As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that a...As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that at least one machine is not eligible for at least one job.PBPMSP and scheduling problems with machine eligibility are frequently considered;however,PBPMSP with machine eligibility is seldom explored.This study investigates PBPMSP with machine eligibility in fabric dyeing and presents a novel shuffled frog-leaping algorithm with competition(CSFLA)to minimize makespan.In CSFLA,the initial population is produced in a heuristic and random way,and the competitive search of memeplexes comprises two phases.Competition between any two memeplexes is done in the first phase,then iteration times are adjusted based on competition,and search strategies are adjusted adaptively based on the evolution quality of memeplexes in the second phase.An adaptive population shuffling is given.Computational experiments are conducted on 100 instances.The computational results showed that the new strategies of CSFLA are effective and that CSFLA has promising advantages in solving the considered PBPMSP.展开更多
This study focuses on the scheduling problem of unrelated parallel batch processing machines(BPM)with release times,a scenario derived from the moulding process in a foundry.In this process,a batch is initially formed...This study focuses on the scheduling problem of unrelated parallel batch processing machines(BPM)with release times,a scenario derived from the moulding process in a foundry.In this process,a batch is initially formed,placed in a sandbox,and then the sandbox is positioned on a BPM formoulding.The complexity of the scheduling problem increases due to the consideration of BPM capacity and sandbox volume.To minimize the makespan,a new cooperated imperialist competitive algorithm(CICA)is introduced.In CICA,the number of empires is not a parameter,and four empires aremaintained throughout the search process.Two types of assimilations are achieved:The strongest and weakest empires cooperate in their assimilation,while the remaining two empires,having a close normalization total cost,combine in their assimilation.A new form of imperialist competition is proposed to prevent insufficient competition,and the unique features of the problem are effectively utilized.Computational experiments are conducted across several instances,and a significant amount of experimental results show that the newstrategies of CICAare effective,indicating promising advantages for the considered BPMscheduling problems.展开更多
In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best exis...In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.展开更多
The paper investigates a semi on-line scheduling problem wherein the largest processing time of jobs done by three uniform machines M1, M2, M3 is known in advance. A speed si (s1=1, s2=r, s3=s, 1≤r≤s) is associated ...The paper investigates a semi on-line scheduling problem wherein the largest processing time of jobs done by three uniform machines M1, M2, M3 is known in advance. A speed si (s1=1, s2=r, s3=s, 1≤r≤s) is associated with machine Mi. Our goal is to maximize Cmin?the minimum workload of the three machines. We present a min3 algorithm and prove its competitive ratio is max{r+1,(3s+r+1)/(1+r+s)}, with the lower bound being at least max{2,r}. We also claim the competitive ratio of min3 algo- rithm cannot be improved and is the best possible for 1≤s≤2, r=1.展开更多
A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary ...A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.展开更多
This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service ...This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels, so each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when its GoS level is no less than that of the machine. The goal is to minimize the makespan. For non-preemptive version, we propose an optimal online al-gorithm with competitive ratio 5/3. For preemptive version, we propose an optimal online algorithm with competitive ratio 3/2.展开更多
In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Ma...In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.展开更多
In view of the fact that traditional job shop scheduling only considers a single factor, which affects the effect of resource allocation, the dual-resource integrated scheduling problem between AGV and machine in inte...In view of the fact that traditional job shop scheduling only considers a single factor, which affects the effect of resource allocation, the dual-resource integrated scheduling problem between AGV and machine in intelligent manufacturing job shop environment was studied. The dual-resource integrated scheduling model of AGV and machine was established by comprehensively considering constraints of machines, workpieces and AGVs. The bidirectional single path fixed guidance system based on topological map was determined, and the AGV transportation task model was defined. The improved A* path optimization algorithm was used to determine the optimal path, and the path conflict elimination mechanism was described. The improved NSGA-Ⅱ algorithm was used to determine the machining workpiece sequence, and the competition mechanism was introduced to allocate AGV transportation tasks. The proposed model and method were verified by a workshop production example, the results showed that the dual resource integrated scheduling strategy of AGV and machine is effective.展开更多
A novel rule-based model for multi-stage multi-product scheduling problem(MMSP)in batch plants with parallel units is proposed.The scheduling problem is decomposed into two sub-problems of order assignment and order s...A novel rule-based model for multi-stage multi-product scheduling problem(MMSP)in batch plants with parallel units is proposed.The scheduling problem is decomposed into two sub-problems of order assignment and order sequencing.Firstly,hierarchical scheduling strategy is presented for solving the former sub-problem,where the multi-stage multi-product batch process is divided into multiple sequentially connected single process stages,and then the production of orders are arranged in each single stage by using forward order assignment strategy and backward order assignment strategy respectively according to the feature of scheduling objective.Line-up competition algorithm(LCA)is presented to find out optimal order sequence and order assignment rule,which can minimize total flow time or maximize total weighted process time.Computational results show that the proposed approach can obtain better solutions than those of the literature for all scheduling problems with more than 10 orders.Moreover,with the problem size increasing,the solutions obtained by the proposed approach are improved remarkably.The proposed approach has the potential to solve large size MMSP.展开更多
