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A mathematical programming model for constructing the confidence interval of process capability index C_pm in evaluating process performance: an example of five-way pipe

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2017年第2期40卷 126-133页

作者： Chen, Kuen-Suan Huang, Cheng-Fu Chang, Tsang-Chuan Natl Chin Yi Univ Technol Dept Ind Engn & Management Taichung Taiwan Feng Chia Univ Dept Business Adm Taichung Taiwan

The process capability index C-pm can reflect process loss as well as process yield, thus is the most frequently used index for evaluating product quality in manufacturing industries. When evaluating the process performance, confidence intervals are often used for assurance with regard to the critical value of the process capability index. Unfortunately, sampling distributions of C-pm are obtained in a very complex way, which leads to difficulty in calculating the confidence interval of C-pm. Hence, this paper develops a mathematical programming model to construct the (1 - alpha) x 100% confidence interval of C-pm. Then for verifying the effectiveness of the proposed approach, the Monte Carlo simulation is used to find the coverage percentage. The proposed mathematical programming model can obtain the (1 - alpha) x 100% confidence interval of C-pm without complex statistical computations. Besides, managers can evaluate and monitor the process performance in an easy way. We also provide a case in which a five-way pipe process is presented as an illustration of how the proposed method is implemented.

关键词： Process capability index confidence interval mathematical programming model Monte Carlo five-way pipe

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A mathematical programming model for facility location optimization of hydrogen production from renewable energy sources

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ENERGY SOURCES PART A-RECOVERY UTILIZATION AND ENVIRONMENTAL EFFECTS 2022年第3期44卷 6648-6659页

作者： Derse, Onur Gocmen, Elifcan Yilmaz, Ebru Erol, Rizvan Tarsus Univ Dept Management & Org Logist Mersin Turkey Munzur Univ Dept Ind Engn Fac Engn Tunceli Turkey Cukurova Univ Dept Ind Engn Fac Engn Adana Turkey

Fossil fuels are the primary energy sources and meet the global energy demands. However, environmental and health problems related with these sources boosted the demand for renewable energy sources. Hydrogen, as an energy carrier has a growing potential for solving these problems. In this article, a mathematical programming model that integrates the production, storage and transportation, safety, location, and staff assignment decisions is presented considering minimization of costs. Although most of the studies focus on location, distribution, storage decisions of hydrogen energy networks, the article also includes production, safety and staff assignment decisions to make this problem more practical. Furthermore, we also investigate the set covering constraint will ensure that each region is covered by minimum number of the hydrogen facilities. The developed model ensures a balance between location, distribution, storage, production, safety and staff decisions by installing two production facilities by assigning total 9 warehouses, 22 tank trucks, 12100 km pipeline, 35 staffs under distance constraint 2000 km in regions 1 and 5. The computational results indicate that the proposed model produces effective solutions for the coverage to all region and minimum total cost for real-case situations.

关键词： Renewable energy sources hydrogen energy hydrogen supply chain network optimization mathematical programming model

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A mathematical programming model for Scheduling of Nurses' Labor Shifts

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JOURNAL OF MEDICAL SYSTEMS 2012年第2期36卷 491-496页

作者： Yilmaz, Ebru Cukurova Univ Dept Ind Engn Fac Engn & Architecture TR-01330 Adana Turkey

In this study, a mathematical programming model is proposed for scheduling problem of nurses' labor shifts. The developed mathematical programming model's aim is to minimize nurses' total idle waiting time during a week planning horizon. In this model, investigated constraints are as follows: (1) Maximum total working time a week for each nurse must not be exceeded. (2) After a nurse works a shift, the nurse can be assigned to another shift after two shifts at least. This constraints-set ensures resting of the nurse after the nurse works a shift. (3) Total number of nurses worked for each shift must be controlled with maximum and minimum bounds given for number of nurses for each shift. In this manner, total number of nurses worked for each shift is between maximum and minimum limit-values given for each shift. This constraint ensures flexibility to the user to determine number of nurses for each shift. (4) The decision variable that shows nurse-shift assignment pairs is 0 or 1. In this study, maximum total working time a week for a nurse, total number of nurses in a health service, maximum and minimum numbers of nurses worked a shift are user-specified parameters. In this way, this model can be adapted for the studies with different values of these parameters. In this study, the developed model is illustrated using a numerical example and then LINGO8.0 software is used to ensure the global optimum solution of the developed model. Results and also sensitivity analysis carried out for this example are presented in the study.

