assignment problem pdf download

Browse Course Material

Course info.

• Dr. Casey Rodriguez

Departments

• Mathematics

As Taught In

• Mathematical Analysis

Learning Resource Types

Real analysis, assignments and exams.

Assignment 1 (PDF)

Assignment 2 (PDF)

Assignment 3 (PDF)

Assignment 4 (PDF)

Assignment 5 (PDF)

Assignment 6 (PDF)

Assignment 7 (PDF)

Assignment 8 (PDF)

Assignment 9 (PDF)

Assignment 10 (PDF)

Assignment 11 (PDF)

Assignment 12 (PDF)

Midterm Exam (PDF)

Final Assignment (PDF)

The assignment problem revisited

• Original Paper
• Published: 16 August 2021
• Volume 16 , pages 1531–1548, ( 2022 )

Cite this article

• Carlos A. Alfaro   ORCID: orcid.org/0000-0001-9783-8587 1 ,
• Sergio L. Perez 2 ,
• Carlos E. Valencia 3 &
• Marcos C. Vargas 1  

991 Accesses

4 Citations

4 Altmetric

Explore all metrics

First, we give a detailed review of two algorithms that solve the minimization case of the assignment problem, the Bertsekas auction algorithm and the Goldberg & Kennedy algorithm. It was previously alluded that both algorithms are equivalent. We give a detailed proof that these algorithms are equivalent. Also, we perform experimental results comparing the performance of three algorithms for the assignment problem: the \(\epsilon \) - scaling auction algorithm , the Hungarian algorithm and the FlowAssign algorithm . The experiment shows that the auction algorithm still performs and scales better in practice than the other algorithms which are harder to implement and have better theoretical time complexity.

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

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges

A Systematic Review of the Whale Optimization Algorithm: Theoretical Foundation, Improvements, and Hybridizations

From approximate to exact integer programming

Bertsekas, D.P.: The auction algorithm: a distributed relaxation method for the assignment problem. Annal Op. Res. 14 , 105–123 (1988)

Article   MathSciNet   Google Scholar  

Bertsekas, D.P., Castañon, D.A.: Parallel synchronous and asynchronous implementations of the auction algorithm. Parallel Comput. 17 , 707–732 (1991)

Article   Google Scholar  

Bertsekas, D.P.: Linear network optimization: algorithms and codes. MIT Press, Cambridge, MA (1991)

MATH   Google Scholar  

Bertsekas, D.P.: The auction algorithm for shortest paths. SIAM J. Optim. 1 , 425–477 (1991)

Bertsekas, D.P.: Auction algorithms for network flow problems: a tutorial introduction. Comput. Optim. Appl. 1 , 7–66 (1992)

Bertsekas, D.P., Castañon, D.A., Tsaknakis, H.: Reverse auction and the solution of inequality constrained assignment problems. SIAM J. Optim. 3 , 268–299 (1993)

Bertsekas, D.P., Eckstein, J.: Dual coordinate step methods for linear network flow problems. Math. Progr., Ser. B 42 , 203–243 (1988)

Bertsimas, D., Tsitsiklis, J.N.: Introduction to linear optimization. Athena Scientific, Belmont, MA (1997)

Google Scholar  

Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. Revised reprint. SIAM, Philadelphia, PA (2011)

Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for network problems. SIAM J. Comput. 18 (5), 1013–1036 (1989)

Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. J. Assoc. Comput. Mach. 35 , 921–940 (1988)

Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by successive approximation. Math. Op. Res. 15 , 430–466 (1990)

Goldberg, A.V., Kennedy, R.: An efficient cost scaling algorithm for the assignment problem. Math. Programm. 71 , 153–177 (1995)

MathSciNet   MATH   Google Scholar  

Goldberg, A.V., Kennedy, R.: Global price updates help. SIAM J. Discr. Math. 10 (4), 551–572 (1997)

Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res. Logist. Quart. 2 , 83–97 (1955)

Kuhn, H.W.: Variants of the Hungarian method for the assignment problem. Naval Res. Logist. Quart. 2 , 253–258 (1956)

Lawler, E.L.: Combinatorial optimization: networks and matroids, Holt. Rinehart & Winston, New York (1976)

Orlin, J.B., Ahuja, R.K.: New scaling algorithms for the assignment ad minimum mean cycle problems. Math. Programm. 54 , 41–56 (1992)

Ramshaw, L., Tarjan, R.E., Weight-Scaling Algorithm, A., for Min-Cost Imperfect Matchings in Bipartite Graphs, : IEEE 53rd Annual Symposium on Foundations of Computer Science. New Brunswick, NJ 2012 , 581–590 (2012)

Zaki, H.: A comparison of two algorithms for the assignment problem. Comput. Optim. Appl. 4 , 23–45 (1995)

Download references

Acknowledgements

This research was partially supported by SNI and CONACyT.

