Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid ...Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.展开更多
This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a com...This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.展开更多
There are many flow shop problems of throughput (denoted by FSPT) with constraints of due date in real production planning and scheduling. In this paper, a decomposition and coordination algorithm is proposed based on...There are many flow shop problems of throughput (denoted by FSPT) with constraints of due date in real production planning and scheduling. In this paper, a decomposition and coordination algorithm is proposed based on the analysis of FSPT and under the support of TOC (theory of constraint). A flow shop is at first decomposed into two subsystems named PULL and PUSH by means of bottleneck. Then the subsystem is decomposed into single machine scheduling problems,so the original NP-HARD problem can be transferred into a serial of single machine optimization problems finally. This method reduces the computational complexity, and has been used in a real project successfully.展开更多
Aiming at the hybrid flow-shop (HFS) scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution (DE) is proposed. By using a...Aiming at the hybrid flow-shop (HFS) scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution (DE) is proposed. By using a special encoding scheme and combining DE based evolutionary search and local search, the exploration and exploitation abilities are enhanced and well balanced for solving the HFS problems. Simulation results based on some typical problems and comparisons with some existing genetic algorithms demonstrate the proposed algorithm is effective, efficient and robust for solving the HFS problems.展开更多
The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this wor...The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.展开更多
The connection between production scheduling and transportation scheduling is getting closer in smart manufacturing system, and both of those problems are summarized as NP-hard problems. However, only a few studies ha...The connection between production scheduling and transportation scheduling is getting closer in smart manufacturing system, and both of those problems are summarized as NP-hard problems. However, only a few studies have considered them simultaneously. This paper solves the integrated production and transportation scheduling problem(IPTSP) in hybrid flow shops, which is an extension of the hybrid flow shop scheduling problem(HFSP). In addition to the production scheduling on machines, the transportation scheduling process on automated guided vehicles(AGVs)is considered as another optimization process. In this problem, the transfer tasks of jobs are performed by a certain number of AGVs. To solve it, we make some preparation(including the establishment of task pool, the new solution representation and the new solution evaluation), which can ensure that satisfactory solutions can be found efficiently while appropriately reducing the scale of search space. Then, an effective genetic tabu search algorithm is used to minimize the makespan. Finally, two groups of instances are designed and three types of experiments are conducted to evaluate the performance of the proposed method. The results show that the proposed method is effective to solve the integrated production and transportation scheduling problem.展开更多
Recent researches show that there are some anomalies,which are not satisfied with common sense,appearing in some special permutation flow shop scheduling problems(PFSPs).These anomalies can be divided into three diffe...Recent researches show that there are some anomalies,which are not satisfied with common sense,appearing in some special permutation flow shop scheduling problems(PFSPs).These anomalies can be divided into three different types,such as changing the processing time of some operations,changing the number of total jobs and changing the number of total machines.This paper summarizes these three types of anomalies showing in the special PFSPs and gives some examples to make them better understood.The extended critical path is proposed and the reason why these anomalies happen in special PFSPs is given:anomalies will occur in these special PFSPs when the time of the operations on the reverse critical path changes.After that,the further reason for these anomalies is presented that when any one of these three types of anomalies happens,the original constraint in the special PFSPs is destroyed,which makes the anomalies appear.Finally,the application of these anomalies in production practice is given through examples and also with the possible research directions.The main contribution of this research is analyzing the intial reason why the anomalies appear in special PFSPs and pointing out the application and the possible research directions of all these three types of anomalies.展开更多
An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effecti...An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy(IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.展开更多
In the environment of customization, disturbances such as rush orders and material shortages often occur in the manufacturing system, so rescheduling is necessary for the manufacturing system. The rescheduling methodo...In the environment of customization, disturbances such as rush orders and material shortages often occur in the manufacturing system, so rescheduling is necessary for the manufacturing system. The rescheduling methodology should be able to dispose of the disturbance efficiently so as to keep production going smoothly. This aims researching flow shop rescheduling problem (FSRP) necessitated by rush orders. Disjunctive graph is employed to demonstrate the FSRP. For a flow shop processing n jobs, after the original schedule has been made, and z out of n jobs have been processed in the flow shop, x rush orders come, so the original n jobs together with x rush orders should be rescheduled immediately so that the rush orders would be processed in the shortest time and the original jobs could be processed subject to some optimized criteria. The weighted mean flow time of both original jobs and rush orders is used as objective function. The weight for rush orders is much bigger than that of the original jobs, so the rush orders should be processed early in the new schedule. The ant colony optimization (ACO) algorithm used to solve the rescheduling problem has a weakness in that the search may fall into a local optimum. Mutation operation is employed to enhance the ACO performance. Numerical experiments demonstrated that the proposed algorithm has high computation repeatability and efficiency.展开更多
Since in most practical cases the processing time of scheduling is not deterministic, flow shop scheduling model with fuzzy processing time is established. It is assumed that the processing times of jobs on the machin...Since in most practical cases the processing time of scheduling is not deterministic, flow shop scheduling model with fuzzy processing time is established. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. In order to find a sequence that minimizes the mean makespan and the spread of the makespan, Lee and Li fuzzy ranking method is adopted and modified to solve the problem. Particle swarm optimization (PSO) is a population-based stochastic approximation algorithm that has been applied to a wide range of problems, but there is little reported in respect of application to scheduling problems because of its unsuitability for them. In the paper, PSO is redefined and modified by introducing genetic operations such as crossover and mutation to update the particles, which is called GPSO and successfully employed to solve the formulated problem. A series of benchmarks with fuzzy processing time are used to verify GPSO. Extensive experiments show the feasibility and effectiveness of the proposed method.展开更多
This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parall...This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡ a (j∈N), and the processing time of job Jj is bj(j∈N) on a batch processor M. We take makespan (Cmax) as our minimization objective. In this paper, for the problem of FSMP-BI (m identical parallel machines on the first stage and a batch processor on the second stage), based on the algorithm given by Sung and Choung for the problem of 1| rj, BI | Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max{O(nlogn), O(nB)} time. A max{O(nlogn), O(nB)} time symmetric Algorithm H2 is given then for the problem of BI-FSMP (a batch processor on the first stage and m identical parallel machines on the second stage).展开更多
A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck (SB) procedure. In this algorithm, a sche...A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck (SB) procedure. In this algorithm, a schedule for the bottleneck machine is first constructed optimally and then the non-bottleneck machines are scheduled around the bottleneck schedule by some effective dispatching rules. Computational results show that the modified bottleneck-based procedure can achieve a tradeoff between solution quality and computational time comparing with SB procedure for medium-size problems. Furthermore it can obtain a good solution in quite short time for large-scale scheduling problems.展开更多
In this paper the scheduling problem to minimize the expected makespan is discussed on two-machine flow shops with random disturbance on job processing times. The problem is represented by a stochastic programming mod...In this paper the scheduling problem to minimize the expected makespan is discussed on two-machine flow shops with random disturbance on job processing times. The problem is represented by a stochastic programming model. We approximate the stochastic problem by a deterministic problem which can be solved by Johnson's rule. The estimation of approximation error is also discussed by analyzing the stochastic model and its approximate LP model.展开更多
A new concept of multi-shop (M ) is put forward which contains all basic shops including open shop (O), job shop (J ), flow shop (F ) and hybrid flow shop (H ) so that these basic shop can be scheduled toget...A new concept of multi-shop (M ) is put forward which contains all basic shops including open shop (O), job shop (J ), flow shop (F ) and hybrid flow shop (H ) so that these basic shop can be scheduled together. Several algorithms including ant colony optimization (ACO), most work remaining (MWR), least work remaining (LWR), longest processing time (LPT) and shortest processing time (SPT) are used for scheduling the M. Numerical experiments of the M adopting data of some car and reC series benchmark instances are tested. The results show that the ACO algorithm has better performance for scheduling the M than the other algorithms, if minimizing the makespan ( Cmax^*) is taken as the objective function. As a comparison, the separate shops contained in the M are also scheduled by the ACO algorithm for the same objective function, when the completing time of the jobs in the previous shop is taken as the ready time of these jobs in the following shop. The results show that the M has the advantage of shortening the makespan upon separate shops.展开更多
基金the National Natural Science Foundation of China(Grant Number 61573264).
文摘Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.
基金supported by the National Natural Science Foundation of China under Grant Nos.62076225 and 62122093the Open Project of Xiangjiang Laboratory under Grant No 22XJ02003.
文摘This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.
