Operations Research Perspectives最新文献_第3页

A branch-and-price solution strategy for integrated process planning and scheduling problems 集成工艺计划和调度问题的分支和价格解决策略

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-06-04 DOI: 10.1016/j.orp.2025.100343

Dung-Ying Lin, Che-Hao Chen

This research investigates the integrated process planning and scheduling (IPPS) problem that considers process planning and production scheduling simultaneously with the aim of minimizing makespan. To solve the IPPS problem, we propose a branch-and-price (B&P) solution strategy that decomposes the problem according to the Dantzig-Wolfe principle and searches for integer solutions with a branch-and-bound framework. The decomposed master problem solves the scheduling problem and determines the corresponding timing information. The subproblem finds the optimal processing route and machine assignment based on the pricing information passed from the master problem. One of the critical features of the decomposition strategy is that the resulting subproblem can be reduced to a shortest path problem and can be solved with a proposed linear time algorithm. Numerical results show that the proposed B&P solution strategy can effectively and efficiently solve benchmark problem instances. Managerial insights are drawn based on the numerical results and sensitivity analysis to demonstrate the practical use of the proposed framework.

研究了以最大完工时间为目标，同时考虑工序规划和生产调度的集成工艺规划与调度问题。为了解决IPPS问题，我们提出了一种分支和价格（B&；P）求解策略，该策略根据dantzigg - wolfe原理对问题进行分解，并使用分支和定界框架搜索整数解。分解的主问题解决调度问题，确定相应的时序信息。子问题根据主问题传递的价格信息找到最优加工路线和机器分配。该分解策略的一个关键特征是，所得到的子问题可以简化为最短路径问题，并可以用提出的线性时间算法求解。数值结果表明，所提出的B&；P求解策略能够有效地求解基准问题实例。根据数值结果和敏感性分析得出管理见解，以证明所提出框架的实际应用。

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引用次数: 0

The interplay between learning effect and order acceptance in production planning 生产计划中学习效应与订单接受的相互作用

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-07-15 DOI: 10.1016/j.orp.2025.100350

Kuo-Ching Ying , Pourya Pourhejazy , Wei-Jie Zhou

Learning takes time and hence its effects should be considered in short-term production planning (i.e., scheduling). This is especially true when human involvement is high and the shop floor experiences changes in workflow, workforce, or technology. The Single-Machine Scheduling Problem (SMSP) with the learning effect is considered to explore this interplay. The study first proves that the shortest processing time scheduling rule can solve the mathematical problems. Pseudo-polynomial solution algorithms based on Dynamic Programming (DP) are developed to solve the SMSPs with learning effects and job rejection to minimize the maximum completion time (makespan), total completion time, and total tardiness, separately. We found that the algorithms tend to reject a small number of orders with longer production times and retain more of those with shorter production times when the objective is to minimize the average response time for the new orders. This is contrary to situations when the system’s resource utilization or the delays in fulfilling demand are sought to be minimized. The study also found that orders requiring longer processing times should be scheduled later to improve all three performance metrics with higher learning rates. Finally, we establish that all three extended problems are solvable in pseudo-polynomial time, with complexities of

O (n^{2} E)

for makespan and total completion time minimization, and

O (n^{2} P E)

for total tardiness minimization. The DP algorithms efficiently solve practical-sized instances, as validated by numerical experiments.

学习需要时间，因此应在短期生产计划（即调度）中考虑其影响。当人工参与程度高，车间在工作流程、劳动力或技术方面经历变化时，尤其如此。考虑了具有学习效应的单机调度问题（SMSP）来探索这种相互作用。研究首先证明了最短加工时间调度规则可以解决数学问题。提出了基于动态规划（DP）的伪多项式求解算法，分别求解具有学习效应和作业拒绝的最大完工时间（makespan）最小化、总完工时间最小化和总延迟最小化的smsp问题。我们发现，当目标是最小化新订单的平均响应时间时，算法倾向于拒绝少量生产时间较长的订单，而保留更多生产时间较短的订单。这与试图将系统的资源利用或满足需求的延迟降至最低的情况相反。该研究还发现，需要更长的处理时间的订单应该安排得更晚，以提高这三个性能指标的学习率。最后，我们建立了这三个扩展问题都是在伪多项式时间内可解的，对于最大完工时间和总完工时间的最小化，其复杂度为0 (n2E)，对于总延误的最小化，其复杂度为0 （n2PE）。数值实验验证了算法的有效性。

