assignment model in operation research pdf

• Operations Research

A Model-Based Approach

• © 2010
• 1st edition
• View latest edition
• H. A. Eiselt 0 ,
• Carl-Louis Sandblom 1

Faculty of Business Administration, University of New Brunswick, Fredericton, Canada

You can also search for this author in PubMed   Google Scholar

Dept. Industrial Engineering, Dalhousie University, Halifax, Canada

• Covers the standard operations research techniques
• Presents an approach to operations research that is heavily based on modeling and makes extensive use of sensitivity analyses
• Emphasis is on getting insight into problems, rather than computing solutions

48k Accesses

5 Citations

3 Altmetric

This is a preview of subscription content, log in via an institution to check access.

Access this book

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as PDF
• Read on any device
• Instant download
• Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

Similar content being viewed by others.

Introduction to Optimization

Surveys in operations research

Necessary condition analysis (NCA): review of research topics and guidelines for good practice

• Industrial Engineering
• Management Science
• Optimization
• Quantitative Methods
• organization
• Engineering Economics

Table of contents (13 chapters)

Front matter, introduction to operations research.

• H. A. Eiselt, C. -L. Sandblom

Linear Programming

Multiobjective programming, integer programming, network models, location models, project networks, machine scheduling, decision analysis, inventory models, stochastic processes and markov chains, waiting line models, back matter.

From the reviews:

“This course resource by Eiselt … is an introduction to operations research at the undergraduate level. The book introduces a wide variety of deterministic and stochastic operations research models, including linear and integer programming, network flows, facility location problems, machine scheduling problems, inventory models, queuing models, and discrete event simulation models. … Summing Up: Recommended. Business and industrial engineering collections serving upper-division undergraduates.” (B. Borchers, Choice, Vol. 48 (3), November, 2010)

“The book gives an overview of the operations research models applied in many practical problems. … The book is a great contribution to the OR models’ application and can be a significant help to the decision makers.”­­­ (Kristina Šorić, Zentralblatt MATH, Vol. 1198, 2010)

Authors and Affiliations

H. A. Eiselt

Carl-Louis Sandblom

Bibliographic Information

Book Title : Operations Research

Book Subtitle : A Model-Based Approach

Authors : H. A. Eiselt, Carl-Louis Sandblom

DOI : https://doi.org/10.1007/978-3-642-10326-1

Publisher : Springer Berlin, Heidelberg

eBook Packages : Business and Economics , Business and Management (R0)

Copyright Information : Springer-Verlag Berlin Heidelberg 2010

eBook ISBN : 978-3-642-10326-1 Published: 17 May 2010

Edition Number : 1

Number of Pages : XII, 448

Number of Illustrations : 162 b/w illustrations

Topics : Operations Research/Decision Theory , Optimization , Engineering, general , Operations Research, Management Science , Engineering Economics, Organization, Logistics, Marketing

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

THE LITERATURE REVIEW FOR ASSIGNMENT AND TRANSPORTATION PROBLEMS.

Operations Research is a logical learning through interdisciplinary collaboration to determine the best usage of restricted assets. In this paper, the importance of Operations research is discussed and the literature of assignment and transportation problem is discussed in detail.

Related Papers

IJIRT Journal

This study discusses the current scenario of Operations Research in the field of Logistics. Five sectors are considered in the study to form a brief understanding of how they use Operations Research techniques and why these techniques are used. Operation research technique help in reducing cost and improve decision making.

Rabindra Mondal

A transportation problem basically deals with the problem, which aims to find the best way to fulfil the demand of n demand points using the capacities of m supply points. Here we studied a new method for solving transportation problems with mixed constraints and described the algorithm to find an optimal more-for-less (MFL) solution. The optimal MFL solution procedure is illustrated with numerical example and also computer programming. Though maximum transportation problems in real life have mixed constraints, these problems are not be solved by using general method. The proposed method builds on the initial solution of the transportation problem which is very simple, easy to understand and apply.

