资源受限工程调度及其在工程供应链设计中的应用
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摘要
工程供应链管理是供应链管理和工程项目管理研究的新领域,关于工程供应链设计问题的研究仍未开展。在以承包商为核心的工程供应链中,供应链构建与运行的驱动来自于工程活动网络,而合作伙伴(如专业分包商、混凝土供应商、原材料供应商等)的资源能力将会对工程调度构成约束,在工程供应链的设计中必须充分考虑各合作伙伴的资源能力约束和工程工期底线约束,促成总的工程活动成本最小。基于此,本文首先对活动成本目标下的资源受限工程调度问题展开研究,然后将有关理论与方法应用到工程供应链设计中。
资源受限工程调度问题的研究中很少关注活动成本目标,而问题中以活动成本最小化为目标时也是一类NP-Hard 问题,并且问题目标是非正规的。考虑活动的单执行模式和可重用资源约束,给出了问题的数学模型,分析了启发式求解问题的基本思想,并提出了三类调度方法:1)、基于活动前置矩阵的调度,给出了活动前置矩阵的构造规则; 2)、基于优先规则的调度,结合活动成本目标改造了传统的串行调度方案和并行调度方案,并设计了相应的优先规则; 3)、改进的遗传算法:采用紧前(后)关系相容链表进行编码,解码方法是一种串行调度方案。针对改造PSPLIB 中的单模式算例,遗传算法的求解效果相对较好,采用确定型多回合计算的效果要优于单优先规则下的同类启发式调度方法。
基于单执行模式问题的研究,进一步讨论了多执行模式下的问题,其中,在进行活动调度的同时也要选择相应的执行模式,文中给出了考虑多模式调度的通用并行调度框架,并基于这个框架提出了两种调度策略:联合调度策略、两步调度策略。针对改造PSPLIB 中的多模式算例,虽然同类算法中在模式的选择时考虑了折衷的先序相关成本因素所得到的有效解数量略少,但得到的平均偏差却是最小的,而且活动-模式两步调度策略下得到的结果平均偏差小于活动-模式联合调度策略。
工程供应链中可重用资源供应商是承包商最直接的合作伙伴,他们的资源能力对工程调度会产生相应的约束,可以基于资源受限工程调度进行工程中多可重用资源的合作伙伴选择。文中给出了问题的数学模型,讨论了问题规模约减的原理。基于问题特性,构造了遗传算法的求解框架,并进行了算例测试,结果表明,改进遗传算法求解此类问题能够获得较好的效果。在多资源供应商选择问题的基础上,随后构造的供应-执行两层工程供应链设计问题中加入了对作为工程执行层的承包商的选择因素,文中描述了的问题的数学模型,给出了其求解方法。
Construction supply chain management is a new area of construction project management and supply chain management. There is still no research on design of construction supply chain. In a construction supply chain where contractor is the kernel, design and operation of the chain is driven by project activity network where capacity of the partners such as specialized subcontractors, ready-mix concrete suppliers, raw material suppliers, will become a constraint to project scheduling. Therefore, resource-constraints from these partners and limitation on project duedate must be considered in design of construction supply chain so that the objective of minimizing activities’cost in project can be achieved. For the above, resource-constrained project scheduling with the objective of minimizing activities’cost will be discussed firstly based on which research on design of construction supply chain is going to be carried out.
There is little attention paid to activities’cost of project in resource-constrained project scheduling problems(RCPSPs). When the objective of minimizing activities’cost is considered as the performance measure, the problem is also NP-hard and the objective is nonregular. A mathematical model is put forward for the cases the activities are executed in one execution mode and renewable resources are consumed. The basic thinking is analyzed for solution of the problems in heuristics and three approaches are developed: 1).Scheduling based on Preposing Acitivity Matrix where some rules are developed to form the matrix. 2).Priority-rule-based Scheduling that is updated to achieve the new objective on the basis of the old one for the RCPSPs with makespan objective and some priority rules are employed in the serial schema and the parallel schema. 3).Improved Genetic Algorithm where the schema of encoding is an activities’chain with precedence relationship and the decoding procedure is a serial scheduling schema. Computational Study with the single-mode instances in updated PSPLIB shows that the efficiency of the genetic algorithm proposed is the best and the results will become better when deterministic multi-pass approaches are used.