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引用次数: 0

Constraint programming models for serial batch scheduling with minimum batch size 最小批量串行批调度的约束规划模型

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-09-02 DOI: 10.1016/j.orp.2025.100352

Jorge A. Huertas, Pascal Van Hentenryck

In serial batch (s-batch) scheduling, jobs are grouped in batches and processed sequentially within their batch. This paper considers multiple parallel machines, nonidentical job weights and release times, and sequence-dependent setup times between batches of different families. Although s-batch has been widely studied in the literature, very few papers have taken into account a minimum batch size, typical in practical settings such as semiconductor manufacturing and the metal industry. The problem with this minimum batch size requirement has been mostly tackled with dynamic programming and meta-heuristics, and no article has ever used constraint programming (CP) to do so. This paper fills this gap by proposing, three CP models for s-batching with minimum batch size: (i) an Interval Assignment model that computes and bounds the size of the batches using the presence literals of interval variables of the jobs. (ii) A Global model that exclusively uses global constraints that track the size of the batches over time. (iii) And a Hybrid model that combines the benefits of the extra global constraints with the efficiency of the sum-of-presences constraints to ensure the minimum batch sizes.The computational experiments on standard cases compare the three CP models with two existing mixed-integer programming (MIP) models from the literature. The results demonstrate the versatility of the proposed CP models to handle multiple variations of s-batching; and their ability to produce, in large instances, better solutions than the MIP models faster.

在串行批处理（s-batch）调度中，作业分批分组，并在其批处理中顺序处理。本文考虑了多台并行机器、不相同的作业权值和释放时间，以及不同家族批次之间的顺序相关的设置时间。虽然s-batch在文献中得到了广泛的研究，但很少有论文考虑到最小批量大小，这在半导体制造和金属工业等实际环境中是典型的。这个最小批大小要求的问题主要是通过动态规划和元启发式来解决的，没有一篇文章使用约束规划（CP）来解决这个问题。本文通过提出最小批大小的s批处理的三个CP模型来填补这一空白：(i)一个区间分配模型，该模型使用作业的区间变量的存在量来计算和限定批的大小。（ii）一个全局模型，专门使用跟踪批次大小的全局约束。（iii）混合模型，该模型结合了额外全局约束的好处和存在和约束的效率，以确保最小批量大小。在标准情况下的计算实验将这三种CP模型与文献中已有的两种混合整数规划（MIP）模型进行了比较。结果表明，所提出的CP模型在处理s批处理的多种变化时具有通用性；以及它们在大型情况下比MIP模型更快地产生更好解决方案的能力。

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引用次数: 0

Development of a robust design optimization algorithm for hierarchical time series pharmaceutical problems 层次时间序列药物问题鲁棒设计优化算法的发展

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.orp.2025.100355

Vo Thanh Nha , Kyungjin Park , Hyeonae Jang , Gyu M. Lee , Tuan-Ho Le , Seong Hoon Jeong , Sangmun Shin

Experimental design and robust design (RD) methodologies have received attention from researchers to improve the performance of many different quality characteristics and solve problems at low costs. However, there is room for improvement to simultaneously solve interdisciplinary optimization problems associated with time-oriented, multiple, and hierarchical responses. This paper proposes a new RD modeling and optimization algorithm for drug development based on three research motivations: Firstly, customized experiments and estimation frameworks for representing pharmaceutical quality characteristics (i.e., time-oriented, multiple, and hierarchical responses) and functional relationships between input factors and hierarchical time-oriented output responses are proposed. Secondly, new hierarchical time-oriented robust design (HTRD) optimization models (i.e., priority-based, weight-based, and integrated models) are developed for these interdisciplinary pharmaceutical formulation problems. Finally, the pharmaceutical case study for drug formulation development is conducted for demonstration purposes. Based on the case study results, the proposed approach can provide optimal solutions with significantly small biases and variances.