Optimization

Hossein Arsham

The family of network optimization problems includes the following prototype models: assignment, critical path, max flow, shortest path, and transportation. Although it is long known that these problems can be modeled as linear programs (LP), this is generally not done. Due to the relative inefficiency and complexity of the simplex methods (primal, dual, and other variations) for network models, these problems are usually treated by one of over 100 specialized algorithms. This leads to several difficulties. The solution algorithms are not unified and each algorithm uses a different strategy to exploit the special structure of a specific problem. Furthermore, small variations in the problem, such as the introduction of side constraints, destroys the special structure and requires modifying andjor restarting the algorithm. Also, these algorithms obtain solution efficiency at the expense of managerial insight, as the final solutions from these algorithms do not have sufficient information to perform postoptimality analysis.Another approach is to adapt the simplex to network optimization problems through network simplex. This provides unification of the various problems but maintains all the inefficiencies of simplex, as well as, most of the network inflexibility to handle changes such as side constraints. Even ordinary sensitivity analysis (OSA), long available in the tabular simplex, has been only recently transferred to network simplex.This paper provides a single unified algorithm for all five network models. The proposed solution algorithm is a variant of the self-dual simplex with a warm start. This algorithm makes available the full power of LP perturbation analysis (PA) extended to handle optimal degeneracy. In contrast to OSA, the proposed PA provides ranges for which the current optimal strategy remains optimal, for simultaneous dependent or independent changes from the nominal values in costs, arc capacities, or suppliesJdemands. The proposed solution algorithm also facilitates incorporation of network structural changes and side constraints. It has the advantage of being computationally practical, easy for managers to understand and use, and provides useful PA information in all cases. Computer implementation issues are discussed and illustrative numerical examples are provided in the Appendix For teaching purposes you may try: Refined Simplex Algorithm for the Classical Transportation Problem with Application to Parametric Analysis, Mathematical and Computer Modelling, 12(8), 1035-1044, 1989. http://home.ubalt.edu/ntsbarsh/KahnRefine.pdf

Journal of Applied Mathematics and Decision Sciences

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties. The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading. We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented."

IJAR Indexing

Assignment problems deal with the question how to assign n objects to m other objects in an injective fashion in the best possible way. An assignment problem is completely specified by its two components the assignments, which represent the underlying combinatorial structure, and the objective function to be optimized, which models \\\\\\\"the best possible way\\\\\\\". The assignment problem refers to another special class of linear programming problem where the objective is to assign a number of resources to an equal number of activities on a one to one basis so as to minimize total costs of performing the tasks at hand or maximize total profit of allocation. In this paper we introduce a new technique to solve assignment problems namely, Divide Row Minima and Subtract Column Minima .For the validity and comparison study we consider an example and solved by using our technique and the existing Hungarian (HA) and matrix ones assignment method(MOA) and compare optimum result shown graphically.

ام محمد لا للشات

The problem of finding the initial basic feasible solution of the Transportation Problem has long been studied and is well known to the research scholars of the field. So far three general methods for solving transportation methods are available in literature, namely Northwest, Least Cost and Vogel?s Approximation methods. These methods give only initial feasible solution. However here we discuss a new alternative method which gives Initial feasible solution as well as optimal or nearly optimal solution. In this paper we provide an alternate method to find IBFS (Initial Basic Feasible Solution) and compared the alternate method and the existing IBFS methods using a Graphical User Interface. It is also to be noticed that this method requires lesser number of iterations to reach optimality as compared to other known methods for solving the transportation problem and the solution obtained is as good as obtained by Vogel?s Approximation Method (VAM).

Omega-international Journal of Management Science

Krzysztof Kowalski

nikky kumari

A new method called zero point method is proposed for finding an optimal solution for transportation problems with mixed constraints in a single stage. Using the zero point method, we propose a new method for finding an optimal more-for-less solution for transportation problems with mixed constraints. The optimal more-for-less solution procedure is illustrated with numerical examples. Mathematics Subject Classifications: 90C08 , 90C90

Handbooks in Operations Research and Management Science

George Nemhauser

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED PAPERS

Int.J. Contemp.Math.Sciences

Dr. P. Senthil Kumar (PSK), M.Sc., B.Ed., M.Phil., PGDCA., PGDAOR., Ph.D.,

Tomasz Kuszewski

Shashini Nawarathne

Journal of Supply Chain Management System

Publishing India Group

International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)

International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) ijarcet

International Journal of Advance and Innovative Research Volume 6, Issue 1 (XXVII): January - March, 2019

Ishfaq Majeed

Juman Abdeen

Prakash Panangaden

International Journal on Advanced …

Adibah Shuib

Anna Nagurney

Carsten Gottschlich

Operations Research Center …

Ankur Chaudhry

Journal of Heuristics

Mehdi Amini

Discrete Applied Mathematics

Rainer Burkard

David Boyce , Hani Mahmassani , Anna Nagurney

European Scientific Journal ESJ

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Research on a vibration model of a superstructure under the vibration load of metro trains.

