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mixed integer programming model Based on Branch Delimitation-Relaxation Variables Application in Sustainable Supply Chain Enterprise Management

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JOURNAL OF ADVANCED MANUFACTURING SYSTEMS 2025年

作者： Zhong, Qi'an Suqian Univ Sch Econ & Management Suqian 223800 Peoples R China

With the advancement of global sustainable development goals, promoting sustainable supply chain management has become the key to enhance the competitiveness of enterprises. However, it is difficult for the existing management methods to deal with the balance between cost, efficiency and environmental impact, and the complexity of decision-making under uncertain conditions has increased significantly. Therefore, a mixed integer programming model based on the branch delimitation method and relaxation variables is proposed to transform the enterprise management problem of the sustainable supply chain into a mathematical programming model. With the goal of minimizing the total cost, the effective search is carried out through boundary conditions and priority queues, and the relaxation variable technique is used to reduce the complexity of the problem and ensure that the model can still obtain a feasible solution when considering the uncertainty factors. The results showed that the hybrid integer programming model had the smallest annual discount cost, the largest number of item searches, and an average processing time of less than 2 s, which effectively solved the problem between supplier selection and order allocation in the supply network, and showed good algorithm efficiency and application efficiency. The model can provide reference guidance for enterprise management decision-making and provide a reference value for the improvement of enterprise environmental, social and economic performance.

关键词： Sustainability supply chain network supplier selection branch demarcation algorithm relaxation factor mixed integer programming model

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modeling hospital infrastructure by optimizing quality, accessibility and efficiency via a mixed integer programming model

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BMC HEALTH SERVICES RESEARCH 2013年第1期13卷 1-9页

作者： Ikkersheim, David Tanke, Marit van Schooten, Gwendy de Bresser, Niels Fleuren, Hein KPMG Plexus Breukelen Netherlands Vrije Univ Amsterdam FALW Amsterdam Netherlands Tilburg Univ NL-5000 LE Tilburg Netherlands

Background: The majority of curative health care is organized in hospitals. As in most other countries, the current 94 hospital locations in the Netherlands offer almost all treatments, ranging from rather basic to very complex care. Recent studies show that concentration of care can lead to substantial quality improvements for complex conditions and that dispersion of care for chronic conditions may increase quality of care. In previous studies on allocation of hospital infrastructure, the allocation is usually only based on accessibility and/or efficiency of hospital care. In this paper, we explore the possibilities to include a quality function in the objective function, to give global directions to how the 'optimal' hospital infrastructure would be in the Dutch context. Methods: To create optimal societal value we have used a mathematical mixed integer programming (MIP) model that balances quality, efficiency and accessibility of care for 30 ICD-9 diagnosis groups. Typical aspects that are taken into account are the volume-outcome relationship, the maximum accepted travel times for diagnosis groups that may need emergency treatment and the minimum use of facilities. Results: The optimal number of hospital locations per diagnosis group varies from 12-14 locations for diagnosis groups which have a strong volume-outcome relationship, such as neoplasms, to 150 locations for chronic diagnosis groups such as diabetes and chronic obstructive pulmonary disease (COPD). Conclusions: In conclusion, our study shows a new approach for allocating hospital infrastructure over a country or certain region that includes quality of care in relation to volume per provider that can be used in various countries or regions. In addition, our model shows that within the Dutch context chronic care may be too concentrated and complex and/or acute care may be too dispersed. Our approach can relatively easily be adopted towards other countries or regions and is very suitable to perform a 'w

关键词： Chronic Obstructive Pulmonary Disease Travel Time Diagnosis Group mixed integer programming model Dutch Hospital

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mixed integer programming model Based on Data Algorithms in Sustainable Supply Chain Management

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INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS 2024年第9期15卷 344-353页

作者： Dong, Shaobin Li, Aihua Huaiyin Inst Technol Fac Business Huaian 223001 Peoples R China Huaiyin Inst Technol Fac Elect & Informat Engn Huaian 223001 Peoples R China

the deepening of globalization and increasing demands for environmental sustainability, modern supply chains are faced with increasingly complex management challenges. To reduce management costs and enhance efficiency, an experimental approach is proposed based on a mixed integer programming model, integrating heuristic algorithms with adaptive genetic algorithms. The objective is to improve both the efficiency and sustainability of supply chain management. Initially, the selection of suppliers within the supply chain is analyzed. Subsequently, heuristic algorithms and genetic algorithms are jointly employed to design, generate, and optimize initial solutions. Results indicate that during initial runs on training and validation sets, the fitness values of the research method reached as high as 99.67 and 96.77 at the 22nd and 68th iterations, respectively. Moreover, on the training set with a dataset size of 112, the accuracy of the research method was 98.56%, significantly outperforming other algorithms. With the system running five times, the time consumed for supplier selection and successful order allocation was merely 0.654s and 0.643s, respectively. In practical application analysis, when the system iterated 99 times, the research method incurred the minimum total cost of 962,700 yuan. These findings demonstrate that the research method effectively minimizes supply chain management costs while maximizing efficiency, offering practical strategies for optimizing and sustainably developing supply chain management.

