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A note on makespan minimization in two-stage flexible flow shops with uniform machines
Abstract
We consider the two-stage flexible flow shop makespan minimization problem with uniform parallel machines. Soewandi and Elmaghraby [Soewandi, H., Elmaghraby, S., 2003. Sequencing on two-stage hybrid flowshops with uniform machines to minimize makespan. IIE Transaction 35, 467–477] developed a heuristic (S–E) and derived a machine speed-dependent worst-case ratio bound for it. We point out that this bound works well when the uniform machines have approximately equal speeds but is not indicative of the performance of the S–E heuristic when the machine speeds are in a wide range. Motivated by this observation, we propose an alternative tight machine-speed dependent worst-case bound for the S–E heuristic that works well when the machine speeds vary significantly. We then combine the two speed-dependent ratio bounds into a speed-independent bound. Our findings facilitate the narrowing of the gap between experimental performance and worst-case bound for the S–E heuristic.
... FFPS has been successfully applied in a wide variety of industries solve a wide range scheduling problems. The industries include the electronics (Jin et al., 2002;Kyparisis and Koulamas, 2006;Wittrock, 1985Wittrock, , 1988, textile (Grabowski and Pempera, 2000), production of concrete (Guinet, 1991), manufacturing of photographic film (Tsubone et al., 1993;Aghezzaf and Van Landeghem, 2002), and others (Yang et al., 2004;Ruiz and Maroto, 2006;Lin and Liao, 2003;Deal et al., 1994;Bertel and Billaut, 2004;Adler et al., 1993;Aghezzaf et al., 1995). FFSP also applied in non-manufacturing areas like civil engineering (Dror and Mullaserif, 1996), internet service architectures (Allahverdi and Al-Anzi, 2006) and container handling systems . ...
... Mixed integer programming formulations for scheduling in flexible flow shop with limited intermediate buffers to minimise maximum completion times has been proposed by Sawik (2000). Kyparisis and Koulamas (2006) have considered flexible flow shop scheduling problems with uniform parallel machines in each stage for minimising makespan. They have proposed an algorithm for assigning jobs to the machines according to the given arbitrary permutation of jobs. ...
In this work, a particle swarm optimisation (PSO) algorithm with chaotic mutation operator is proposed to solve flexible flow shop scheduling problems. Mutation, a commonly used operator in genetic algorithm, has been introduced so that common problem of trapping of solutions at local minima in PSO can be avoided. Chaotic sequence using logistic mapping is used instead of random numbers to improve the diversity in solution space. The performance of schedules is evaluated in terms of total completion time or makespan (C max ). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound (LB). The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average percentage deviation is observed as 6.390 whereas GA produces an average percentage deviation of 9.657. Finally, influence of various PSO parameters on solution quality has been investigated.
... They proposed constructive algorithms using job insertion techniques and iterative algorithms based on local search. Kyparisis and Koulamas (2006) surveyed scheduling literature in heuristics for worstcase ratio and suggested a new heuristic for minimizing makespan, which gives a worst-case performance guarantee when the speed of parallel machines in a given stage vary significantly and provided a definition of uniform machines for hybrid flow shop (i.e. parallel machines with different speed). ...
... It seems that the two-stage hybrid flow shop examined in this paper, with parallel batching machines at each stage for processing parallel batches with sequence-independent setup times, has not been dealt with in the literature. In addition, a definition of uniform setup inspired from that originally proposed by Kyparisis and Koulamas (2006) is applied to setup instead of machines. ...
Cited By (since 1996):1, Export Date: 13 November 2013, Source: Scopus
... They proposed constructive algorithms using job insertion techniques and iterative algorithms based on local search. Kyparisis and Koulamas (2006) surveyed scheduling literature in heuristics for worstcase ratio and suggested a new heuristic for minimizing makespan, which gives a worst-case performance guarantee when the speed of parallel machines in a given stage vary significantly and provided a definition of uniform machines for hybrid flow shop (i.e. parallel machines with different speed). ...
