划分系统资源分配问题的拉格朗日松弛与分支价格算法

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Shiming Chen, Chengkuan Zeng, Yu Zhang, Jiafu Tang, Chongjun Yan
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引用次数: 0

摘要

本文研究了分制血清生产系统(SPS)中的血清形成问题,重点研究了每个血清中作业-血清分配、工人-血清分配和操作-工人分配。该问题是一个以最小化工人的培训和加工成本为目标的混合整数非线性规划(MINLP)模型。一旦确定了作业-服务分配,我们采用混合整数线性规划(MILP)模型来描述每个服务中的工人-服务和操作-工人分配。为应对这一挑战,我们建议分两阶段解决这一问题。在第一阶段,我们提出了一种拉格朗日松弛算法来确定作业-任务分配,该方法可以通过列举所有可能的作业-任务分配来快速计算MILP的下界,并消除不希望的作业-任务分配。随后,在第二阶段,对于每个剩余的作业序列分配,我们开发了一个分支和价格算法来精确求解MILP。在分支定界框架下,采用列生成(CG)算法求解各节点。在CG中,我们采用Dantzig Wolfe分解法将原始问题分解为主问题和定价问题。根据定价问题的特点,提出了一种新的标签设置算法。此外,我们引入了有效的加速策略,如优势规则和启发式定价。它有利于选择最优的作业序列分配,并得到整个问题的最优解。最后,通过大量的实验验证了算法的有效性和优越性。我们还讨论了所选参数对成本的影响,并提供了管理见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lagrangian relaxation and branch-and-price algorithm for resource assignment problem in divisional seru systems
This paper addresses seru formation problem in divisional seru production system (SPS), which focuses on job-seru assignment, worker-seru assignment and operation-worker assignment in each seru. The problem is formulated as a mixed-integer nonlinear programming (MINLP) model with the objective of minimizing training and processing costs of workers. Once the job-seru assignment is determined, we employ a mixed-integer linear programming (MILP) model to describe worker-seru and operation-worker assignment in each seru. To tackle this challenge, we propose a two-phase approach to deal with this problem. In the first phase, we propose a Lagrangian relaxation algorithm to determine job-seru assignment, this approach can quickly compute the lower bound of the MILP by enumerating all possible job-seru assignments and eliminate unpromising ones. Subsequently, in the second phase, for each remaining job-seru assignment, we develop a branch-and-price algorithm to solve the MILP exactly. It is in the branch-and-bound framework, each node is solved by column generation (CG) algorithm. In CG, we apply a Dantzig Wolfe decompose to divide the original problem into a master problem and the pricing problems. A novel label-setting algorithm is employed based on the characteristics of the pricing problem. Additionally, we introduce effective acceleration strategies such as dominance rules and heuristic pricing. It facilitates the selection of the optimal job-seru assignment and obtains the optimal solution for the entire problem. Finally, extensive experiments validate the effectiveness and superiority of our proposed algorithm. We also discuss the impact of selected parameters on the cost and offer managerial insights.
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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