实验设计和稳健设计（robust design， RD）方法已受到研究人员的关注，以提高许多不同质量特性的性能，并以低成本解决问题。然而，在同时解决与时间导向、多重和分层响应相关的跨学科优化问题方面，仍有改进的空间。本文基于三个研究动机，提出了一种新的药物研发建模和优化算法：首先，提出了表征药物质量特征（即时间导向、多重响应和层次响应）的定制实验和估计框架，以及输入因素与层次时间导向输出响应之间的函数关系；其次，针对这些跨学科的药物配方问题，建立了新的分层面向时间的稳健设计（HTRD）优化模型（即基于优先级、基于权重和集成模型）。最后，进行药物配方开发的药物案例研究以进行演示。基于实例研究结果，该方法可以提供偏差和方差都很小的最优解。

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引用次数: 0

Cloud seeding optimization under uncertainty: A Markov chain approach in a two-stage fuzzy-stochastic framework 不确定性下的播云优化：两阶段模糊随机框架下的马尔可夫链方法

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-10-10 DOI: 10.1016/j.orp.2025.100356

Mohammad Sadeghi, Saeed Yaghoubi

The occurrence of sequential droughts and various forms of water shortages globally underscores the urgent need for sustainable water management solutions. In this context, cloud seeding has gained attention for its potential to enhance precipitation, yet its effectiveness is often uncertain due to complex cloud microphysics and atmospheric conditions. Acknowledging the inherent uncertainty in this endeavor, in this study, we employ a two-stage stochastic framework, integrating strategic decisions (facility location and network design) and operational realizations (seeding planning according to storm trajectories). Additionally, our model also considers fuzzy nature of seeding parameters. Above all, we develop a Markov chain procedure to mathematically model the prediction of expected increase in precipitation across cloud seeding decision-making processes. The integration of these stochastic methods into existing deterministic models from the literature results in a multi-objective Mixed-Integer Linear Programming (MILP) model designed to maximize rain probability and coverage while minimizing system-wide costs. To enhance the scalability and efficiency of the model, valid inequalities are developed to reduce the domain of binary variables. Additionally, a Lagrangian relaxation technique is proposed, yielding exact optimal solutions within reasonable timeframes and facilitating the handling of continuous space instances. Finally, a real-world case study in Iran demonstrates significant enhancements in precipitation predictions, with the Markov chain procedure showing an average 55 % increase in expected rain probability based on optimized seeding decisions. Scenario-based stochastic programming yields an 11.7 % value of stochastic solution and 16.5 % expected value of perfect information for cloud seeding initiatives.

全球接连发生的干旱和各种形式的水资源短缺突出表明迫切需要可持续的水管理解决办法。在这种情况下，人工降雨因其增强降水的潜力而受到关注，但由于复杂的云微物理和大气条件，其有效性往往不确定。考虑到这一努力中固有的不确定性，在本研究中，我们采用了一个两阶段的随机框架，整合了战略决策（设施选址和网络设计）和业务实现（根据风暴轨迹进行播种规划）。此外，我们的模型还考虑了种子参数的模糊性。最重要的是，我们开发了一个马尔可夫链过程来数学模拟在云播决策过程中预期降水增加的预测。将这些随机方法整合到现有的确定性模型中，得到一个多目标混合整数线性规划（MILP）模型，该模型旨在最大化降雨概率和覆盖范围，同时最小化系统范围的成本。为了提高模型的可扩展性和效率，提出了有效的不等式来减少二元变量的定义域。此外，提出了一种拉格朗日松弛技术，在合理的时间范围内得到精确的最优解，并便于处理连续空间实例。最后，伊朗的一个实际案例研究表明，降水预测的显著增强，马尔可夫链程序显示，基于优化的播种决策，预期降雨概率平均增加55%。基于场景的随机规划得到的播云方案的随机解值为11.7%，完美信息期望值为16.5%。