... It seems that the two-stage hybrid flow shop examined in this paper, with parallel batching machines at each stage for processing parallel batches with sequence-independent setup times, has not been dealt with in the literature. In addition, a definition of uniform setup inspired from that originally proposed by Kyparisis and Koulamas (2006) is applied to setup instead of machines. ...
The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times,
parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements.
... Huang and Li [99] consider the two-stage problem with uniform machines in the second stage, i.e. the HF2ð0; QM ð2Þ Þ case. Whereas, Dessouky et al. [100], Soewandi and Elmaghraby [101] and Kyparisis and Koulamas [102] consider uniform machines in both stages. ...
... They also derive the worst-case performance bound for the first heuristic. Kyparisis and Koulamas [102] noted that this bound works well only when the uniform machines have approximately equal speed and propose an alternative worst case ratio bound valid when the machine speeds vary significantly. Kyparisis and Koulamas [105] study HFkðQM ð1Þ ; . . . ...
In this paper, an extensive review of recently published papers on hybrid flow shop (HFS) scheduling problems is presented. The papers are classified first according to the HFS characteristics and production limitations considered in the respective papers. This represents a new approach to the classification of papers in the HFS environment. Second, the papers have been classified according to the solution approach proposed. These two classification categories give a comprehensive overview on the state of the art of the problem and can guide the reader with respect to future research work.
... Overall, they observed up to 50% in the makespan improvements with the new BalancedPools algorithm. G. J. Kyparisis and C. Koulamas [7] considered a scheduling problem in a twostage hybrid flow shop, where the first stage consists of two machines forming an open shop and the other stage has only one machine. The main objective is to minimize the makespan, i.e., the maximum completion time of all jobs. ...
The amount of data generated in today's environment is increasing at an exponential rate. These data are structured, semi-structured, or unstructured in some cases. Processing vast amounts of data is a difficult task. MapReduce is a technique for processing large amounts of data. For storing big data sets, Hadoop data file system (HDFS) is employed. A MapReduce workload is made up of a number of jobs, each of which has multiple map tasks and numerous reduce tasks. In this paper, we propose the Shortest Task Ordering (SJA) algorithm for optimising Mkspan (Makespan) and TCTime (Total completion time) for MapReduce Workloads using dynamic job ordering and slot design. We conducted a comparison analysis on data sets of various sizes. By comparing objective measurements such as Mkspan and TCTime, the experimental results show that performance in terms of speed has improved. Each set of jobs, such as WordCount, CharCount, LineCount, and Anagram, displays comparative improvement in our work. When compared to previous algorithms such as MkJR and MkTctJR, the results demonstrate an improvement in time efficiency, slot usage, and execution speed. In terms of Mkspan and TCTime, the Shortest Task Assigned (SJA) method for job ordering yielded results that were up to 95% better than MkJR. In comparison to the previous algorithms MkSfJR and MkTctSfJR, there is also an increase in slot usage. In terms of Mkspan and TCTime, the Shortest Job Assigned (SJA) algorithm achieved results that were up to 150 percent better than MkSfJR.KeywordsMapReduce workloadsHadoopScheduling algorithmsJob orderSlot configuration
... They first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances [2]. ...
In today's world the quantity of data being generated is growing exponentially. Some of these data are structured, semi-structured or unstructured. This poses a great challenge when these data are to be analyzed because conventional data processing techniques are not suited to handling such data. Map Reduce is a programming model and an associated implementation for processing and generating large data sets. A Map Reduce workload generally contains a set of jobs, each of which consists of multiple map tasks followed by multiple reduce tasks. This system proposes of algorithms to optimize the makespan and the total completion time for an offline MapReduce workload. Our algorithms focus on the job ordering optimization for a MapReduce workload and we can perform optimization of Makespan and total completion for a MapReduce workload. Our work is focuses on resolving the time efficiency problems as well as memory utilization problem. By using MK_TCT_JR algorithm produced the result that are up to, 90 % better than MK_JR. Our algorithm will improve the system performance in terms of makepan and total completion time.
... Soewandi and Elmaghraby (2003) presented the study of 2-stages FFS sequencing problem with uniform machines in each stage. Kyparisis and Koulamas (2006a) presented an extension of Soewandi's paper which considered 2-stage uniform 78% 8% 14% ...
The Flexible flow shop (FFS) is defined as a multi-stage flow shops with multiple parallel machines. FFS scheduling problem is a complex combinatorial problem which has been intensively studied in many real world industries. This review paper gives a comprehensive exploration review on the FFS scheduling problem and guides the reader by considering and understanding different environmental assumptions, system constraints and objective functions for future research works. The published papers are classified into two categories. First is the FFS system characteristics and constraints including the problem differences and limitation defined by different studies. Second, the scheduling performances evaluation are elaborated and categorized into time, job and multi related objectives. In addition, the resolution approaches that have been used to solve FFS scheduling problems are discussed. This paper gives a comprehensive guide for the reader with respect to future research work on the FFS scheduling problem.
... They first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances [2]. ...
Abstract: In today’s world the quantity of data being
generated is growing exponentially. Some of these
data are structured, semi-structured or unstructured.
This poses a great challenge when these data are to
be analyzed because conventional data processing
techniques are not suited to handling such data. Map
Reduce is a programming model and an associated
implementation for processing and generating large
data sets. A Map Reduce workload generally
contains a set of jobs, each of which consists of
multiple map tasks followed by multiple reduce tasks.
This system proposes of algorithms to optimize the
makespan and the total completion time for an offline
MapReduce workload. Our algorithms focus on the
job ordering optimization for a MapReduce
workload and we can perform optimization of
Makespan and total completion for a MapReduce
workload. Our work is focuses on resolving the time
efficiency problems as well as memory utilization
problem. By using MK_TCT_JR algorithm produced
the result that are up to, 90 % better than MK_JR.
Our algorithm will improve the system performance
in terms of makepan and total completion time
... MROrder is designed to be flexible for different optimization metrics, e.g., makespan and total completion time. Kyparisis and Koulamas[7]considered a scheduling problem in two-stage hybrid flow shop, where the first stage consists of two machines formed an open shop and the other stage has only one machine. The main objective is to minimize the makespan, i.e., the maximum completion time of all jobs. ...
... Another important assumption in manufacturing systems which we considered is the uniform parallel machines for processing. Huang and Li (1998) contemplated the twostage problem with uniform machines in the second stage, whereas Dessouky et al. (1998), Soewandi and Elmaghraby (2003), Kyparisis and Koulamas (2006a) considered uniform machines in both stages. The three stages problem has been investigated in Bertel and Billaut (2004). ...
According to the state of the art of no-wait scheduling problem, practitioners have mostly concentrated on pure no-wait flow shop scheduling problem. In the most real world production cases, flow shops operate with uniform parallel machines at each stage to eliminate or reduce the bottleneck stages with aim of enhancing the efficiency of production. This paper deals with a no-wait scheduling problem considering anticipatory sequence-dependent setup times on the flexible flow shop environment with uniform parallel machines. The objective is to find the sequence which minimizes maximum completion time of jobs (i.e. makespan). Since this problem is known to be NP-hard, we introduce a novel approach to tackle the problem. In the solution approach, firstly a heuristic formulation is used for objective function evaluation. Afterwards, principles of meta-heuristic algorithms namely invasive weed optimization, variable neighborhood search and simulated annealing algorithms are hybridized as solution method of the problem. In addition, a Taguchi method is employed for calibration of parameters and operators of the proposed hybrid meta-heuristic. Various computational experiments in two scales of small and large are established to illustrate the effectiveness and robustness of the proposed method. Finally, the experimental results revealed the superiority of the performance of the hybrid meta-heuristic in comparison with original ones singularly.
... Nepalli et al. [21] used genetic algorithm in a bi-criteria problem. Koulamas and Kypasisis [22] developed an asymptotically optimal heuristic for the problem with uniform parallel machines. Allahverdi and Al-Anzi [3] proposed three heuristics; simple earliest due date, particle swarm optimization (PSO), and tabu search heuristics in which both PSO and tabu search proved to yield good results. ...