关键词： Scheduling of nurses' labor shifts mathematical programming model Optimization Integer linear programming model Shift systems Health services

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Medical waste management during coronavirus disease 2019 (COVID-19) outbreak: A mathematical programming model

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 162卷 107668页

作者： Govindan, Kannan Nasr, Arash Khalili Mostafazadeh, Parisa Mina, Hassan Shanghai Maritime Univ China Inst FTZ Supply Chain Shanghai 201306 Peoples R China Yonsei Univ Yonsei Frontier Lab Seoul South Korea Univ Southern Denmark Ctr Sustainable Supply Chain Engn Danish Inst Adv Study Dept Technol & Innovat Campusvej 55 Odense M Denmark Sharif Univ Technol Grad Sch Management & Econ Tehran Iran Univ Tehran Coll Engn Sch Ind Engn Tehran Iran

Municipal solid waste (MSW) directly impacts community health and environmental degradation;therefore, the management of MSW is crucial. Medical waste is a specific type of MSW which is generally divided into two categories: infectious and non-infectious. Wastes generated by coronavirus disease 2019 (COVID-19) are classified among infectious medical wastes;moreover, these wastes are hazardous because they threaten the environment and living organisms if they are not appropriately managed. This paper develops a bi-objective mixedinteger linear programming model for medical waste management during the COVID-19 outbreak. The proposed model minimizes the total costs and risks, simultaneously, of the population's exposure to pollution. This paper considers some realistic assumptions for the first time, including location-routing problem, time window-based green vehicle routing problem, vehicles scheduling, vehicles failure, split delivery, population risk, and loaddependent fuel consumption to manage both infectious and non-infectious medical waste. We apply a fuzzy goal programming approach for solving the proposed bi-objective model, and the efficiency of the proposed model and solution approach is assessed using data related to 13 nodes of medical waste production in a location west of Tehran.

关键词： Municipal solid waste Medical waste management mathematical programming model Fuzzy goal programming approach Coronavirus disease 2019 (COVID-19)

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Transmission expansion planning: A deep learning approach☆

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2025年 41卷

作者： Dong, Jizhe Cao, Jianshe Lu, Yu Zhang, Yuexin Li, Jiulong Xu, Chongshan Zheng, Danchen Han, Shunjie Changchun Univ Technol Sch Elect & Elect Engn Changchun 130000 Peoples R China State Grid Jilin Elect Power Co Ltd Changchun 130000 Peoples R China

This paper proposes a transmission expansion planning (TEP) method based on deep learning (DL) to address the increasing complexity and excessive reliance on mathematical formulas in current TEP models. First, we utilize a traditional mathematical programming model to obtain unit outputs and line construction decisions by varying loads, thereby generating the dataset required for DL training. Next, we build a convolutional neural network (CNN) based DL model, which includes convolutional layers, pooling layers and fully connected layers, and whose inputs consist of load data and unit output data, while output is line construction data. We use Bayesian optimization (BO) to select the best hyperparameters for the model. We conducted both single and multiple training experiments on the Garver's 6-bus, IEEE 24-bus and IEEE 118-bus systems. In the single training experiments, the R2 values achieved by our proposed method on these three systems were 0.99471, 0.99594 and 0.99676, respectively, with K-fold cross-validation showing stable results. In the multiple training experiments, we repeated the CNN training 50 times and obtained confidence intervals for each metric to further validate the model's effectiveness. Additionally, we performed significance testing on the BO results, showing that among the three comparative experiments, two had P-values less than 0.001, indicating a significant difference. The remaining one has a P-value is larger than 0.05 indicating a difference but not significant.

关键词： Bayesian optimization (BO) Convolutional neural network (CNN) Dataset generation Deep learning (DL) K -fold mathematical programming model Significance testing Transmission expansion planning (TEP)

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A mathematical programming approach for assessing the impact of climate change on Mediterranean farming systems: A Tunisian case study

SCIENTIFIC AFRICAN

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SCIENTIFIC AFRICAN 2025年 27卷

作者： Ben Mimoun, Anouar Mazhoud, Houda Chemak, Fraj Natl Agron Inst Tunisia INAT Dept Econ Agr & Agrifood Management Tunis Tunisia Univ Carthage Natl Inst Agr Res Tunisia INRAT Rural Econ Lab LR16INRAT07 1004 El Menzah 1 Tunis 1001 Tunisia

The paper aims to assess the short-term effects of climate change on economic and social performance of selected farming systems in Tunisia. The purpose is to analyze the evolution of land use and water allocation under different climate change scenarios at regional and local levels. In order to achieve the objective, a regional mathematical programming model was developed considering 2 regions and 7 farming production systems. Results showed that farming systems are affected differently by climate change. Large farming whose profitability is confirmed at the current state, their sustainability is not strongly threatened in the case of the climate change scenario. The subsistence and the small farming systems which are in difficulty because of their modest productive resources, their technological backwardness, and their structural constraints. Water availability will have modest welfare impacts, with an average decrease of 16 %. Despite the small aggregated effects, it is expected that climate change will have uneven consequences across regional income. For instance, even though the Medium farming system in Tell inferior showed the smallest income changes 1 % (average), the impacts within the others systems (large farm system, subsistence system and small farm system) range from 2 % to 16 % decrease in agricultural income. This situation suggests large distributional consequences of climate change for the Tunisian agricultural sector.

