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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年第0期

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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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 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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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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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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Resource allocation and route planning under the collection price uncertainty for the biomass supply chain

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BIOSYSTEMS ENGINEERING 2024年 241卷 68-82页

作者： Wang, Xiang Ting Cao, Jin Xin Lv, Ying Beijing Jiaotong Univ Sch Syst Sci Beijing 100044 Peoples R China Inner Mongolia Acad Sci & Technol Hohhot 010010 Peoples R China Inner Mongolia Univ Inst Transportat Engn Hohhot 010070 Peoples R China

The escalating severity of global warming has drawn worldwide attention to ecological problems. Nevertheless, with the introduction of environmental policies, biomass resources have been effectively developed as a renewable energy source. This paper investigates an advanced biomass supply chain design wherein biomass resources are initially converted into bio-oil through widely distributed fast pyrolysis facilities, and are subsequently transported to a centralised biorefinery for further refining into biofuels. This novel biomass supply chain addressed three key issues: (1) The number of fast pyrolysis facilities, (2) The allocation of resources, and (3) The routes of resources transport. In respect of these problems, a two-stage stochastic mixed integer programming model is established to minimise the total cost of the biomass supply chain considering the uncertainty collection price of fast pyrolysis facilities. A hybrid simulated annealing algorithm which incorporates the sample average approximation method is proposed to solve the stochastic model and is effectiveness for large-scale examples. Finally, a sensitivity analysis is performed using the proposed algorithm and the results show that the proposed stochastic model outperforms the deterministic model under uncertain collection price. The model allows optimising the biomass supply chain economic performances and minimise financial risk on investment by determining the fast pyrolysis facility locations, reasonable resource allocation and optimal transport routes under uncertain collection price.

关键词： Stochastic programming mixed integer programming model Hybrid simulated annealing algorithm Sample average approximation

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A Location-allocation model for Bio-waste Management in the Hospitality Sector

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NETWORKS & SPATIAL ECONOMICS 2023年第3期23卷 611-639页

作者： Santos-Penate, Dolores R. Suarez-Vega, Rafael R. de la Nuez, Carmen Florido Univ Las Palmas Gran Canaria Dpto Metodos Cuantitat Econ & Gest TIDES Las Palmas De GC Spain Univ Las Palmas Gran Canaria Dpto Anal Econ Aplicado TIDES Las Palmas De GC Spain

Tourism generates huge amounts of waste. It has been estimated that about half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. In this paper, we consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. The general objective is twofold: i) to avoid waste transportation from generation to treatment points and product transportation from production to demand points, and ii) to implement a circular model in which the hotels themselves become the suppliers of the products they need (compost and pellets) by transforming the bio-waste that they generate. Any bio-waste not processed by the hotels has to be treated at private or state-run plants. A mathematical optimization model is presented to locate the facilities and allocate the waste and products. The application of the proposed location-allocation model is illustrated with an example.

关键词： Circular economy Tourism Sustainability mixed integer programming model

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Optimizing two-dimensional vehicle loading and dispatching decisions in freight logistics

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期302卷 954-969页

作者： Yucel, Eda Salman, F. Sibel Erdogan, Gunes TOBB Univ Econ & Technol Dept Ind Engn Sogutozu Caddesi 43 TR-06560 Ankara Turkey Koc Univ Dept Ind Engn Rumelifeneri YoluSariyer TR-34450 Istanbul Turkey Univ Bath Sch Management Bath BA1 7AY England

This paper introduces a multi-period, two-dimensional vehicle loading and dispatching problem, called Two-Dimensional Vehicle Loading and Dispatching Problem with Incompatibility Constraints (VLDP). The problem concerns preparing a single-origin single-destination transportation plan of loading required orders to vehicles at the origin and dispatching the vehicles to deliver the orders to the destination within their due dates. The decision maker uses their own fleet of vehicles, with each vehicle having a fixed transportation cost per trip, and may outsource additional vehicles at a higher cost. VLDP involves constraints regarding the due dates of the orders, pairwise incompatibility of orders packed in the same vehicle, incompatibility of orders and vehicles, as well as area and weight capacity of the vehicles. An order can be delivered earlier than its due date, incurring an earliness penalty due to storage requirements at the destination. The objective is to minimize the total vehicle usage and earliness penalty costs. A mixed-integer Linear programming model (MILP) is provided, as well as an Adaptive Large Neighbourhood Search (ALNS) algorithm. Results of computational experiments on instances derived from real-world data show the effectiveness of the ALNS algorithm. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Logistics Long-haul freight logistics Vehicle loading and dispatching mixed integer programming model Adaptive large neighborhood search

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