Author information

Authors and affiliations.

Banco de México, Mexico City, Mexico

Carlos A. Alfaro & Marcos C. Vargas

Mountain View, CA, 94043, USA

Sergio L. Perez

Departamento de Matemáticas, CINVESTAV del IPN, Apartado postal 14-740, 07000, Mexico City, Mexico

Carlos E. Valencia

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Carlos A. Alfaro .

Ethics declarations

Conflict of interest.

There is no conflict of interest.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors were partially supported by SNI and CONACyT.

Rights and permissions

Reprints and permissions

About this article

Alfaro, C.A., Perez, S.L., Valencia, C.E. et al. The assignment problem revisited. Optim Lett 16 , 1531–1548 (2022). https://doi.org/10.1007/s11590-021-01791-4

Download citation

Received : 26 March 2020

Accepted : 03 August 2021

Published : 16 August 2021

Issue Date : June 2022

DOI : https://doi.org/10.1007/s11590-021-01791-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Assignment problem
• Bertsekas auction algorithm
• Combinatorial optimization and matching
• Find a journal
• Publish with us
• 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

Solving the Unbalanced Assignment Problem: Simpler Is Better

American Journal of Operations Research

Related Papers

Dr Avanish Kumar

Bhausaheb G Kore

In this paper I have proposed a new approach to solve an unbalanced assignment problem (UBAP). This approach includes two parts. First is to obtain an initial basic feasible solution (IBFS) and second part is to test optimality of an IBFS. I have proposed two new methods Row Penalty Assignment Method (RPAM) and Column Penalty Assignment Method (CPAM) to obtain an IBFS of an UBAP. Also I have proposed a new method Non-basic Smallest Effectiveness Method (NBSEM) to test optimality of an IBFS. We can solve an assignment problem of maximization type using this new approach in opposite sense. By this new approach, we achieve the goal with less number of computations and steps. Further we illustrate the new approach by suitable examples. INTRODUCTION The assignment problem is a special case of the transportation problem where the resources are being allocated to the activities on a one-to-one basis. Thus, each resource (e.g. an employee, machine or time slot) is to be assigned uniquely to a particular activity (e.g. a task, site or event). In assignment problems, supply in each row represents the availability of a resource such as a man, machine, vehicle, product, salesman, etc. and demand in each column represents different activities to be performed such as jobs, routes, factories, areas, etc. for each of which only one man or vehicle or product or salesman respectively is required. Entries in the square being costs, times or distances. The assignment method is a special linear programming technique for solving problems like choosing the right man for the right job when more than one choice is possible and when each man can perform all of the jobs. The ultimate objective is to assign a number of tasks to an equal number of facilities at minimum cost (or maximum profit) or some other specific goal. Let there be 'm' resources and 'n' activities. Let c ij be the effectiveness (in terms of cost, profit, time, etc.) of assigning resource i to activity j (i = 1, 2, …., m; j = 1, 2,…., n). Let x ij = 0, if resource i is not assigned to activity j and x ij = 1, if resource i is assigned to activity j. Then the objective is to determine x ij 's that will optimize the total effectiveness (Z) satisfying all the resource constraints and activity constraints. 1. Mathematical Formulation Let number of rows = m and number of columns = n. If m = n then an AP is said to be BAP otherwise it is said to be UBAP. A) Case 1: If m < n then mathematically the UBAP can be stated as follows:

Malaya Journal of Matematik

DR ANJU KHANDELWAL

International Journal for Research in Applied Science & Engineering Technology (IJRASET)

IJRASET Publication

In this paper a new method is proposed for finding an optimal solution of a wide range of assignment problems, directly. A numerical illustration is established and the optimality of the result yielded by this method is also checked. The most attractive feature of this method is that it requires very simple arithmetical and logical calculations. The method is illustrated through an example.