This paper addresses the two-stage assembly flow-shop problem (TSAFP) with multiple non-identical assembly machines in second stage with the objective function of makespan minimization. This problem is a generalization of previously proposed problems in TSAFP. Mathematical mixed-integer linear programming model of this problem is defined, and for it being NP-hard, a hybrid SA heuristic is proposed. The heuristic is proved to solve the problem in reduced time with negligible error. To validate the proposed method, a real-life example is presented and solved in which the efficiency of the proposed heuristic is shown.
... For years, this characteristics of flow line layout has brought numerous advantages, which includes the reduction of total production time per unit, a smoother flow line, less inventories, etc. Huang et al. (2002) revealed that the buffer allocation problem is in itself a difficult NP-hard combinatorial optimisation problem, it is made even more difficult by the fact that the objective function is not obtainable in closed form for interrelating the integer decision variables (i.e., buffer sizes) and the performance measures of the system. Kyparisis and Koulamas (2006) on the other hand reviewed the two-stage flexible (hybrid) flow shop makespan minimisation problem with uniform parallel machines derived by Soewandi and Elmaghraby (2003). They found a speed-independent ratio bound that facilitated the narrowing of the gap between average experimental performance and worst-case performance for the S-E heuristic. ...
Flow line layout has the characteristics of meeting high volume with low product variety production. However, the market trend nowadays focuses on customisation where product orders come in small batches but with high product variety. Therefore, cellular layout becomes a preferable type of layout due to its ability to cope with low volume and high product variety. The conversion of flow line to cellular layout is focused in this study and assembly line conversion approach is suggested as a guideline on designing the basic structure of cellular layout. The conversion will adopt lean concept on the manufacturing line. The converted layout will be further tested for its performance by using simulation modelling. Then, the behaviours of cellular layout are described and performance measures that show significant effect on the layout are reviewed by using analysis of variance (ANOVA).
... For years, this characteristics of flow line layout has brought numerous advantages, which includes the reduction of total production time per unit, a smoother flow line, less inventories, etc. Huang et al. (2002) revealed that the buffer allocation problem is in itself a difficult NP-hard combinatorial optimisation problem, it is made even more difficult by the fact that the objective function is not obtainable in closed form for interrelating the integer decision variables (i.e., buffer sizes) and the performance measures of the system. Kyparisis and Koulamas (2006) on the other hand reviewed the two-stage flexible (hybrid) flow shop makespan minimisation problem with uniform parallel machines derived by Soewandi and Elmaghraby (2003). They found a speed-independent ratio bound that facilitated the narrowing of the gap between average experimental performance and worst-case performance for the S-E heuristic. ...
... [33] proposed heuristics and provided worst-case analyses for the same problem and [200] study the case when machines at the second stage are unrelated. The 2-stage case with any number of uniform parallel machines is studied in [181] and later revisited by [108]. [30] considers a problem with a set of initial batches, and jobs have a predefined sequence inside each batch. ...
The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.
The continuous advancement in computer technology over the years, the quantity of data being generated is growing exponentially. Some of these data are structured, semi-structured or unstructured. This poses a great challenge when these data are to be analyzed because conventional data processing techniques are not suited to handling such data. Map Reduce is a programming model and an associated implementation for processing and generating large data sets. A Map Reduce workload generally contains a set of jobs, each of which consists of multiple map tasks followed by multiple reduce tasks. This system proposes of algorithms to minimize the makespan and the total completion time for an offline MapReduce workload. Our algorithms focuses on the job ordering optimization for a MapReduce workload and we can perform optimization of Makespan and total completion for a MapReduce workload. So to overcome that a new greedy job ordering algorithm to minimize the makespan and total completion time together.