The above research is extended to the cases activities have multiple possible execution modes in the following. In the new problems, the execution modes must be selected for the activities when they are scheduled. A general parallel schedule generation schema is
proposed for multi-mode scheduling and two heuristic procedures are developed: united scheduling and two-step scheduling. Computational study with the multi-mode instances in updated PSPLIB shows that, when the factors about the compromised transitively relative cost is considered for selecting execution modes, a relatively fewer valid schedules will be got than the heuristics considering other factors in the same approach, but the average error is the minimal. Additionally, the average error of the heuristics with two-step scheduling is less than that of the heuristics with united scheduling. The renewable resources suppliers are the most immediate partners for contractor in construction supply chain and their capacities will form the constraints to project scheduling. That’s to say, when selecting these partners, the RCPSPs must be taken into account. The mathematical model for selecting these suppliers in construction project is proposed and the principle to reduce the solution space is discussed. Following that, a schema with GA to solve the problems is designed that is test by an example. The results show that a fine efficiency can be got with the improved GA. Whereafter, a problem about design of supply-execution construction supply chain is proposed, where one of candidate contractors should be selected to execute the construction project, and the representation of the problems and the approach for solution are all given. Suppliers selection is to solve the problems of designing supply chain in a local facet, but design of supply chain network is in the whole. Based on the analysis about the structure of construction supply chain network, integrated project scheduling and material ordering problems with limited capacities are proposed firstly where bilevel capacities about renewable resources and raw materials are all described. This type of problems can be decomposed to two types of problems: single-mode RCPSP with the objective of minimizing activities’cost(SMRCPSP-AC) and material ordering problem in a finite planning horizon with limited supply capacity(MOP-LSC), where the latter can be solved by dynamic programming. A feasible solution for the integrated problem may be got by searching a feasible solution for SMRCPSP-AC and then solving the relative MOP-LSC, and the optimal one will be found out in the set of feasible solutions for the integrated problem. A schema with improved GA is developed to solve the integrated problems. The numerical computation shows that the efficiency is fine when selection scheme is represented by stochastic tournament model with elitist preservation. This type of problems can be extended to design construction supply chain networks. To solve the proposed
problems with GA, the schema of encoding is an integrated one including two segments where suppliers and activities are encoded by different schemas and the decoding procedures are processed separately after which, SMRCPSP-AC and MOP-LSC are formed and solved in turn to get a feasible solution of designing construction supply chain network. Different operators are used on the two segments in the chromosome. It can be concluded based on the computational study that this type of problems can be solved by using the above genetic algorithm.
资源受限工程调度问题的研究中很少关注活动成本目标,而问题中以活动成本最小化为目标时也是一类NP-Hard 问题,并且问题目标是非正规的。考虑活动的单执行模式和可重用资源约束,给出了问题的数学模型,分析了启发式求解问题的基本思想,并提出了三类调度方法:1)、基于活动前置矩阵的调度,给出了活动前置矩阵的构造规则; 2)、基于优先规则的调度,结合活动成本目标改造了传统的串行调度方案和并行调度方案,并设计了相应的优先规则; 3)、改进的遗传算法:采用紧前(后)关系相容链表进行编码,解码方法是一种串行调度方案。针对改造PSPLIB 中的单模式算例,遗传算法的求解效果相对较好,采用确定型多回合计算的效果要优于单优先规则下的同类启发式调度方法。
基于单执行模式问题的研究,进一步讨论了多执行模式下的问题,其中,在进行活动调度的同时也要选择相应的执行模式,文中给出了考虑多模式调度的通用并行调度框架,并基于这个框架提出了两种调度策略:联合调度策略、两步调度策略。针对改造PSPLIB 中的多模式算例,虽然同类算法中在模式的选择时考虑了折衷的先序相关成本因素所得到的有效解数量略少,但得到的平均偏差却是最小的,而且活动-模式两步调度策略下得到的结果平均偏差小于活动-模式联合调度策略。
工程供应链中可重用资源供应商是承包商最直接的合作伙伴,他们的资源能力对工程调度会产生相应的约束,可以基于资源受限工程调度进行工程中多可重用资源的合作伙伴选择。文中给出了问题的数学模型,讨论了问题规模约减的原理。基于问题特性,构造了遗传算法的求解框架,并进行了算例测试,结果表明,改进遗传算法求解此类问题能够获得较好的效果。在多资源供应商选择问题的基础上,随后构造的供应-执行两层工程供应链设计问题中加入了对作为工程执行层的承包商的选择因素,文中描述了的问题的数学模型,给出了其求解方法。
Construction supply chain management is a new area of construction project management and supply chain management. There is still no research on design of construction supply chain. In a construction supply chain where contractor is the kernel, design and operation of the chain is driven by project activity network where capacity of the partners such as specialized subcontractors, ready-mix concrete suppliers, raw material suppliers, will become a constraint to project scheduling. Therefore, resource-constraints from these partners and limitation on project duedate must be considered in design of construction supply chain so that the objective of minimizing activities’cost in project can be achieved. For the above, resource-constrained project scheduling with the objective of minimizing activities’cost will be discussed firstly based on which research on design of construction supply chain is going to be carried out.