关键词： mixed integer programming model sustainable supply chain management heuristic algorithm adaptive genetic algorithm

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A mixed integer programming model for optimizing project time limit and cost

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Jianghan Shiyou Xueyuan Xuebao/Journal of Jianghan Petroleum Institute 2002年第3期24卷 98-100+viii页

作者： Yao, Jin-Xing Ming, Yan Jianghan Petroleum Institute Jingzhou 434023 China

The problems of optimizing cost and project time limit occur when the curve of the project cost and project time is nonlinear. By establishing a mixed integer programming model, an optimizing method of project planning for integratively considering the relations of cost and time is suggested, thus the accuracy of optimized result is improved.

关键词： Cost mixed integer programming model Project time limit

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Route Design Problem of Customized Buses: mixed integer programming model and Case Study

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JOURNAL OF TRANSPORTATION ENGINEERING PART A-SYSTEMS 2018年第11期144卷

作者： Guo, Rongge Guan, Wei Zhang, Wenyi Beijing Jiaotong Univ MOE Key Lab Urban Transportat Complex Syst Theory Beijing 100044 Peoples R China

In recent years, the customized bus (CB) has been introduced and popularized in China to improve the attraction and service level of public transportation. A key point of the CB system, the route design problem, is always formulated as a vehicle routing problem with pickup and delivery (VRPPD). However, VRPPD cannot sufficiently describe the in-vehicle passengers of multiple vehicles involved. In this paper, a mixed integer programming model is developed to formulate a multivehicle routing problem, with suggestions for bus stop locations and routes. Meanwhile, the model can determine passenger-to-vehicle assignment based on a series of constraints, like operation standard and number of stations. In solving the problem, a numerical example is used to compare a genetic algorithm (GA) and branch-andcut algorithm. The comparison results illustrate that GA is more efficient with lower complexity. Finally, in order to apply and evaluate the proposed model, a real-world case study using smartcard data is conducted to compare the approach with the current CB route design method in Beijing. (C) 2018 American Society of Civil Engineers.

关键词： Customized bus Route design problem mixed integer programming model Smartcard data

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Application of a mixed integer programming model in Coordinating Stopping Schedules of Intra-and Inter-trains for a High Speed Rail Line

Application of a Mixed Integer Programming Model in Coordina...

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2018 2nd International Conference on Applied Mathematics, modeling and Simulation (AMMS 2018)

作者： Hui-ling FU Madison Merrill Billy BERTO Hong ZHANG School of Traffic and Transportation Beijing Jiaotong University

In a high speed rail network,there are usually two types of trains running on a single rail line,which are intra-trains and *** stopping schedules for both types of trains may cause negative influence on train operation,e.g.,stopping schedules lack regularity,inter-trains consume too much route capacity of intra-trains,and intra-passengers are transported by inter-trains *** paper applies a mixed integer programming model in coordinating stopping schedules of intra-and inter-trains for a high speed rail *** goal is to increase regularity of both types of trains on a main rail line,in the meanwhile,to rationalize the division of labor of intra-and inter-trains in term of transporting intra-and inter-passengers.A numerical experiment is implemented based on a real-world *** results show that a series of coordination indicators are improved compared to those of an original train stopping schedule,which demonstrates the effectiveness of our application approach.

关键词： Train stopping schedule mixed integer programming model High speed rail

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A mixed-integer programming model for integrated production and maintenance

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IFAC-PapersOnLine 2016年第12期49卷 556-561页

作者： Hnaien, F. Yalaoui, F. Mhadhbi, A. Nourelfath, M. ICD-LOSI UMR-CNRS 6281 University of Technology of Troyes 12 rue Marie Curie Troyes10010 France Finaxys 27 Rue des Poissonniers Neuilly-sur-Seine92200 France Department of Mechanical Engineering Laval University QuebecQCG1V 0A6 Canada

This paper deals with the production planning and preventive maintenance scheduling on a single machine multi-product capacitated lot-sizing problem (CLSP). The machine is assumed to be subject to random failures. Preventive maintenances at the beginning of each production period to reduce the risk of failure and minimal repairs at failure is considered. The aim is to minimize the sum of the total production and maintenance costs related to inventory, backorder, production, set-up, preventive maintenance (PM), and minimal repair (MR) under demand satisfaction and machine capacities constraints over the entire horizon. Using the Weibull model, we present a mixed-integer linear programming (MIP) model to solve the problem. © 2016

关键词： Preventive maintenance integer programming Planning Problem solving Production control Repair Scheduling algorithms Capacitated lot sizing problem Integrated production Minimal repair mixed integer linear programming mixed integer Linear programming (MIP) mixed integer programming model Preventive maintenance (pm) Production Planning

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A robust mixed-integer binary programming model for operating theater scheduling to the patient and the surgeon under uncertainty in an open-heart Surgery Department

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PERIOPERATIVE CARE AND OPERATING ROOM MANAGEMENT 2024年 35卷 100391-100391页

作者： Manshadi, Bahareh Rahmani Univ Tehran Fac Ind & Syst Engn Tehran Iran

In hospitals, the surgical ward is both a cost and revenue center. In this ward, hospitals face challenges such as increasing demand, limited resources, and rising costs. Consequently, the decisions made have an implications effect on the hospital's performance. Therefore, in this paper a robust mixed-integer binary programming model is proposed with three objectives of maximizing the efficiency of available resources, minimizing the patients waiting time, and minimizing surgery costs that are formulated utilizing the augmented epsilon constraint approach. This model allocates the operating room to the patient and the surgeon and then obtains the required bed capacity inside the downstream units for stand-alone cardiac hospitals. This model includes different preferences for hospital, surgeon, and patient: waiting time, patient cancellations, tardiness, uncertainties in surgery durations, the patient operation start times, the overtime per working day, time windows, SICU beds, planning horizon, and the idle times of the surgeons, operating theater, and working day. The proposed model is solved using robust optimization to deal with stochastic. The proposed model is formulated on the stochastic programming method proposed by Bertsimas and Sim. In the proposed model, a rolling horizon method is used to reschedule the program after cancellation. The computational results illustrate that the rolling horizon method reduces waiting time and increases throughput. The results illustrate that the benefit obtained from the introduced model has improvements in reducing the surgery costs, and patient waiting time, and increasing the efficiency of available resources. This study has been performed at Shahid Rajaei Heart Hospital in Iran.

关键词： Robust optimization Operating theater scheduling mixed integer programming model Augmented epsilon-constraint Simulation

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An epsilon-free approach for finding the most efficient unit in DEA

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APPLIED MATHEMATICAL modelLING 2014年第13期38卷 3182-3192页

作者： Toloo, Mehdi Tech Univ Ostrava Fac Econ Dept Business Adm Ostrava Czech Republic

Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition. Recently, Toloo (2012) [13] proposed a new mixed integer programming (MIP) model to find the most BCC-efficient unit. Based on this study, we propose a new basic integrated linear programming (LP) model to identify candidate DMUs for being the most efficient unit;next a new MIP integrated DEA model is introduced for determining the most efficient DMU. Moreover, these models exclude the non-Archimedean epsilon and consequently the optimal solution of these models can be obtained, straightforwardly. We claim that the most efficient unit, which could be obtained from all other integrated models, has to be one of the achieved candidates from the basic integrated LP model. Two numerical examples are illustrated to show the variant use of these models in different important cases. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Data envelopment analysis mixed integer programming model Epsilon-free approach The most efficient unit Common set of weights Facility layout design

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Cross-Border Interconnectors in South Asia: Market-Oriented Dispatch and Planning

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IEEE ACCESS 2020年 8卷 120361-120374页

作者： Chattopadhyay, Debabrata Chitkara, Puneet Curiel, Ilka Deleque Draugelis, Gailius World Bank 1818 H St NW Washington DC 20433 USA Johns Hopkins Univ Dept Environm Hlth & Engn Baltimore MD 21218 USA

Regional trade in South Asia has progressed well over the last decade to exceed 3 GW in interconnection capacity, connecting India with Bhutan, Bangladesh and Nepal. We present an analysis of the benefits of the next 10.6 GW of interconnection capacity under construction and planning stages across four major corridors connecting five countries, including the proposed HVDC interconnector between India and Sri Lanka. It is important that these interconnectors are assessed not only for long-term benefits as part of a least cost portfolio of investments, but also for short-term, market-based benefits that can be gained from new opportunities for cross border electricity trade (CBET) in India's power exchanges. The Electricity Planning model (EPM) is developed for analysis of regional markets. A combination of market price driven short-term dispatch analysis and long-term planning optimization (for 2019-2035) is conducted using EPM. The analysis shows a strong economic case for development of a South Asian Regional Electricity Market (SAREM). Conservative estimates of (discounted) benefits exceed $1 billion accrued over only 10-12 years for each of the incumbent four major corridors. The short-term analysis using historic spot prices in the Indian Energy Exchange (IEX) also reveals a strong case with annual benefits in the range of $100-400+m pa for these corridors. The model is made available to system operators and planners in the region and used for building their capacity to develop further assessment and inform policy dialogues.

关键词： Cross-border interconnection dispatch optimization mixed integer programming model long term planning regional electricity market

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