基金Supported by National Natural Science Foundation of P. R. China (60274013)
文摘There are many flow shop problems of throughput (denoted by FSPT) with constraints of due date in real production planning and scheduling. In this paper, a decomposition and coordination algorithm is proposed based on the analysis of FSPT and under the support of TOC (theory of constraint). A flow shop is at first decomposed into two subsystems named PULL and PUSH by means of bottleneck. Then the subsystem is decomposed into single machine scheduling problems,so the original NP-HARD problem can be transferred into a serial of single machine optimization problems finally. This method reduces the computational complexity, and has been used in a real project successfully.
基金supported by the National Natural Science Fundation of China (60774082 70871065+2 种基金 60834004)the Program for New Century Excellent Talents in University (NCET-10-0505)the Doctoral Program Foundation of Institutions of Higher Education of China(20100002110014)
文摘Aiming at the hybrid flow-shop (HFS) scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution (DE) is proposed. By using a special encoding scheme and combining DE based evolutionary search and local search, the exploration and exploitation abilities are enhanced and well balanced for solving the HFS problems. Simulation results based on some typical problems and comparisons with some existing genetic algorithms demonstrate the proposed algorithm is effective, efficient and robust for solving the HFS problems.
基金Projects(61573144,61773165,61673175,61174040)supported by the National Natural Science Foundation of ChinaProject(222201717006)supported by the Fundamental Research Funds for the Central Universities,China
文摘The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.
基金Supported by National Key R&D Program of China (Grant No. 2019YFB1704603)National Natural Science Foundation of China (Grant Nos. U21B2029 and 51825502)。
文摘The connection between production scheduling and transportation scheduling is getting closer in smart manufacturing system, and both of those problems are summarized as NP-hard problems. However, only a few studies have considered them simultaneously. This paper solves the integrated production and transportation scheduling problem(IPTSP) in hybrid flow shops, which is an extension of the hybrid flow shop scheduling problem(HFSP). In addition to the production scheduling on machines, the transportation scheduling process on automated guided vehicles(AGVs)is considered as another optimization process. In this problem, the transfer tasks of jobs are performed by a certain number of AGVs. To solve it, we make some preparation(including the establishment of task pool, the new solution representation and the new solution evaluation), which can ensure that satisfactory solutions can be found efficiently while appropriately reducing the scale of search space. Then, an effective genetic tabu search algorithm is used to minimize the makespan. Finally, two groups of instances are designed and three types of experiments are conducted to evaluate the performance of the proposed method. The results show that the proposed method is effective to solve the integrated production and transportation scheduling problem.
基金Supported by National Natural Science Foundation of China(Grant No.51825502).
文摘Recent researches show that there are some anomalies,which are not satisfied with common sense,appearing in some special permutation flow shop scheduling problems(PFSPs).These anomalies can be divided into three different types,such as changing the processing time of some operations,changing the number of total jobs and changing the number of total machines.This paper summarizes these three types of anomalies showing in the special PFSPs and gives some examples to make them better understood.The extended critical path is proposed and the reason why these anomalies happen in special PFSPs is given:anomalies will occur in these special PFSPs when the time of the operations on the reverse critical path changes.After that,the further reason for these anomalies is presented that when any one of these three types of anomalies happens,the original constraint in the special PFSPs is destroyed,which makes the anomalies appear.Finally,the application of these anomalies in production practice is given through examples and also with the possible research directions.The main contribution of this research is analyzing the intial reason why the anomalies appear in special PFSPs and pointing out the application and the possible research directions of all these three types of anomalies.
基金Projects(61174040,61104178,61374136) supported by the National Natural Science Foundation of ChinaProject(12JC1403400) supported by Shanghai Commission of Science and Technology,ChinaProject supported by the Fundamental Research Funds for the Central Universities,China
文摘An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy(IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.
