that a genetic algorithm with optimized parameters for controlling the evolution of solutions consistently performs significantly better than the heuristic for blocking flowshops developed in a recent Ph.D. thesis by Abadi. The comparison is made for the problems with sizes up to 20 machines and 250 jobs.
This paper develops a branch and bound algorithm for the two-stage assembly scheduling problem. In this problem, there are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule the jobs on the machines so that the maximum completion time, or makespan, is minimized. A lower bound based on solving an artificial two-machine flow shop problem is derived. Also, several dominance theorems are established and incorporated into the branch and bound algorithm. Computational experience with the algorithm is reported for problems with up to 8000 jobs and 10 first-stage machines.
The assembly flowshop scheduling problem has been addressed recently in the literature. There are many problems that can be modeled as assembly flowshop scheduling problems including queries scheduling on distributed database systems and computer manufacturing. The problem has been addressed with respect to either makespan or total completion time criterion in the literature. In this paper, we address the problem with respect to a due date-based performance measure, i.e., maximum lateness. We formulate the problem and obtain a dominance relation. Moreover, we propose three heuristics for the problem: particle swarm optimization (PSO), Tabu search, and EDD. PSO has been used in the areas of function optimization, artificial neural network training, and fuzzy system control in the literature. In this paper, we show how it can be used for scheduling problems. We have conducted extensive computational experiments to compare the three heuristics along with a random solution. The computational analysis indicates that Tabu outperforms the others for the case when the due dates range is relatively wide. It also indicates that the PSO significantly outperforms the others for difficult problems, i.e., tight due dates. Moreover, for difficult problems, the developed dominance relation helps reduce error by 65%.
This paper considers a 2-stage assembly flowshop scheduling problem where each job is assembled with two types of components and makespan is the objective measure. For the assembly, one type of the components is outsourced subject to job-dependent lead time but the other type is fabricated in-house, at the first stage. The problem is shown to be NP-complete in the strong sense. Some solution properties are characterized, based on which three heuristic algorithms are derived. A branch-and-bound algorithm is also derived by use of the associated three lower bounds and several dominance properties. Numerical experiments are conducted to evaluate the performances of the proposed branch-and-bound and heuristic algorithms.
This paper addresses a three-machine assembly-type flowshop scheduling problem, which frequently arises from manufacturing process management as well as from supply chain management. Machines one and two are arranged in parallel for producing component parts individually, and machine three is an assembly line arranged as the second stage of a flowshop for processing the component parts in batches. Whenever a batch is formed on the second-stage machine, a constant setup time is required. The objective is to minimize the makespan. In this study we establish the strong NP-hardness of the problem for the case where all the jobs have the same processing time on the second-stage machine. We then explore a useful property, based upon which a special case can be optimally solved in polynomial time. We also study several heuristic algorithms to generate quality approximate solutions for the general problem. Computational experiments are conducted to evaluate the effectiveness of the algorithms.
This research proposes a simulated annealing (SA) approach to minimize makespan for a single batch-processing machine. Each job has a corresponding processing time and size. The machine can process the jobs in batches as long as the machine capacity is not exceeded. The processing time of a batch is equal to the longest processing time among all jobs in the batch. Random instances were generated to test our approach with respect to solution quality and run time. The results of the SA approach were compared to CPLEX. Our approach outperforms CPLEX on all the instances.
In this paper the two stage assembly flow shop problem (TSAFSP) with bi-objective of number of tardy and makespan minimization is addressed. The problem is known to be NP-hard and is thus solved with two metaheuristics: Simulated Annealing (SA) and Variable Neighborhood Search (VNS) and the Pareto-optimal solutions approach is taken to find optimal solutions of the problem. Computational experiments have been executed and a comparison of the metaheuristics has been carried out. It is indicated that for this problem SA works better in small problems, but is outperformed by VNS as the size of the problem grows; while in general SA is faster than VNS.
We consider the three-stage assembly flowshop scheduling problem with the objective of minimizing the makespan. The three-stage assembly problem generalizes both the serial three machine flowshop problem and the two-stage assembly flowshop scheduling problem and is therefore strongly NP-hard. We analyze the worst-case ratio bound for several heuristics for this problem. We also analyze the worst-case absolute bound for a heuristic based on compact vector summation techniques and we point out that, for a large number of jobs, this heuristic becomes asymptotically optimal.