In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two po...In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two possible widths mj = 1 or m, we present an optimal online algorithm by using ＂temporary schedule＂.展开更多
This paper considers two parallel machine scheduling problems, where the objectives of both problems are to minimize the makespan, and the jobs arrive over time, on two uniform machines with speeds 1 and s （s 〉 1）,...This paper considers two parallel machine scheduling problems, where the objectives of both problems are to minimize the makespan, and the jobs arrive over time, on two uniform machines with speeds 1 and s （s 〉 1）, and on m identical machines, respectively. For the first problem, the authors show that the on-line LPT algorithm has a competitive ratio of （1 ＋ √5）/2 ≈ 1.6180 and the bound is tight. Furthermore, the authors prove that the on-line LPT algorithm has the best possible competitive ratio if s ≥ 1.8020. For the second problem, the authors present a lower bound of （15 - √17）/8 ≈ 1.3596 on the competitive ratio of any deterministic on-line algorithm. This improves a previous result of 1.3473.展开更多
In this paper we consider an on-line scheduling problem, where jobs with similar processing times within [1, r] arrive one by one to be scheduled in an on-line setting on two identical parallel processors without pree...In this paper we consider an on-line scheduling problem, where jobs with similar processing times within [1, r] arrive one by one to be scheduled in an on-line setting on two identical parallel processors without preemption. The objective is to nlinimize makespan. We devise a randomized on-line algorithm for this problem along with a lower bound.展开更多
In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance tim...In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.展开更多
In this paper, we consider the on-line scheduling of unit time jobs with rejection on rn identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty ...In this paper, we consider the on-line scheduling of unit time jobs with rejection on rn identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty of the rejected jobs. We give an on-line algorithm for the problem with competitive ratio 1/2 （2 ＋√3） ≈ 1.86602.展开更多
Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi....Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.展开更多
The authors consider the problem of on-line scheduling of unit execution time jobs on uniform machines with rejection penalty. The jobs arrive one by one and can be either accepted and scheduled, or be rejected. The o...The authors consider the problem of on-line scheduling of unit execution time jobs on uniform machines with rejection penalty. The jobs arrive one by one and can be either accepted and scheduled, or be rejected. The objective is to minimize the total completion time of the accepted jobs and the total penalty of the rejection jobs. The authors propose an on-line algorithm and prove that the competitive ratio is 1/2 （2 W √3） ≈ 1.86602.展开更多
We address the problem of preemptively schedule on-line jobs on arbitrary m uniformly related machines with the objective of minimizing the schedule length. We provide the first on-line algorithm for this general prob...We address the problem of preemptively schedule on-line jobs on arbitrary m uniformly related machines with the objective of minimizing the schedule length. We provide the first on-line algorithm for this general problem, and show that the algorithm has a competitive ratio of 1 ± σ, where a (m - 1)s1/(si +…+ sm), S1 S2 Sm being the speeds of the m machines.展开更多
This paper considers an on-line scheduling and routing problem concerning the automated storage and retrieval system from tobacco industry. In this problem, stacker cranes run on one common rail between two racks. Mul...This paper considers an on-line scheduling and routing problem concerning the automated storage and retrieval system from tobacco industry. In this problem, stacker cranes run on one common rail between two racks. Multiple input/output-points are located at the bottom of the racks. The stacker cranes transport bins between the input/output-points and cells on the racks to complete requests generated over time. Each request should be accomplished within its response time. The objective is to minimize the time by which all the generated requests are completed. Under a given physical layout, the authors study the complexity of the problem and design on-line algorithms for both one-stacker-crane model and two-stacker-crane model. The algorithms axe validated by instances and numerical simulations.展开更多
In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, w...In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, we consider such a model. We study the scheduling problem P(n1,n2), where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon as all jobs in the first group are assigned, the second job group appears. The objective is to minimize the longest job completion time (makespan). We show a lower bound of 3/2 even for very special cases. Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed for the general case. The main contribution of this paper is to discuss the impact of the quantity of available information in designing an on-line algorithm. It is interesting to note that the absence of even a little bit information may significantly affect the performance of an algorithm.展开更多
基金supported by the National Natural Science Foundation of China(Grant Number 61573264).
文摘As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that at least one machine is not eligible for at least one job.PBPMSP and scheduling problems with machine eligibility are frequently considered;however,PBPMSP with machine eligibility is seldom explored.This study investigates PBPMSP with machine eligibility in fabric dyeing and presents a novel shuffled frog-leaping algorithm with competition(CSFLA)to minimize makespan.In CSFLA,the initial population is produced in a heuristic and random way,and the competitive search of memeplexes comprises two phases.Competition between any two memeplexes is done in the first phase,then iteration times are adjusted based on competition,and search strategies are adjusted adaptively based on the evolution quality of memeplexes in the second phase.An adaptive population shuffling is given.Computational experiments are conducted on 100 instances.The computational results showed that the new strategies of CSFLA are effective and that CSFLA has promising advantages in solving the considered PBPMSP.
基金the National Natural Science Foundation of China(Grant Number 61573264).
文摘This study focuses on the scheduling problem of unrelated parallel batch processing machines(BPM)with release times,a scenario derived from the moulding process in a foundry.In this process,a batch is initially formed,placed in a sandbox,and then the sandbox is positioned on a BPM formoulding.The complexity of the scheduling problem increases due to the consideration of BPM capacity and sandbox volume.To minimize the makespan,a new cooperated imperialist competitive algorithm(CICA)is introduced.In CICA,the number of empires is not a parameter,and four empires aremaintained throughout the search process.Two types of assimilations are achieved:The strongest and weakest empires cooperate in their assimilation,while the remaining two empires,having a close normalization total cost,combine in their assimilation.A new form of imperialist competition is proposed to prevent insufficient competition,and the unique features of the problem are effectively utilized.Computational experiments are conducted across several instances,and a significant amount of experimental results show that the newstrategies of CICAare effective,indicating promising advantages for the considered BPMscheduling problems.
文摘In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.
文摘The paper investigates a semi on-line scheduling problem wherein the largest processing time of jobs done by three uniform machines M1, M2, M3 is known in advance. A speed si (s1=1, s2=r, s3=s, 1≤r≤s) is associated with machine Mi. Our goal is to maximize Cmin?the minimum workload of the three machines. We present a min3 algorithm and prove its competitive ratio is max{r+1,(3s+r+1)/(1+r+s)}, with the lower bound being at least max{2,r}. We also claim the competitive ratio of min3 algo- rithm cannot be improved and is the best possible for 1≤s≤2, r=1.
文摘A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.
基金Project supported by the National Natural Science Foundation of China (No. 10271110) and the Teaching and Research Award Pro-gram for Outstanding Young Teachers in Higher Education, Institu-tions of MOE, China
文摘This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels, so each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when its GoS level is no less than that of the machine. The goal is to minimize the makespan. For non-preemptive version, we propose an optimal online al-gorithm with competitive ratio 5/3. For preemptive version, we propose an optimal online algorithm with competitive ratio 3/2.
基金Project (No. Y605316) supported by the Natural Science Foundationof Zhejiang Province, China and the Natural Science Foundation of the Education Department of Zhejiang Province (No. 20060578), China
文摘In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.
基金Project(BK20201162)supported by the General Program of Natural Science Foundation of Jiangsu Province,ChinaProject(JC2019126)supported by the Science and Technology Plan Fundamental Scientific Research Funding Project of Nantong,China+1 种基金Project(CE20205045)supported by the Changzhou Science and Technology Support Plan(Social Development),ChinaProject(51875171)supported by the National Nature Science Foundation of China。
文摘In view of the fact that traditional job shop scheduling only considers a single factor, which affects the effect of resource allocation, the dual-resource integrated scheduling problem between AGV and machine in intelligent manufacturing job shop environment was studied. The dual-resource integrated scheduling model of AGV and machine was established by comprehensively considering constraints of machines, workpieces and AGVs. The bidirectional single path fixed guidance system based on topological map was determined, and the AGV transportation task model was defined. The improved A* path optimization algorithm was used to determine the optimal path, and the path conflict elimination mechanism was described. The improved NSGA-Ⅱ algorithm was used to determine the machining workpiece sequence, and the competition mechanism was introduced to allocate AGV transportation tasks. The proposed model and method were verified by a workshop production example, the results showed that the dual resource integrated scheduling strategy of AGV and machine is effective.
基金Supported by the National Natural Science Foundation of China(21376185)
文摘A novel rule-based model for multi-stage multi-product scheduling problem(MMSP)in batch plants with parallel units is proposed.The scheduling problem is decomposed into two sub-problems of order assignment and order sequencing.Firstly,hierarchical scheduling strategy is presented for solving the former sub-problem,where the multi-stage multi-product batch process is divided into multiple sequentially connected single process stages,and then the production of orders are arranged in each single stage by using forward order assignment strategy and backward order assignment strategy respectively according to the feature of scheduling objective.Line-up competition algorithm(LCA)is presented to find out optimal order sequence and order assignment rule,which can minimize total flow time or maximize total weighted process time.Computational results show that the proposed approach can obtain better solutions than those of the literature for all scheduling problems with more than 10 orders.Moreover,with the problem size increasing,the solutions obtained by the proposed approach are improved remarkably.The proposed approach has the potential to solve large size MMSP.
基金Project supported by the National Natural Science Foundation of China (Grant No.10971131)the Shanghai Leading AcademicDiscipline Project (Grant No.S30104)the Innovation Foundation of Shanghai University (Grant No.SHUCX091077)
文摘In this paper we consider an online scheduling of parallel jobs with preemption on identical machines, where jobs arrive over time. The objective is to minimize the makespan. For the problem that jobs have only two possible widths mj = 1 or m, we present an optimal online algorithm by using ＂temporary schedule＂.
基金supported by the Special Funds of the National Natural Science Foundation of China under Grant No.61340045the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20123705110003Innovation Project of Shangdong Graduate Education under Grant No.SDYC13036
文摘This paper considers two parallel machine scheduling problems, where the objectives of both problems are to minimize the makespan, and the jobs arrive over time, on two uniform machines with speeds 1 and s （s 〉 1）, and on m identical machines, respectively. For the first problem, the authors show that the on-line LPT algorithm has a competitive ratio of （1 ＋ √5）/2 ≈ 1.6180 and the bound is tight. Furthermore, the authors prove that the on-line LPT algorithm has the best possible competitive ratio if s ≥ 1.8020. For the second problem, the authors present a lower bound of （15 - √17）/8 ≈ 1.3596 on the competitive ratio of any deterministic on-line algorithm. This improves a previous result of 1.3473.
文摘In this paper we consider an on-line scheduling problem, where jobs with similar processing times within [1, r] arrive one by one to be scheduled in an on-line setting on two identical parallel processors without preemption. The objective is to nlinimize makespan. We devise a randomized on-line algorithm for this problem along with a lower bound.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271338,11171313,61070229,10901144,11001117supported by the Ph.D.Programs Foundation of Ministry ofEducation of China under Grant No.20111401110005the Henan Province Natural Science Foundation under Grant No.112300410047
文摘In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.
基金This work is supported by Natural Science Foundation of China under Grant No. 10171054.
文摘In this paper, we consider the on-line scheduling of unit time jobs with rejection on rn identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty of the rejected jobs. We give an on-line algorithm for the problem with competitive ratio 1/2 （2 ＋√3） ≈ 1.86602.
文摘Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.
基金the National Natural Science Foundation of China under Grant No.10671108
文摘The authors consider the problem of on-line scheduling of unit execution time jobs on uniform machines with rejection penalty. The jobs arrive one by one and can be either accepted and scheduled, or be rejected. The objective is to minimize the total completion time of the accepted jobs and the total penalty of the rejection jobs. The authors propose an on-line algorithm and prove that the competitive ratio is 1/2 （2 W √3） ≈ 1.86602.
基金This research is supported by National Natural Science Foundation of China Shandong Province the Foundation for University
文摘We address the problem of preemptively schedule on-line jobs on arbitrary m uniformly related machines with the objective of minimizing the schedule length. We provide the first on-line algorithm for this general problem, and show that the algorithm has a competitive ratio of 1 ± σ, where a (m - 1)s1/(si +…+ sm), S1 S2 Sm being the speeds of the m machines.
基金supported by the National Natural Science Foundation of China under Grant No.11371137Research Fund for the Doctoral Program of China under Grant No.20120074110021
文摘This paper considers an on-line scheduling and routing problem concerning the automated storage and retrieval system from tobacco industry. In this problem, stacker cranes run on one common rail between two racks. Multiple input/output-points are located at the bottom of the racks. The stacker cranes transport bins between the input/output-points and cells on the racks to complete requests generated over time. Each request should be accomplished within its response time. The objective is to minimize the time by which all the generated requests are completed. Under a given physical layout, the authors study the complexity of the problem and design on-line algorithms for both one-stacker-crane model and two-stacker-crane model. The algorithms axe validated by instances and numerical simulations.
基金Research partially supported by a Hong Kong Government RGC Earmarked Grant.Ref.No.CUHK356/96E Research partially supported by National 973 Fundamental Research Project of china and National Natural Science Foundation of China (19801032)
文摘In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, we consider such a model. We study the scheduling problem P(n1,n2), where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon as all jobs in the first group are assigned, the second job group appears. The objective is to minimize the longest job completion time (makespan). We show a lower bound of 3/2 even for very special cases. Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed for the general case. The main contribution of this paper is to discuss the impact of the quantity of available information in designing an on-line algorithm. It is interesting to note that the absence of even a little bit information may significantly affect the performance of an algorithm.