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引用次数: 0

Inventory prepositioning of relief material under the Joint Government-Enterprise Storage mode 政企联储模式下的救灾物资库存预配置

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-11-01 DOI: 10.1016/j.orp.2025.100361

Li Zhang, Jianqin Zhou, Xufeng Yang

To ensure the timely supply of relief materials at a low cost, many countries have adopted the Joint Government and Enterprises Storage (JGES) mode to prepositioning relief materials, where some enterprises replace the government in stockpiling emergency supplies for disasters. A critical problem faced by the enterprise is how to manage its inventory considering its daily business demand and the possible emergency demand. The government also wants to know the performance of the mode and how to subsidize the enterprise. To address these questions, we first consider the single-period problem and formulate it as a newsvendor-type model. We obtain the optimal conditions and analyze the impacts of some parameters on the optimal policy. Furthermore, we consider the multi-period case and the government’s optimal subsidy for the enterprise. For the former, we show that the optimal inventory policy is still the base-stock policy if the fixed ordering cost is zero, and is the

(s, S)

policy if the cost is positive. The government’s subsidy to the firm increases first and then decreases as the occurrence probability of the emergency increases. Finally, we conduct numerical experiments to compare the performance of the mode with that of the Separate Government-Enterprise Storage (SGES) mode, to demonstrate its advantages and the impacts of some parameters on its performance.

为了保证救灾物资的及时、低成本供应，许多国家都采取了政府与企业联合储备（JGES）的方式来预置救灾物资，由一些企业代替政府储备救灾应急物资。考虑到企业的日常业务需求和可能出现的紧急需求，如何对库存进行管理是企业面临的一个关键问题。政府也想知道这种模式的效果以及如何对企业进行补贴。为了解决这些问题，我们首先考虑单周期问题，并将其表述为一个报贩类型的模型。得到了最优条件，并分析了一些参数对最优策略的影响。此外，我们还考虑了多时期的情况和政府对企业的最优补贴。对于前者，我们证明了当固定订购成本为零时，最优库存策略仍然是基本库存策略；当固定订购成本为正时，最优库存策略是（s, s）策略。随着突发事件发生概率的增加，政府对企业的补贴先增加后减少。最后，通过数值实验对该模式与政企分离存储模式的性能进行了比较，论证了该模式的优点以及一些参数对其性能的影响。

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引用次数: 0

Customer order scheduling in a permutation flow shop environment 排列流车间环境中的客户订单调度

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-11-03 DOI: 10.1016/j.orp.2025.100362

Julius Hoffmann , Janis S. Neufeld , Udo Buscher

Various recent scheduling literature has studied the so called customer order scheduling problem. In this class of scheduling problems, there are multiple customer orders, and each of them consists of several jobs. The order finishes and is ready to be shipped when the last job of the order finishes. In this paper, we consider the customer order scheduling problem in a permutation flow shop environment with

m

machines. There are

n

orders and each order has

o

jobs. The objective is to minimize the total completion time of the orders. We present multiple problem properties and a MINLP formulation of the problem. Furthermore, four heuristics which follow the Iterated Greedy Algorithm are developed. In a computational experiment, we evaluated the four heuristics on their practicability. They showed good results in short calculation time when compared with the MINLP solution from a solver. Afterwards, we compared the four heuristics with each other for different problem sizes.

最近的各种调度文献都研究了所谓的客户订单调度问题。在这类调度问题中，有多个客户订单，每个订单由几个作业组成。当订单的最后一个作业完成时，订单完成并准备发货。本文研究了有m台机器的置换流车间环境下的客户订单调度问题。有n个订单，每个订单有0个工作。目标是最小化订单的总完成时间。我们提出了该问题的多个性质和一个MINLP公式。在此基础上，提出了迭代贪心算法的四种启发式算法。在计算实验中，我们评估了四种启发式的实用性。与求解器的MINLP解决方案相比，它们在较短的计算时间内显示出良好的结果。之后，我们对不同问题规模的四种启发式进行了比较。