Hussein Ali Hussein Al-Dallal Al-Saeedi

archana pandey

Assignment problems arise in different situation where we have to find an optimal way to assign n-objects to mother objects in an injective fashion. The assignment problems are a well studied topic in combinatorial optimization. These problems find numerous application in production planning, telecommunication VLSI design, economic etc. The assignment problems is a special case of Transportation problem. Depending on the objective we want to optimize, we obtain the typical assignment problems. Assignment problem is an important subject discussed in real physical world we endeavor in this paper to introduce a new approach to assignment problem namely, matrix ones assignment method or MOA-method for solving wide range of problem. An example using matrix ones assignment methods and the existing Hungarian method have been solved and compared it graphically. Also some of the variations and some special cases in assignment problem and its applications have been discussed in the paper.

Sultana Rafi

The assignment problem is a particular type of linear programming problem. In this paper, we analyzed the standard and existing proposed methods. After studying these methods, we proposed a new alternative method for solving the assignment problem. We examined the newly proposed method by a couple of numerical examples and compare this result with the standard method. The main characteristic of this newly proposed method is that it constructed a very easy logical and arithmetical algorithm. Here we point out some advantages and limitations of the new proposed method. Programming code for the newly proposed method has been added in this paper.

Ranjan Kumar Mondal

Thecloudcomputingpresentsatypeofassignmentsandsystemswhichoccupydistributedresources toexecutearoleinadistributedway.Cloudcomputingmakeuseoftheonlinesystemsonthewebto assisttheimplementationofcomplicatedassignments;thatneedhuge-scalecomputation.Itwassaid withtheintentionofinourlivingworld;wecanfinditchallengingtobalanceworkloadsofcloud computingamongassignments(jobsortasks)andsystems(machinesornodes),sothemajorityofthe timewehavetopromoteaconditiontounbalancedassignmentproblems(unequaltaskallocations). The present article submits a new technique to solve the unequal task allocation problems. The techniqueisofferedinanalgorithmicmodelandputintopracticeontheseveralgroupsofinputto investigatethepresentationandusefulnessoftheworks.Anevaluationispreparedwiththepresented approach.Itmakessurethattheproposedapproachprovidesabetteroutcomebycomparingwith someotherexistingalgorithms.

Industrial Engineering Journal

Shridhar Mhalsekar

Journal of Advances in Mathematics and Computer Science

Hudu Mohammed

Assignment problem is an important area in Operation Research and is also discussed in real physical world. In this paper an attempt has been made to solve the assignment problem using a new Method called the Penalty method. We discuss a numerical example by using the new Method and compare it with standard existing method which is the Hungarian method. We compare the optimal solution of the new Method and the Hungarian method. The new method is a simple procedure, easy to apply for solving assignment problem.

RELATED PAPERS

Diogo Luiz Cordeiro Rodrigues

Luis Angeles

sally neouchi

Irfan S Damanik

Engin Yilmaz

Macromolecular Bioscience

Wanda Guedens

Journal of Occupational and Environmental Medicine

Jessica Grossmeier

Mónica Lamas

Türkiye Peyzaj Araştırmaları Dergisi

Bioconjugate chemistry

Vijay Gulumkar

Physical Review B

Surgical Ophthalmic Oncology

Svetlana Saakyan

Revue d'économie du développement

Patrick Plane

Ankara Üniversitesi İlahiyat Fakültesi Dergisi

Ali Rıza Gül

Chemischer Informationsdienst

Renzo Ruzziconi

Jurnal Pendidikan Matematika Unpatti

Magy Gaspersz magy0002pasca.2022

fira puspita

Managerial and Decision Economics

Mickey Mouse

AKSY Jurnal Ilmu Akuntansi dan Bisnis Syariah

Khoirun Nazilah

Poster Presentations

Weiming Tang

Mauricio Peña Cadavid

Indula Subash

Journal of Medical Radiation Sciences

Shelley Park

Bulletin of the American Physical Society

Phillip Broussard

International Journal Of Community Medicine And Public Health

Shailaja Daral

RELATED TOPICS

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