There is little attention paid to activities’cost of project in resource-constrained project scheduling problems(RCPSPs). When the objective of minimizing activities’cost is considered as the performance measure, the problem is also NP-hard and the objective is nonregular. A mathematical model is put forward for the cases the activities are executed in one execution mode and renewable resources are consumed. The basic thinking is analyzed for solution of the problems in heuristics and three approaches are developed: 1).Scheduling based on Preposing Acitivity Matrix where some rules are developed to form the matrix. 2).Priority-rule-based Scheduling that is updated to achieve the new objective on the basis of the old one for the RCPSPs with makespan objective and some priority rules are employed in the serial schema and the parallel schema. 3).Improved Genetic Algorithm where the schema of encoding is an activities’chain with precedence relationship and the decoding procedure is a serial scheduling schema. Computational Study with the single-mode instances in updated PSPLIB shows that the efficiency of the genetic algorithm proposed is the best and the results will become better when deterministic multi-pass approaches are used.
The above research is extended to the cases activities have multiple possible execution modes in the following. In the new problems, the execution modes must be selected for the activities when they are scheduled. A general parallel schedule generation schema is
proposed for multi-mode scheduling and two heuristic procedures are developed: united scheduling and two-step scheduling. Computational study with the multi-mode instances in updated PSPLIB shows that, when the factors about the compromised transitively relative cost is considered for selecting execution modes, a relatively fewer valid schedules will be got than the heuristics considering other factors in the same approach, but the average error is the minimal. Additionally, the average error of the heuristics with two-step scheduling is less than that of the heuristics with united scheduling. The renewable resources suppliers are the most immediate partners for contractor in construction supply chain and their capacities will form the constraints to project scheduling. That’s to say, when selecting these partners, the RCPSPs must be taken into account. The mathematical model for selecting these suppliers in construction project is proposed and the principle to reduce the solution space is discussed. Following that, a schema with GA to solve the problems is designed that is test by an example. The results show that a fine efficiency can be got with the improved GA. Whereafter, a problem about design of supply-execution construction supply chain is proposed, where one of candidate contractors should be selected to execute the construction project, and the representation of the problems and the approach for solution are all given. Suppliers selection is to solve the problems of designing supply chain in a local facet, but design of supply chain network is in the whole. Based on the analysis about the structure of construction supply chain network, integrated project scheduling and material ordering problems with limited capacities are proposed firstly where bilevel capacities about renewable resources and raw materials are all described. This type of problems can be decomposed to two types of problems: single-mode RCPSP with the objective of minimizing activities’cost(SMRCPSP-AC) and material ordering problem in a finite planning horizon with limited supply capacity(MOP-LSC), where the latter can be solved by dynamic programming. A feasible solution for the integrated problem may be got by searching a feasible solution for SMRCPSP-AC and then solving the relative MOP-LSC, and the optimal one will be found out in the set of feasible solutions for the integrated problem. A schema with improved GA is developed to solve the integrated problems. The numerical computation shows that the efficiency is fine when selection scheme is represented by stochastic tournament model with elitist preservation. This type of problems can be extended to design construction supply chain networks. To solve the proposed
problems with GA, the schema of encoding is an integrated one including two segments where suppliers and activities are encoded by different schemas and the decoding procedures are processed separately after which, SMRCPSP-AC and MOP-LSC are formed and solved in turn to get a feasible solution of designing construction supply chain network. Different operators are used on the two segments in the chromosome. It can be concluded based on the computational study that this type of problems can be solved by using the above genetic algorithm.
引文
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