引用次数: 0

Smart home economic operation under uncertainty: comparing monte carlo and stochastic optimization using gaussian and KDE-based data 不确定性下的智能家居经济运行：使用高斯和基于kde的数据比较蒙特卡罗和随机优化

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-07-13 DOI: 10.1016/j.orp.2025.100348

Spyros Giannelos, Danny Pudjianto, Goran Strbac

This paper investigates optimal day-ahead operation of a building-scale energy hub equipped with photovoltaics and a battery. Electricity demand and PV availability are uncertain and are represented in two ways: (i) thin-tailed normal distributions and (ii) kernel density estimation (KDE) fitted to empirical CityLearn data. For each representation we evaluate (a) deterministic Monte Carlo analysis, where the hub is optimised separately for 1 000 daily scenarios, and (b) a two-stage stochastic optimisation that fixes one set of decisions for hours 0–11 and adapts for hours 12–23 after conditions are observed. Gaussian inputs yield clustered costs (mean= $51.6, σ= $0.2) and a 99 % CVaR below $52, suggesting negligible risk. KDE inputs raise the Monte Carlo mean to $80.6 and lift the 99 % CVaR to $114, exposing heavy-tailed risk. Within the stochastic model the identical first-stage policy costs $79.0 with Gaussian data but only $71.3 with KDE, as recourse exploits sunny scenarios and trims the 95 % CVaR from $106.4 to $93.5. Consequently, Gaussian assumptions obscure true operating costs and financial exposure, whereas incorporating empirically derived KDE uncertainty within stochastic optimisation both lowers the average cost and provides stronger protection against extreme cost outcomes.

本文研究了一个配备光伏和电池的建筑规模能源枢纽的最优日前运行。电力需求和光伏可用性是不确定的，并以两种方式表示：(i)细尾正态分布和（ii）核密度估计（KDE）拟合经验CityLearn数据。对于每个表示，我们评估(a)确定性蒙特卡罗分析，其中枢纽分别针对1,000个日常场景进行优化，以及(b)两阶段随机优化，该优化在0-11小时内固定一组决策，并在观察到条件后适应12-23小时。高斯输入产生聚类成本（平均值= 51.6美元，σ= 0.2美元），99%的CVaR低于52美元，这表明风险可以忽略不计。KDE输入将蒙特卡罗平均值提高到80.6美元，并将99% CVaR提高到114美元，暴露了重尾风险。在随机模型中，相同的第一阶段政策在高斯数据下的成本为79.0美元，而在KDE数据下仅为71.3美元，因为索赔权利用阳光明媚的情景，将95%的CVaR从106.4美元削减到93.5美元。因此，高斯假设模糊了真实的运营成本和财务风险，而在随机优化中结合经验推导的KDE不确定性既降低了平均成本，又为极端成本结果提供了更强的保护。

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引用次数: 0

Robust optimization model for closed-loop supply chain planning with collected material quality uncertainty 具有采集物料质量不确定性的闭环供应链规划鲁棒优化模型

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-11-21 DOI: 10.1016/j.orp.2025.100368

Joonrak Kim , Seunghoon Lee

This study develops a robust optimization framework for closed-loop supply chain (CLSC) planning that explicitly accounts for uncertainty in the quality of recycled and remanufactured inputs. While such materials are critical for sustainability, their variable quality poses risks to production feasibility and supply reliability. To address this challenge, we propose an ordering-proportion-based robust model that distributes uncertainty across sourcing proportions and leverages the Bertsimas–Sim budget of uncertainty to balance conservatism and flexibility. A reformulation ensures tractability and preserves robust feasibility. Computational experiments demonstrate that the proposed model reduces shortages and stabilizes performance under independently realized uncertainties, while quantity-based robust models are more effective when uncertainties are correlated. Additional scalability tests confirm that the model remains computationally tractable for medium-sized networks. The findings highlight practical implications for managers, showing how proportion-based sourcing improves resilience, supports reliable demand fulfillment, and strengthens sustainability in CLSCs facing quality risks.