Traditionally, scheduling problems usually deal with the objectives related to production efficiency (e.g., the make-span, the total completion time, the maximum lateness and the number of tardy jobs). However, sustainable manufacturing should minimise the energy consumption during production process. Energy consumption not only constitutes a major portion of total production cost but also results in significant environmental effects. In this chapter, we discuss a multi-objective scheduling problem in a hybrid flow shop. Two objectives considered in the proposed model are to minimise make-span and energy consumption. These two objectives are often in conflict with each other. A Preference Vector Ant Colony System (PVACS) is developed to search for a set of Pareto-optimal solutions using meta-heuristics for multi-objective optimisation. PVACS allows the search in the solution space to focus on the specific areas which are of particular interest to decision-makers, instead of searching for the entire Pareto frontier. This is achieved by maintaining a separate pheromone matrix for each objective, respectively and assigning each ant a preference vector that represents the preference between the two objectives of the decision-makers. The performance of PVACS was compared to two well-known multi-objective genetic algorithms: SPEA2 and NSGA-II. The experimental results show that PVACS outperforms the other two algorithms.
At the first, the present chapter overviews the framework of a wide variety of scheduling methods, and thereby we can expect to become able to grasp the trends and perspectives in the researches on scheduling. Secondly, we observe the classification of models related to scheduling decisions. The well known classification may be deterministic scheduling versus stochastic scheduling, or static scheduling versus dynamic scheduling. In addition, we also consider a classification by online scheduling versus offline scheduling to clarify how we can discuss the online scheduling within the framework of scheduling problems. Finally, we summarize various scheduling models based on the famous triplet , i.e. manufacturing environments(), restrictions and constraints (), and the performance measures ().
In this paper a two stage scheduling problem is considered. In the first stage there are identical batch processors, which are burnout ovens, and in the second stage there are identical furnaces processing jobs as discrete processors. Jobs need to be loaded on the appropriate grate before they can be loaded in the burnout ovens. In this context, several grate types exist and they can be mixed and loaded in the burnout ovens only based on predefined layout patterns. There is a blocking constraint between stage one and two, meaning if all of the furnaces are busy then the grates currently loaded in the burnout ovens block the burnout ovens from being loaded with new grates. Furnaces are responsible for casting jobs and jobs are casted using pots, and each pot can only be used for a predefined maximum number of castings. At stage two, a setup might be required based on the job type or the status of the pot. We focus on minimizing weighted completion times of all jobs. The weight of each job is defined based on its due date. In this research we present a mathematical model for this problem. The model is implemented in CPLEX and results are presented.
MapReduce is a popular parallel computing paradigm for large-scale data processing in clusters and data centers. A MapReduce workload generally contains a set of jobs, each of which consists of multiple map tasks followed by multiple reduce tasks. Due to 1) that map tasks can only run in map slots and reduce tasks can only run in reduce slots, and 2) the general execution constraints that map tasks are executed before reduce tasks, different job execution orders and map/reduce slot configurations for a MapReduce workload have significantly different performance and system utilization. This paper proposes two classes of algorithms to minimize the makespan and the total completion time for an offline MapReduce workload. Our first class of algorithms focuses on the job ordering optimization for a MapReduce workload under a given map/reduce slot configuration. In contrast, our second class of algorithms considers the scenario that we can perform optimization for map/reduce slot configuration for a MapReduce workload. We perform simulations as well as experiments on Amazon EC2 and show that our proposed algorithms produce results that are up to 15 ∼ 80 percent better than currently unoptimized Hadoop, leading to significant reductions in running time in practice.
This paper considers a scheduling problem in two-stage hybrid flow shop, where the first stage consists of two machines formed an open shop and the other stage has only one machine. The objective is to minimize the makespan, i.e., the maximum completion time of all jobs. We first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances.
Online scheduling is recognized as the crucial decision-making process of production control at a phase of "being in production" according to the released shop floor schedule. Online scheduling can be also considered as one of key enablers to realize prompt capable-to-promise as well as available-to-promise to customers along with reducing production lead times under recent globalized competitive markets. Online Scheduling in Manufacturing introduces new approaches to online scheduling based on a concept of cumulative delay. The cumulative delay is regarded as consolidated information of uncertainties under a dynamic environment in manufacturing and can be collected constantly without much effort at any points in time during a schedule execution. In this approach, the cumulative delay of the schedule has the important role of a criterion for making a decision whether or not a schedule revision is carried out. The cumulative delay approach to trigger schedule revisions has the following capabilities for the practical decision-making: 1. To reduce frequent schedule revisions which do not necessarily improve a current situation with much expense for its operation; 2. To avoid overreacting to disturbances dependent on strongly an individual shop floor circumstance; and 3. To simplify the monitoring process of a schedule status. Online Scheduling in Manufacturing will be of interest to both practitioners and researchers who work in planning and scheduling in manufacturing. Readers will find the importance of when-to-revise policies during a schedule execution and their influences on scheduling results.
