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作 者:孙文娟 刘鹏[1] 宫华[1,2] SUN Wenjuan;LIU Peng;GONG Hua(School of Management,Shenyang University of Technology,Shenyang 110870,China;School of Science,Shenyang Ligong University,Shenyang 110159,China)
机构地区:[1]沈阳工业大学管理学院,辽宁沈阳110870 [2]沈阳理工大学理学院,辽宁沈阳110159
出 处:《运筹与管理》2024年第12期115-121,I0048,I0049,共9页Operations Research and Management Science
基 金:辽宁省“兴辽英才计划”项目(XLYC2006017);辽宁省教育厅科学研究项目(LG202025,LJKQZ2021057)。
摘 要:利用合作博弈理论研究了批处理机生产与成批运输协调调度问题。具有初始调度顺序的工件经过单台相同批处理机加工完成后,由一辆具有容量限制的运输车分批次运输到下一工序或客户端。考虑到工件可以通过结盟,并在联盟内重新调度以达到总成本节省,以工件联盟最大成本节省为特征函数建立合作博弈模型。分析博弈性质,并通过合理稳定的成本节省分配方法降低各工件成本。当运输车满批运输时,证明了合作博弈既是σ0-组可加博弈也是凸博弈,β规则和Shapley值均能得到核心分配,且Shapley值可以表述成一种简单可计算形式。当运输车无需满批运输时,通过反例分析了合作博弈的性质。In the production process of the process industry,there are many complicated processes.The continuous production processes require the coordination of production and transportation scheduling.The coordinated scheduling problem of batch production and batch delivery(CSP-BPBD)has a wide range of application scenarios in process industries such as iron and steel industry.The CSP-BPBD is described as follows:there are n jobs belonging to different customers,each of which needs to be processed on an identical batching machine with production capacity limits and then transported in batches by a transporter with limited capacity to the downstream process(or a customer).Furthermore,there is an initial processing order on the jobs of customers.It takes the same time for the batching machine to produce a batch of jobs and the same time for the transporter to transport a batch of jobs,which are independent of the number of jobs in the batch.Considering that jobs are willing to form a coalition by cooperation and rearrange their processing and transportation orders to gain cost savings,we can allocate the cost savings reasonably,so that all customers in the coalition can benefit.Therefore,it is of certain practical significance to study a coordinated scheduling problem of production and transportation by taking a cooperative game theoretical approach.In this paper,we take the cooperative game theory to study CSP-BPBD.The customer’s cost is defined as a linear function of the job’s completion time.The cooperative game models are proposed for CSP-BPBD with jobs as players and the maximal cost savings of the coalition as the characteristic function.For two different cases of whether the transporter delivers jobs in full batch or not,the properties of corresponding games are analyzed,and some fair and stable allocations of cost savings are presented.Firstly,the conditions of feasible schedule scheme and optimal schedule scheme are given.For each scheduling order,there can be different feasible schedule schemes corresponding
关 键 词:批处理机 批运输 合作博弈 SHAPLEY值 核心分配
分 类 号:O225[理学—运筹学与控制论] C931.1[理学—数学]
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