关键词： Climate change Farming systems mathematical programming model Tunisia

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mathematical programming models for Competitive Two-Agent Single-Machine Scheduling with Flexible Periodic Maintenance Activities

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2014年第5期39卷 3715-3722页

作者： Xu, Dehua Liu, Aihua Yang, Dar-Li E China Inst Technol Sch Sci Nanchang 330013 Jiangxi Peoples R China E China Inst Technol Sch Sci Fuzhou 344000 Jiangxi Peoples R China Natl Formosa Univ Dept Informat Management Yunlin 632 Taiwan

Competitive multi-agent scheduling has attracted increasingly more and more researchers' attention recently. Inspired by the observation that a machine may not be always available during the whole planning horizon, we study a new category of scheduling problems where competitive two-agent scheduling and flexible periodic maintenance are considered simultaneously. As a start of this new topic, we focus our attention on establishing mathematical programming models for some of these scheduling problems. Specifically, we first present a framework for the general problem, and then construct various constraint blocks, which include common constraint block, constraint block for the relationship between start times and completion times of the jobs, constraint block for the relationship between the jobs and the maintenance activities, constraint block for various regular objective functions of the two agents, constraint block for the ranges of variables, and constraint block for the other constraint factors. One can establish mathematical programming models for at least 512 scheduling scenarios of this category easily based on these constraint blocks. The work presented in this paper is extremely useful for the production managers and software developers who are seeking for optimization models to generate optimal schedules for their problems.

关键词： Scheduling Two-agent Single-machine mathematical programming model

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A Quadratic programming model for Blast Scheduling

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International Journal of Minerals,Metallurgy and Materials 1999年第3期13卷 165-167页

作者： Chunyan Meng Samuel Frimpong Mingjian Zuo(Ph. D. Student (correspondent). 606-Chemical-Mineral Building. Dept of Civil and Environmental Engineering. University of Alberta. T6G 2G6.Edmonton, AB. Canada)(Associate protessor, School of Mining and Petrole Univ Alberta Dept Civil & Environm Engn Edmonton AB T6G 2G6 Canada Univ Alberta Sch Min & Petr Engn Edmonton AB T6G 2M7 Canada Univ Alberta Dept Mech Engn Edmonton AB T6G 2M7 Canada

A quadratic programming model is established to choose the blocks to be blasted in a given period. The length of this period depends on the production planning requirements. During the given period, the blocks' parameters are available from the geological database of the mine. The objective is to minimize the deviation of the average ore grade of blasted blocks from the standard ore grade required by the mill. Transportation ability constraint. production quantity demand constraint. minimum safety bench constraint. block size constraint and block, bench precedence constraints are considered in forming the programming model. This model has more practical objective function and reasonable constraints compared with the existing model for this kind of problems.

关键词： quadratic programming open pit mining blast scheduling mine production scheduling mathematical programming model

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Strategic and tactical mathematical programming models within the crude oil supply chain context-A review

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COMPUTERS & CHEMICAL ENGINEERING 2014年 68卷 56-77页

作者： Sahebi, Hadi Nickel, Stefan Ashayeri, Jalal Karlsruhe Inst Technol Dept Econ & Management D-76131 Karlsruhe Germany Iran Univ Sci & Technol Dept Ind Engn Tehran *** Iran Tilburg Univ Tilburg Sch Econ & Management NL-5000 LE Tilburg Netherlands

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Crude oil supply chain Strategic and tactical decisions mathematical programming model Literature review

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A programming model for Consistency and Consensus in Group Decision Making with Probabilistic Hesitant Fuzzy Preference Relations

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2018年第8期20卷 2399-2414页

作者： Li, Jian Wang, Zhong-xing Guangxi Univ Sch XingJian Coll Sci & Liberal Arts Nanning 530005 Guangxi Peoples R China Guangxi Univ Sch Math & Informat Sci Nanning 530004 Guangxi Peoples R China

Individual consistency and group consensus are important topics in group decision-making process with preference relations. This study introduces a programming model to meet the individual consistency level and group consensus threshold value simultaneously. First, the distance measure between two probabilistic hesitant fuzzy preferences (PHFPRs) is proposed, and a consistency index for PHFPR is defined based on the proposed distance measure. Then, a mathematical programming model is constructed to improve its consistency when the PHFPR does not meet the consistency level. Second, considering that some values in PHFPRs provided by the decision makers may be missing in the decision-making process, a mathematical programming model is constructed to derive the missing values. Third, the proximity degree between any two decision makers is proposed, and a consensus index among the decision makers is defined based on the proposed proximity degree. Then, a mathematical programming model is constructed to obtain the expected consistency level and consensus threshold value simultaneously. Finally, an example is provided to illustrate the effectiveness of the proposed method. Comparative studies with several existing methods are also provided.

关键词： Group decision making Individual consistency Group consensus Probabilistic hesitant fuzzy preference relations mathematical programming model

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