文摘In the environment of customization, disturbances such as rush orders and material shortages often occur in the manufacturing system, so rescheduling is necessary for the manufacturing system. The rescheduling methodology should be able to dispose of the disturbance efficiently so as to keep production going smoothly. This aims researching flow shop rescheduling problem (FSRP) necessitated by rush orders. Disjunctive graph is employed to demonstrate the FSRP. For a flow shop processing n jobs, after the original schedule has been made, and z out of n jobs have been processed in the flow shop, x rush orders come, so the original n jobs together with x rush orders should be rescheduled immediately so that the rush orders would be processed in the shortest time and the original jobs could be processed subject to some optimized criteria. The weighted mean flow time of both original jobs and rush orders is used as objective function. The weight for rush orders is much bigger than that of the original jobs, so the rush orders should be processed early in the new schedule. The ant colony optimization (ACO) algorithm used to solve the rescheduling problem has a weakness in that the search may fall into a local optimum. Mutation operation is employed to enhance the ACO performance. Numerical experiments demonstrated that the proposed algorithm has high computation repeatability and efficiency.
基金The National Natural Science Foundation of China ( No.60774078)Innovation Foundation of Shanghai University ,Scientific Research Special Fund of Shanghai Excellent Young Teachers , Chenguang Project ( No.2008CG48)Shanghai Leading Academic Discipline Project ( No.T0103)
文摘Since in most practical cases the processing time of scheduling is not deterministic, flow shop scheduling model with fuzzy processing time is established. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. In order to find a sequence that minimizes the mean makespan and the spread of the makespan, Lee and Li fuzzy ranking method is adopted and modified to solve the problem. Particle swarm optimization (PSO) is a population-based stochastic approximation algorithm that has been applied to a wide range of problems, but there is little reported in respect of application to scheduling problems because of its unsuitability for them. In the paper, PSO is redefined and modified by introducing genetic operations such as crossover and mutation to update the particles, which is called GPSO and successfully employed to solve the formulated problem. A series of benchmarks with fuzzy processing time are used to verify GPSO. Extensive experiments show the feasibility and effectiveness of the proposed method.
基金Sponsored by the Innovation Foundation of Shanghai University(Grant No.A.10-0101-07 -406)NNSF of China(Grant No.60874039)
文摘This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡ a (j∈N), and the processing time of job Jj is bj(j∈N) on a batch processor M. We take makespan (Cmax) as our minimization objective. In this paper, for the problem of FSMP-BI (m identical parallel machines on the first stage and a batch processor on the second stage), based on the algorithm given by Sung and Choung for the problem of 1| rj, BI | Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max{O(nlogn), O(nB)} time. A max{O(nlogn), O(nB)} time symmetric Algorithm H2 is given then for the problem of BI-FSMP (a batch processor on the first stage and m identical parallel machines on the second stage).
基金This project is supported by National Natural Science Foundation of China (No.60274013, No.60474002)Shanghai City Development Found for Science and Technology, China(No.04DZ11008)
文摘A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck (SB) procedure. In this algorithm, a schedule for the bottleneck machine is first constructed optimally and then the non-bottleneck machines are scheduled around the bottleneck schedule by some effective dispatching rules. Computational results show that the modified bottleneck-based procedure can achieve a tradeoff between solution quality and computational time comparing with SB procedure for medium-size problems. Furthermore it can obtain a good solution in quite short time for large-scale scheduling problems.
文摘In this paper the scheduling problem to minimize the expected makespan is discussed on two-machine flow shops with random disturbance on job processing times. The problem is represented by a stochastic programming model. We approximate the stochastic problem by a deterministic problem which can be solved by Johnson's rule. The estimation of approximation error is also discussed by analyzing the stochastic model and its approximate LP model.
基金This project is supported by National Natural Science Foundation of China (No. 50575137)Provincial Natural Science Foundation of Zhejiang, China (No. Z604342)Scientific Research Fund of Zhejiang Provincial Educational Committee, China (No. 20051643).
文摘A new concept of multi-shop (M ) is put forward which contains all basic shops including open shop (O), job shop (J ), flow shop (F ) and hybrid flow shop (H ) so that these basic shop can be scheduled together. Several algorithms including ant colony optimization (ACO), most work remaining (MWR), least work remaining (LWR), longest processing time (LPT) and shortest processing time (SPT) are used for scheduling the M. Numerical experiments of the M adopting data of some car and reC series benchmark instances are tested. The results show that the ACO algorithm has better performance for scheduling the M than the other algorithms, if minimizing the makespan ( Cmax^*) is taken as the objective function. As a comparison, the separate shops contained in the M are also scheduled by the ACO algorithm for the same objective function, when the completing time of the jobs in the previous shop is taken as the ready time of these jobs in the following shop. The results show that the M has the advantage of shortening the makespan upon separate shops.