We consider a two-agent scheduling problem on a two-machine flowshop setting, where the objective is to minimize the total tardiness of the first agent with the restriction that the number of tardy jobs of the second agent is zero. It is reported in the literature that the complexity of even two-machine flowshop problem, where both agents wish to complete their jobs as soon as possible, is shown NP-hard. Motivated by the limitation and suggestions, this paper proposes a branch-and-bound algorithm and a simulated annealing heuristic algorithm to search for the optimal solution and near-optimal solutions, respectively. Computational results are also presented to evaluate the performance of the proposed algorithms.
This paper proposes a hybrid metaheuristic for the minimization of makespan in scheduling problems with parallel machines and sequence-dependent setup times. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) for solution evolution, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. The hybridization of an ACO, SA with VNS, combining the advantages of these three individual components, is the key innovative aspect of the approach. Two algorithms of a hybrid VNS-based algorithm, SA/VNS and ACO/VNS, and the VNS algorithm presented previously are used to compare with the proposed hybrid algorithm to highlight its advantages in terms of generality and quality for large instances.
The Silences of the Archives, the Reknown of the Story.
The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, before captivated judges and a guilty feeling Bertrande de Rols. The historian wanted to go beyond the known story in order to discover the world of the heroes. This research led to disappointments and surprizes as documents were discovered concerning the environment of Artigat’s inhabitants and bearing directly on the main characters thanks to notarial contracts. Along the way, study of the works of Coras and Lesueur took a new direction. Coming back to the affair a quarter century later did not result in finding new documents (some are perhaps still buried in Spanish archives), but by going back over her tracks, the historian could only be struck by the silences of the archives that refuse to reveal their secrets and, at the same time, by the possible openings they suggest, by the intuition that almost invisible threads link here and there characters and events.
A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two-dimensional rigid-sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four-term virial coefficient expansion.
A general method, suitable for fast computing machines, for investigating
such properties as equations of state for substances consisting of
interacting individual molecules is described. The method consists
of a modified Monte Carlo integration over configuration space. Results
for the two-dimensional rigid-sphere system have been obtained on
the Los Alamos MANIAC and are presented here. These results are compared
to the free volume equation of state and to a four-term virial coefficient
expansion. The Journal of Chemical Physics is copyrighted by The
American Institute of Physics.
This paper addresses the parameter modelling and optimisation issues in the application of a bio-inspired model for the scheduling of dynamic flexible job shop with sequence-dependent setups. The study sets the model parameters using two steps, termed mapping and tuning. Mapping establishes a set of coefficients to link the model parameters with the scheduling problem characteristics. Tuning determines good values of these coefficients and is then used to compute the model parameters. Such a tuning procedure is accomplished by extensive computational experiments and statistical analyses. A data set from semiconductor manufacturing was used to show the effectiveness of the parameter setting approach. The performance of the proposed multiagent model was compared with that of another scheduling method which is based on dispatching rules. It is concluded that the proposed parameter setting method is effective and worth considering when applying bio-inspired division of labour to dynamic manufacturing scheduling. [Received 5 October 2006; Revised 2 January 2007; Accepted 1 March 2007]
Today, firms have to compete on international openness markets. The resulting production organisation is a multi-site production system. Several production units called sites have to supply irregular demands at the lower costs. We propose a two-level production management approach to control such systems. It results in a global multi-site production planning and in local multi-workshop scheduling. This paper focuses on the multi-site production planning problem. A primal–dual approach is proposed to solve this problem. It allows us to minimise variable and fixed costs. This heuristic has been experimented on a wide range of problem test data.
Lesson 12: Introduction to operations scheduling Operations Management II lecture Retrieved from University of Windsor website
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Baki, M.F. Lesson 12: Introduction to operations scheduling. Operations
Management II lecture; 2008; (slide NO.7). Retrieved from University of
Windsor website: 〈http://web4.uwindsor.ca/users/b/baki%20fazle/main.nsf/
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$FILE/Chapter_08_Lecture_12_to_19_w08_431_scheduling.ppt〉.
Solving assembly flowshop scheduling problem with parallel machines using variable neighborhood search
- N Javadian
- A Mozdgir
- Gazani Koohi
- Davallo Qajar
- M R Shiraqai
Javadian N, Mozdgir A, Gazani Koohi E, Davallo Qajar MR, Shiraqai ME. Solving
assembly flowshop scheduling problem with parallel machines using variable
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Equation minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing
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The two-stage assembly scheduling problem: complexity and approximation
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