MapReduce has become a widely used computing model for large-scale data processing in clusters and data centers. A MapReduce workload generally contains multiple jobs. Due to the general execution constraints that map tasks are executed before reduce tasks, different job execution orders in a MapReduce workload can have significantly different performance and system utilization. This paper proposes a prototype system called MROrder to dynamically optimize the job order for online MapReduce workloads. Moreover, MROrder is designed to be flexible for different optimization metrics, e.g., makespan and total completion time. The experimental results show that MROrder is able to improve the system performance by up to 31% for makespan and 176% for total completion time.
Hybrid flow shop (HFS) scheduling has been extensively examined and the main objective has been to improve production efficiency. However, limited attention has been paid to the consideration of energy consumption with the advent of green manufacturing. This paper proposes a new ant colony optimization (MOACO) meta-heuristic considering not only production efficiency but also electric power cost (EPC) with the presence of time-of-use (TOU) electricity prices. The solution is encoded as a permutation of jobs. A list schedule algorithm is applied to construct the sequence by artificial ants and generate a complete schedule. A right-shift procedure is then used to adjust the start time of operations aiming to minimize the EPC for the schedule. In terms of theoretical research aspect, the results from computational experiments indicate that the efficiency and effectiveness of the proposed MOACO are comparable to NSGA-II and SPEA2. In terms of practical application aspect, the guideline about how to set preference over multiple objectives has been studied. This result has significant managerial implications in real life production. The parameter analysis also shows that durations of TOU periods and processing speed of machines have great influence on scheduling results as longer off-peak period and use of faster machines provide more flexibility for shifting high-energy operations to off-peak periods.
This paper studies a two-stage production system with n job orders where each job needs two sequential operations. In addition to the two in-house production facilities, the manufacturer
has another option of outsourcing some stage-one operations to a remote outside supplier. The jobs with their stage-one operations
outsourced are subject to a batch transportation delay from the outside supplier before their respective stage-two operations
can be started in-house. The problem is to design an integrated schedule that considers both the in-house production and the
outsourcing with the aim of optimally balancing the outsourcing cost and the makespan. The problem is NP-hard. We have developed
an optimal algorithm and a heuristic algorithm to solve the problem, and conducted computational experiments to validate our
model and algorithms. Our modeling and algorithm framework can be extended to handle other more general cases such as when
the outside supplier has a production facility with a different processing efficiency and when there are many outside suppliers
on a spot market.
In a proportionate flow shop problem, jobs have to be processed through a fixed sequence of machines, and processing time
for each job is equal on all machines. Such a problem has seldom been tackled. Proportionate flexible flow shop (PFFS) scheduling
problems combine the properties of proportionate flow shop scheduling problems and parallel machine scheduling problems. This
study presents a combined approach based on column generation (CG) for a PFFS problem with the criterion to minimize the objective
of the total weighted completion time (TWCT). Minimizing TWCT in a PFFS problem significantly differs from the parallel-identical-machine
scheduling problem, an optimal schedule in which jobs on each machine are in the weighted shortest processing time (WSPT)
order. This combined approach adopts a CG approach to effectively handle job assignments to machines, and a constructive heuristic
to obtain an optimal sequence for a single machine. Experimental results show the effectiveness of the combined approach in
obtaining excellent quality solutions in a reasonable time, especially for large-scale problems.
In this paper, we consider hybrid flow shop (HFS) scheduling problem with a special blocking constraint. Objective function is makespan minimization. HFS and RCb blocking constraint are firstly presented. Then, an integer linear model is presented to find the optimal solution and a lower bound is proposed for high size problems. In order to faster obtain a solution, especially for big size problems, an electromagnetism-like (EM) algorithm is proposed and some mechanisms are introduced to adapt EM-algorithm to HFS scheduling problems. Its performances are compared with optimal solutions when they have been obtained and lower bound for more complex problems. Opportunity to develop and adapt such a meta-heuristic is clearly demonstrated with presented solutions accuracy and time.