1. Introduction

2. methodology, 2.1. modeling of vehicle–track interaction dynamics, 2.2. development of a three-dimensional finite element model for analyzing track structures, surrounding strata, and building interactions, 3. field testing and model verification processes, 3.1. overview of test sites, 3.2. evaluation indicators, 3.3. model validation, 4. refined prediction of structural vibrations and secondary noise in building structures, 4.1. influence zone of the pharyngeal area’s upper lid, 4.2. impact radius of the test line, 4.3. impact assessment of maintenance and material depots, and loading/unloading lines, 5. conclusions, author contributions, data availability statement, conflicts of interest.

• Ma, M.; Liu, W.; Qian, C.; Deng, G.; Li, Y. Study of the train-induced vibration impact on a historic Bell Tower above two spatially overlapping metro lines. Soil Dyn. Earthq. Eng. 2016 , 81 , 58–74. [ Google Scholar ] [ CrossRef ]
• Handy, S. Smart growth and the transportation-land use connection: What does the research tell us? Int. Reg. Sci. Rev. 2005 , 28 , 146–167. [ Google Scholar ] [ CrossRef ]
• Sheng, X.; Jones, C.J.C.; Thompson, D.J. A theoretical study on the influence of the track on train-induced ground vibration. J. Sound Vib. 2004 , 272 , 909–936. [ Google Scholar ] [ CrossRef ]
• Connolly, D.P.; Kouroussis, G.; Giannopoulos, A.; Verlinden, O.; Woodward, P.K.; Forde, M.C. Assessment of railway vibrations using an efficient scoping model. Soil Dyn. Earthq. Eng. 2014 , 58 , 37–47. [ Google Scholar ] [ CrossRef ]
• Lund, A.; Dahlberg, T. Dynamic train/track interaction including model for track settlement evolvement. Veh. Syst. Dynamics 2004 , 66 , 667–676. [ Google Scholar ]
• Zou, C.; Moore, J.A.; Sanayei, M.; Tao, Z.; Wang, Y. Impedance Model of Train-Induced Vibration Transmission Across a Transfer Structure into an Overtrack Building in a Metro Depot. J. Struct. Eng. 2022 , 148 , 1–46. [ Google Scholar ] [ CrossRef ]
• Lei, X.; Jiang, C. Analysis of vibration reduction effect of steel spring floating slab track with finite elements. J. Vib. Control 2014 , 22 , 1462–1471. [ Google Scholar ] [ CrossRef ]
• Federico Rossi, A.N. A simple model to predict train-induced vibration: Theoretical formulation and experimental validation. Environ. Impact Assess. Rev. 2003 , 23 , 305–322. [ Google Scholar ] [ CrossRef ]
• Sanayei, M.; Anish, P.K.; Moore, J.A.; Brett, C.R. Measurement and prediction of train-induced vibrations in a full-scale building. Eng. Struct. 2014 , 77 , 119–128. [ Google Scholar ] [ CrossRef ]
• Liu, Q.; Li, X.; Zhang, X.; Zhou, Y.; Chen, Y.F. Applying constrained layer damping to reduce vibration and noise from a steel-concrete composite bridge: An experimental and numerical investigation. J. Sandw. Struct. Mater. 2018 , 22 , 1743–1769. [ Google Scholar ] [ CrossRef ]
• Liu, Q.; Thompson, D.J.; Xu, P.; Feng, Q.; Li, X. Investigation of train-induced vibration and noise from a steel-concrete composite railway bridge using a hybrid finite element-statistical energy analysis method. J. Sound Vib. 2020 , 471 , 115197. [ Google Scholar ] [ CrossRef ]
• Liang, R.; Liu, W.; Ma, M.; Liu, W. An efficient model for predicting the train-induced ground-borne vibration and un-certainty quantification based on bayesian neural network. J. Sound Vib. 2021 , 495 , 115908. [ Google Scholar ] [ CrossRef ]
