A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there...A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there is an initial scheduling order for processing jobs on the machines.The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value.The properties of cooperative games under two different types of admissible rearrangements are analysed.For TFS-PTCS problems with identical processing time,it is proved that,the corresponding games areσ_(0)-component additive and convex under one admissible rearrangement.The Shapley value gives a core allocation,and is provided in a computable form.Under the other admissible rearrangement,the games neither need to beσ_(0)-component additive nor convex,and an allocation rule of modified Shapley value is designed.The properties of the cooperative games are analysed by a counterexample for general problems.展开更多
This paper systematically studies the two machine flow-shop scheduling problems with no-wait and deterministic unavailable interval constraints.To minimize the makespan,three integer programming mathematical models ar...This paper systematically studies the two machine flow-shop scheduling problems with no-wait and deterministic unavailable interval constraints.To minimize the makespan,three integer programming mathematical models are formulated for two-machine flow-shop with no-wait constraint,two-machine flow-shop with resumable unavailable interval constraint,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problems,respectively.The optimal conditions of solv-ing the two-machine flow-shop with no-wait constraint problem by the permutation schedules,the two-machine flow-shop with resumable unavailable interval constraint problem by the Johnson algorithm,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem by the Gilmore and Gomory Algorithm(GGA)are presented,respectively.And the tight worst-case performance bounds of Johnson and GGA algorithms for these problems are also proved to be 2.Several instances are generated to demonstrate the proposed theorems.Based on the experimental results,GGA obtains the optimal solution for the two-machine flow-shop with no-wait constraint problem.Although it cannot reach the optimal solution for the two-machine flow-shop with resumable unavailable interval constraint problem,the optimal gap is 0.18%on average when the number of jobs is 100.Moreover,under some special conditions,it yields the optimal solution for the two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem.Therefore,GGA is an efficient heuristic to solve these problems.展开更多
In the“shared manufacturing”environment,based on fairness,shared manufacturing platforms often require manufacturing service enterprises to arrange production according to the principle of“order first,finish first...In the“shared manufacturing”environment,based on fairness,shared manufacturing platforms often require manufacturing service enterprises to arrange production according to the principle of“order first,finish first”which leads to a series of scheduling problems with fixed processing sequences.In this paper,two two-machine hybrid flow-shop problems with fixed processing sequences are studied.Each job has two tasks.The first task is flexible,which can be processed on either of the two machines,and the second task must be processed on the second machine after the first task is completed.We consider two objective functions:to minimize the makespan and tominimize the total weighted completion time.First,we show the problem for any one of the two objectives is ordinary NP-hard by polynomial-time Turing Reduction.Then,using the Continuous ProcessingModule(CPM),we design a dynamic programming algorithm for each case and calculate the time complexity of each algorithm.Finally,numerical experiments are used to analyze the effect of dynamic programming algorithms in practical operations.Comparative experiments show that these dynamic programming algorithms have comprehensive advantages over the branch and bound algorithm(a classical exact algorithm)and the discrete harmony search algorithm(a high-performance heuristic algorithm).展开更多
基金supported in part by the Liaoning Province Xingliao Talents Plan Project under Grant No.XLYC2006017in part by the Scientific Research Funds Project of Educational Department of Liaoning Province under Grant Nos.LG202025 and LJKZ0260。
文摘A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there is an initial scheduling order for processing jobs on the machines.The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value.The properties of cooperative games under two different types of admissible rearrangements are analysed.For TFS-PTCS problems with identical processing time,it is proved that,the corresponding games areσ_(0)-component additive and convex under one admissible rearrangement.The Shapley value gives a core allocation,and is provided in a computable form.Under the other admissible rearrangement,the games neither need to beσ_(0)-component additive nor convex,and an allocation rule of modified Shapley value is designed.The properties of the cooperative games are analysed by a counterexample for general problems.
基金supported in part by the National Natural Sci-ence Foundation of China(NSFC)under Grant No.71801051.
文摘This paper systematically studies the two machine flow-shop scheduling problems with no-wait and deterministic unavailable interval constraints.To minimize the makespan,three integer programming mathematical models are formulated for two-machine flow-shop with no-wait constraint,two-machine flow-shop with resumable unavailable interval constraint,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problems,respectively.The optimal conditions of solv-ing the two-machine flow-shop with no-wait constraint problem by the permutation schedules,the two-machine flow-shop with resumable unavailable interval constraint problem by the Johnson algorithm,and two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem by the Gilmore and Gomory Algorithm(GGA)are presented,respectively.And the tight worst-case performance bounds of Johnson and GGA algorithms for these problems are also proved to be 2.Several instances are generated to demonstrate the proposed theorems.Based on the experimental results,GGA obtains the optimal solution for the two-machine flow-shop with no-wait constraint problem.Although it cannot reach the optimal solution for the two-machine flow-shop with resumable unavailable interval constraint problem,the optimal gap is 0.18%on average when the number of jobs is 100.Moreover,under some special conditions,it yields the optimal solution for the two-machine flow-shop with no-wait and non-resumable unavailable interval constraints problem.Therefore,GGA is an efficient heuristic to solve these problems.
基金This work was partially supported by the Zhejiang Provincial Philosophy and Social Science Program of China(Grant No.19NDJC093YB)the National Social Science Foundation of China(Grant No.19BGL001)+1 种基金the Natural Science Foundation of Zhejiang Province of China(Grant No.LY19A010002)the Natural Science Foundation of Ningbo of China(The design of algorithms and cost-sharing rules for scheduling problems in shared manufacturing,Acceptance No.20211JCGY010241).
文摘In the“shared manufacturing”environment,based on fairness,shared manufacturing platforms often require manufacturing service enterprises to arrange production according to the principle of“order first,finish first”which leads to a series of scheduling problems with fixed processing sequences.In this paper,two two-machine hybrid flow-shop problems with fixed processing sequences are studied.Each job has two tasks.The first task is flexible,which can be processed on either of the two machines,and the second task must be processed on the second machine after the first task is completed.We consider two objective functions:to minimize the makespan and tominimize the total weighted completion time.First,we show the problem for any one of the two objectives is ordinary NP-hard by polynomial-time Turing Reduction.Then,using the Continuous ProcessingModule(CPM),we design a dynamic programming algorithm for each case and calculate the time complexity of each algorithm.Finally,numerical experiments are used to analyze the effect of dynamic programming algorithms in practical operations.Comparative experiments show that these dynamic programming algorithms have comprehensive advantages over the branch and bound algorithm(a classical exact algorithm)and the discrete harmony search algorithm(a high-performance heuristic algorithm).
基金国家科技公关计划项目(the Key Technologies R&D Program of China under Grant No.2001BA201A32)国家高技术研究发展计划(863) (the National High-Tech Research and Development Plan of China under Grant No.2002AA415270)