In this paper we study the production scheduling problem for a two-stage flow shop in which there are options of outsourcing some operations to subcontractors. The basic objective is to look for a production schedule that can optimally utilize the resources of both the in-house production and outsourcing so that the makespan is minimized. The logistics issue between the subcontractor and the in-house shop further complicates the problem. We present models for different situations of outsourcing. For each model, we develop optimization algorithms and conduct computational experiments to study the managerial insights for the models and the algorithms.
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.
This paper studies a two-stage supply chain scheduling problem with n job orders where each job needs two sequential operations. In addition to the two in-house machines each for one operation, the manufacturer has another option of outsourcing some stage-one operations to an outside subcontractor. The jobs with their stage-one operation outsourced are subject to a single batch delivery from the subcontractor before their respective stage-two operations can be started in-house. The problem is to design an integrated scheduling that considers both the in-house production and the outsourcing with the aim of optimally balancing the outsourcing cost and the makespan. The problem is NP-hard. We have developed a heuristic algorithm to solve the problem, and conducted computational experiments to validate our model and algorithm.
We study the problem of sequencing n simultaneously available jobs on a two-stage hybrid flowshop with uniform machines at each stage. The objective is to minimize the makespan. This problem belongs to the class of strongly NP-complete problems. We develop three heuristic procedures with time complexity of O ( n log n ). We derive the worst-case performance bound for heuristic 1 which ignores the dependence of the start time of the second stage on the completion time of the first stage. Heuristics 2 and 3 take such a dependence into account. Several lower bounds are derived, and the best among them serves as the benchmark for evaluation. Extensive computational experiments have been conducted to evaluate the performance of the proposed procedures. They demonstrate the efficacy of the first heuristic in the case of symmetric processing times. The last two heuristics are significantly better in the case of nonsymmetric processing times.
We address the well-known problem of scheduling multiprocessor flow shops. For a given k-stage processing facility, where at each stage one or more identical machines are available, and a given collection of independent jobs, each comprising k tasks to be processed in order, one per stage, find a schedule that minimizes the makespan. Owing to the intractability of the problem, approximation has been the subject of extensive research. In this paper we review the main advances in this aspect, and establish a new result.
Each of a collection of items are to be produced on two machines (or stages). Each machine can handle only one item at a time and each item must be processed through machine one and then through machine two. The setup time plus work time for each item for each machine is known. A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum. A three-machine problem is also discussed and solved for a restricted case.
We consider flowshop environments that consist of multiple stages and multiple machines in each stage. The flowshops are flexible in the sense that a task within a stage can be processed by any of the machines in the stage. We refer to this design as the hybrid flowshop. Our objective is to schedule a set of n jobs so as to minimize makespan. The problem is N P-complete even in the case of a single stage.We develop a heuristic H for the 2-stage hybrid flowshop that has complexity O (n log n) (where n is the number of jobs) and an error bound of 2 −1/max {m1, m2} (where mi is the number of machines at stage i, i = 1, 2). This bound extends a recent bound for the case m1 = 1, m2 = m and significantly improves all other results that have been developed for some special cases of the 2-stage hybrid flowshop. We develop five new lower bounds which are used in a computational experiment to show that the relative gap of H from optimality is small. We extend H to the case of more than two stages. We perform error bound analysis on the resulting heuristic H′ whose complexity is O (kn log n) (where k is the number of stages). This is the first error bound analysis for the general hybrid flowshop problem and extends the current best error bound for the traditional k-machine flowshop problem.
We discuss the performance of scheduling algorithms for a certain kind of manufacturing environment, called the “Flexible Flowshop”, which consists of a certain number of machine centers. Each center has one or more identical parallel machines. Each part is processed by at most one machine in each center. The problem of finding minimum finish time schedules is considered. Heuristic algorithms are presented and are studied in the worst and average case performance contexts.