• Connolly, D.; Giannopoulos, A.; Forde, M.C. Numerical modelling of ground borne vibrations from high speed rail lines on embankments. Soil Dyn. Earthq. Eng. 2013 , 46 , 13–19. [ Google Scholar ] [ CrossRef ]
• Zhai, W.; Wang, K. Lateral hunting stability of railway vehicles running on elastic track structures. J. Comput. Nonlinear Dynamics 2010 , 5 , 041009-1–041009-9. [ Google Scholar ] [ CrossRef ]
• Torstensson, P.T.; Nielsen, J.C.O. Simulation of dynamic vehicle–track interaction on small radius curves. Veh. Syst. Dyn. 2011 , 49 , 1711–1732. [ Google Scholar ] [ CrossRef ]
• Kouroussis, G.; Gazetas, G.; Anastasopoulos, I.; Conti, C.; Verlinden, O. Discrete modelling of vertical track–soil coupling for vehicle–track dynamics. Soil Dyn. Earthq. Eng. 2011 , 31 , 1711–1723. [ Google Scholar ] [ CrossRef ]
• Qiu, Y.; Zou, C.; Hu, J.; Chen, J. Prediction and mitigation of building vibrations caused by train operations on concrete floors. Appl. Acoust. 2024 , 219 , 109941. [ Google Scholar ] [ CrossRef ]
• Kouroussis, G.; Verlinden, O.; Conti, C. A two-step time simulation of ground vibrations induced by the railway traffic. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2011 , 226 , 454–472. [ Google Scholar ] [ CrossRef ]
• Pyl, L.; Degrande, G.; Lombaert, G.; Haegeman, W. Validation of a source-receiver model for road traffic-induced vibra-tions in buildings. I: Source model. J. Eng. Mech. 2004 , 130 , 1377–1393. [ Google Scholar ] [ CrossRef ]
• Galvín, P.; Mendoza, D.L.; Connolly, D.P.; Degrande, G.; Lombaert, G.; Romero, A. Scoping assessment of free_field vibrations due to railway traffic. Soil Dyn. Earthq. Eng. 2018 , 114 , 598–614. [ Google Scholar ] [ CrossRef ]
• He, L.; Tao, Z. Building vibration measurement and prediction during train operations. Buildings 2024 , 14 , 142. [ Google Scholar ] [ CrossRef ]
• Zou, C.; Wang, Y.; Zhang, X.; Tao, Z. Vibration isolation of over-track buildings in a metro depot by using trackside wave barriers. J. Build. Eng. 2020 , 30 , 101270. [ Google Scholar ] [ CrossRef ]
• Zou, C.; Wang, Y.; Moore, J.A.; Sanayei, M. Train-induced field vibration measurements of ground and over-track buildings. Sci. Total. Environ. 2017 , 575 , 1339–1351. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Costa, P.A.; Calçada, R.; Cardoso, A.S. Influence of train dynamic modelling strategy on the prediction of track–ground vibrations induced by railway traffic. Proc. Inst. Mech. Eng. Part F-J. Rail Rapid Transit 2012 , 226 , 434–450. [ Google Scholar ] [ CrossRef ]
• Li, H.; He, C.; Gong, Q.; Zhou, S.; Li, X.; Zou, C. Tlm-cfspml for 3d dynamic responses of a layered transversely isotropic half-space. Comput. Geotech. 2024 , 168 , 106131. [ Google Scholar ] [ CrossRef ]
• Ma, M.; Xu, L.; Liu, W.; Tan, X. Semi-analytical solution of a coupled tunnel-soil periodic model with a track slab under a moving train load, Applied Mathematical Modelling. Simul. Comput. Eng. Environ. Syst. 2024 , 128 , 588–608. [ Google Scholar ]
• Zhai, W.; Wang, K.; Cai, C. Fundamentals of vehicle-track coupled dynamics. Veh. Syst. Dyn. 2009 , 47 , 1349–1376. [ Google Scholar ] [ CrossRef ]
• Sheng, X.; Jones, C.J.C.; Thompson, D.J. A theoretical model for ground vibration from trains generated by vertical track irregularities. J. Sound Vib. 2003 , 272 , 937–965. [ Google Scholar ] [ CrossRef ]
