We consider the resumable version of the two-agent single machine scheduling prob- lems with forbidden intervals in which the jobs cannot be processed. The goal is to minimize the sum of the objective functions of the...We consider the resumable version of the two-agent single machine scheduling prob- lems with forbidden intervals in which the jobs cannot be processed. The goal is to minimize the sum of the objective functions of the two agents. Polynomial and pseudo-polynomial time algorithms are presented for various combinations of regular scheduling objective functions.展开更多
A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs...A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average.展开更多
In a recent paper,Feng et al.[5](Two-agent scheduling with rejection on a single machine.Appl.Math.Model.39(2015)1183-1193)studied some two-agent scheduling problems with rejection on a single machine.The authors show...In a recent paper,Feng et al.[5](Two-agent scheduling with rejection on a single machine.Appl.Math.Model.39(2015)1183-1193)studied some two-agent scheduling problems with rejection on a single machine.The authors showed that all problems are NP-hard and then provided four dynamic programming algorithms.Unfortunately,we observe that some mistakes are contained in the two dynamic programming algorithms.In this note,we first show by a counter-example that the above two algorithms are incorrect.Furthermore,we also provide two new dynamic programming algorithms to solve the same problems.展开更多
A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide ...A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide a new approximation algorithm called CLPT. On the one hand, we compare the performance between the CLPT algorithm and the optimal solution and find that the solution obtained by the CLPT algorithm is very close to the optimal solution. On the other hand, we design different experimental frameworks to compare the CLPT algorithm and the A-LS algorithm for a comprehensive performance evaluation. A large number of numerical simulation results show that the CLPT algorithm outperformed the A-LS algorithm.展开更多
This paper studies the two-agent scheduling on a bounded parallel-batching machine.In the problem,there are two agents A and B each having their own job sets with the restriction that the processing times of jobs of a...This paper studies the two-agent scheduling on a bounded parallel-batching machine.In the problem,there are two agents A and B each having their own job sets with the restriction that the processing times of jobs of agent B are equal.The jobs of different agents can be processed in a common batch.Moreover,each agent has its own objective function to be minimized.The objective function of agent A is the makespan of its jobs,and the objective function of agent B is the maximum lateness of its jobs.We present a polynomial-time algorithm for finding all Pareto optimal solutions of this two-agent parallel-batching scheduling problem.展开更多
Two-agent single-machine scheduling problem is considered in this paper.Agent A’s goal is to minimize the sum of the total weighted delivery time and the total delivery cost,and agent B has the delivery time window.F...Two-agent single-machine scheduling problem is considered in this paper.Agent A’s goal is to minimize the sum of the total weighted delivery time and the total delivery cost,and agent B has the delivery time window.First,the NP-hardness of the general problem is proved,and then two special cases are considered.One case is that A’s jobs have agreeable ratio and this problem is still NP-hard.A pseudo-polynomial dynamic programming algorithm and a 32-approximation algorithm are designed.In the other case,A’s jobs have agreeable ratio and B’s jobs have deadline at the same time.This problem is polynomial solvable.展开更多
基金Supported by National Natural Science Foundation of China(11401604,11401605,11271338,11326191)National Natural Science Foundation of Henan(132300410392)the Ph.D Programs Foundation of Ministry of Education of China(20111401110005)
文摘We consider the resumable version of the two-agent single machine scheduling prob- lems with forbidden intervals in which the jobs cannot be processed. The goal is to minimize the sum of the objective functions of the two agents. Polynomial and pseudo-polynomial time algorithms are presented for various combinations of regular scheduling objective functions.
基金This work was supported in part by the Project of Liaoning BaiQianWan Talents Program under Grand No.2021921089the Science Research Foundation of Educational Department of Liaoning Province under Grand No.LJKQZ2021057 and WJGD2020001+2 种基金the Key Program of Social Science Planning Foundation of Liaoning Province under Grant L21AGL017the special project of SUT on serving local economic and social development decision-making under Grant FWDFGD2021019the“Double First-Class”Construction Project in Liaoning Province under Grant ZDZRGD2020037.
文摘A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average.
基金Supported by National Natural Science Foundation of China(Grant Nos.11901168,11971443 and 12271491)。
文摘In a recent paper,Feng et al.[5](Two-agent scheduling with rejection on a single machine.Appl.Math.Model.39(2015)1183-1193)studied some two-agent scheduling problems with rejection on a single machine.The authors showed that all problems are NP-hard and then provided four dynamic programming algorithms.Unfortunately,we observe that some mistakes are contained in the two dynamic programming algorithms.In this note,we first show by a counter-example that the above two algorithms are incorrect.Furthermore,we also provide two new dynamic programming algorithms to solve the same problems.
文摘A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide a new approximation algorithm called CLPT. On the one hand, we compare the performance between the CLPT algorithm and the optimal solution and find that the solution obtained by the CLPT algorithm is very close to the optimal solution. On the other hand, we design different experimental frameworks to compare the CLPT algorithm and the A-LS algorithm for a comprehensive performance evaluation. A large number of numerical simulation results show that the CLPT algorithm outperformed the A-LS algorithm.
基金This research was supported in part by the National Natural Science Foundation of China(Nos.11401604,11571323,11701595,11501279)also supported by Program for Interdisciplinary Direction Team in Zhongyuan University of Technology,China.
文摘This paper studies the two-agent scheduling on a bounded parallel-batching machine.In the problem,there are two agents A and B each having their own job sets with the restriction that the processing times of jobs of agent B are equal.The jobs of different agents can be processed in a common batch.Moreover,each agent has its own objective function to be minimized.The objective function of agent A is the makespan of its jobs,and the objective function of agent B is the maximum lateness of its jobs.We present a polynomial-time algorithm for finding all Pareto optimal solutions of this two-agent parallel-batching scheduling problem.
基金the National Natural Science Foundation of China(No.11371137)。
文摘Two-agent single-machine scheduling problem is considered in this paper.Agent A’s goal is to minimize the sum of the total weighted delivery time and the total delivery cost,and agent B has the delivery time window.First,the NP-hardness of the general problem is proved,and then two special cases are considered.One case is that A’s jobs have agreeable ratio and this problem is still NP-hard.A pseudo-polynomial dynamic programming algorithm and a 32-approximation algorithm are designed.In the other case,A’s jobs have agreeable ratio and B’s jobs have deadline at the same time.This problem is polynomial solvable.