本研究为闭环供应链（CLSC）规划开发了一个强大的优化框架，该框架明确考虑了回收和再制造投入质量的不确定性。虽然这些材料对可持续发展至关重要，但它们的质量变化不定对生产可行性和供应可靠性构成了风险。为了应对这一挑战，我们提出了一个基于排序比例的鲁棒模型，该模型将不确定性分配到采购比例中，并利用不确定性的Bertsimas-Sim预算来平衡保守性和灵活性。重新制定确保可追溯性和保持稳健的可行性。计算实验表明，该模型在独立实现的不确定性下减少了不足并稳定了性能，而基于数量的鲁棒模型在不确定性相关时更有效。额外的可伸缩性测试证实，该模型在计算上仍然适用于中型网络。研究结果强调了对管理者的实际意义，显示了基于比例的采购如何提高弹性，支持可靠的需求满足，并加强面临质量风险的CLSCs的可持续性。

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引用次数: 0

Forecasting efficiency of two-stage Petrochemical sustainable supply chains using Deep Learning and DNDEA Model 基于深度学习和DNDEA模型的两阶段石化可持续供应链效率预测

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Perspectives

Pub Date : 2025-12-01 Epub Date: 2025-09-16 DOI: 10.1016/j.orp.2025.100354

Sina Sayardoost Tabrizi , Saeed Yousefi , Keikhosro Yakideh

The efficiency of supply chains is essential for improving managerial decision-making and enhancing strategic planning capabilities. This research presents a novel integration of deep learning with a two-stage supply chain framework to assess the efficiency of 28 petrochemical units over a period of 90 months. Based on sustainability principles, a dynamic network data envelopment analysis (DEA) model is employed to measure and compare the relative efficiency of supply chains operating across different time horizons. To forecast future input–output relationships in the supply chain, an advanced two-layer Long Short-Term Memory (LSTM) model is proposed. This LSTM-based prediction system demonstrated exceptional accuracy, achieving a low Mean Squared Error (MSE) of 0.0004 and a Root Mean Square Error (RMSE) of 0.0208. Additionally, the trend of the loss function during training confirmed the reliability and stability of the proposed deep learning approach. The precise forecasting capability of the LSTM model enables managers to proactively identify and address inefficiencies in production facilities before they occur, rather than relying on reactive strategies. This proactive approach allows for better resource allocation and improved operational performance across petrochemical supply chains. By integrating deep learning with dynamic network DEA models, this study offers a robust framework for predictive efficiency analysis and performance evaluation in industrial applications. The suggested framework provides decision-makers with a pragmatic assessment instrument to identify efficient and underperforming supply chains and set realistic benchmarks for improvement. This methodology is designed to be scalable and adaptable, making it suitable for real-world evaluations of multi-stage supply chains and production systems. The research culminates in a two-phase case study, illustrating the practical applicability of the proposed framework.

供应链的效率对于改善管理决策和增强战略规划能力至关重要。本研究提出了一种新颖的深度学习与两阶段供应链框架的集成，以评估28个石化装置在90个月内的效率。基于可持续性原则，采用动态网络数据包络分析（DEA）模型，对不同时间跨度供应链的相对效率进行测度和比较。为了预测供应链中未来的投入产出关系，提出了一种先进的两层长短期记忆模型。该基于lstm的预测系统显示出优异的准确性，均方误差（MSE）为0.0004，均方根误差（RMSE）为0.0208。此外，训练过程中损失函数的变化趋势也证实了所提出的深度学习方法的可靠性和稳定性。LSTM模型的精确预测能力使管理人员能够主动识别和解决生产设施的低效率问题，而不是依赖于被动的策略。这种主动的方法可以更好地分配资源，提高整个石化供应链的运营绩效。通过将深度学习与动态网络DEA模型相结合，本研究为工业应用中的预测效率分析和绩效评估提供了一个强大的框架。建议的框架为决策者提供了一个实用的评估工具，以确定高效和表现不佳的供应链，并为改进设定现实的基准。该方法具有可扩展性和适应性，适用于多阶段供应链和生产系统的实际评估。研究在两个阶段的案例研究中达到高潮，说明了所提出框架的实际适用性。

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引用次数: 0