• Hussein, M.F.M.; Hunt, H.E.M. A numerical model for calculating vibration from a railway tunnel embedded in a full-space. J. Sound Vib. 2007 , 305 , 401–431. [ Google Scholar ] [ CrossRef ]
• Auersch, L. Wave propagation in the elastic half-space due to an interior load and its application to ground vibration problems and buildings on pile foundations. Soil Dyn. Earthq. Eng. 2010 , 30 , 925–936. [ Google Scholar ] [ CrossRef ]
• Auersch, L. Dynamic interaction of various beams with the underlying soil–finite and infinite, half–space and Winkler models. Eur. J. Mech. A/solids 2008 , 27 , 933–958. [ Google Scholar ] [ CrossRef ]
• Xu, L.; Ma, M. Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil. J. Zhejiang Univ. A 2023 , 24 , 637–652. [ Google Scholar ] [ CrossRef ]
• Auersch, L. Dynamic stiffness of foundations on inhomogeneous soils for a realistic prediction of vertical building resonance. J. Geotech. Geoenviron. Eng. 2008 , 134 , 328–340. [ Google Scholar ] [ CrossRef ]
• François, S.; Pyl, L.; Masoumi, H.; Degrande, G. The influence of dynamic soil–structure interaction on traffic induced vibrations in buildings. Soil Dyn. Earthq. Eng. 2006 , 27 , 655–674. [ Google Scholar ] [ CrossRef ]
• Hu, J.; Zou, C.; Liu, Q.; Li, X.; Tao, Z. Floor vibration predictions based on train-track-building coupling model. J. Build. Eng. 2024 , 89 , 109340. [ Google Scholar ] [ CrossRef ]
• Ditommaso, R.; Mucciarelli, M.; Gallipoli, M.R.; Ponzo, F.C. Effect of a single vibrating building on free-field ground motion: Numerical and experimental evidences. Bull. Earthq. Eng. 2009 , 8 , 693–703. [ Google Scholar ] [ CrossRef ]
• Iacovino, C.; Ditommaso, R.; Ponzo, F.C.; Limongelli, M.P. The interpolation evolution method for damage localization in structures under seismic excitation. Earthq. Eng. Struct. Dyn. 2018 , 47 , 2117–2136. [ Google Scholar ] [ CrossRef ]
• JGJ/T 170-2009 ; Standard for Limits of Vibration and Secondary Radiated Noise of Buildings Caused by Urban Rail Transit and its Measurement Methods. China Architecture & Building Press: Beijing, China, 2009.
• GB 10070-88 ; Methods for Measurement of Ambient Vibration in Urban Areas. Standards Press of China: Beijing, China, 1988.
• Li, X.; Chen, Y.; Zo, C.; Wang, H.; Zheng, B.; Chen, J. Building structure-borne noise measurements and estimation due to train operations in tunnel. Sci. Total Environ. 2024 , 926 , 172080. [ Google Scholar ] [ CrossRef ]

Click here to enlarge figure

Share and Cite

Liu, Y.; Xu, H.; Xia, W.; Cai, W.; Zheng, S. Research on a Vibration Model of a Superstructure under the Vibration Load of Metro Trains. Buildings 2024 , 14 , 2342. https://doi.org/10.3390/buildings14082342

Liu Y, Xu H, Xia W, Cai W, Zheng S. Research on a Vibration Model of a Superstructure under the Vibration Load of Metro Trains. Buildings . 2024; 14(8):2342. https://doi.org/10.3390/buildings14082342

Liu, Yang, Haodong Xu, Wei Xia, Wenfeng Cai, and Senlin Zheng. 2024. "Research on a Vibration Model of a Superstructure under the Vibration Load of Metro Trains" Buildings 14, no. 8: 2342. https://doi.org/10.3390/buildings14082342

Article Metrics

Article access statistics, further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals