Help | Advanced Search
Mathematics > Optimization and Control
Title: sensitivity analysis for bottleneck assignment problems.
Abstract: In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.
Submission history
Access paper:.
- Other Formats
References & Citations
- Google Scholar
- Semantic Scholar
BibTeX formatted citation
Bibliographic and Citation Tools
Code, data and media associated with this article, recommenders and search tools.
- Institution
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .
A robust optimization solution to bottleneck generalized assignment problem under uncertainty
- Published: 29 May 2014
- Volume 233 , pages 123–133, ( 2015 )
Cite this article
- Yelin Fu 1 , 2 ,
- Jianshan Sun 3 ,
- K. K. Lai 2 , 4 &
- John W. K. Leung 5
798 Accesses
13 Citations
Explore all metrics
We consider two versions of bottleneck (or min–max) generalized assignment problem (BGAP) under capacity uncertainty: Task–BGAP and Agent–BGAP. A robust optimization approach is employed to study this issue. The decision maker’s degree of risk aversion and the penalty weighting parameter are incorporated into the objective function. A state-of-the-art linearization method is introduced to deal with the mathematical model and find the solution scheme. Two penalties of weighting parameters that realize the trade-off between solution robustness and model robustness are obtained. Illustrative examples are presented with managerial implications highlighted for decision-making considerations.
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
Distributionally robust bottleneck combinatorial problems: uncertainty quantification and robust decision making
Weijun Xie, Jie Zhang & Shabbir Ahmed
Exact algorithms for the robust uncapacitated multiple allocation p-hub median problem
Nader Ghaffarinasab
Adjustable robust balanced hub location problem with uncertain transportation cost
Reza Rahmati & Hossein Neghabi
Ahmed, S., & Garcia, R. (2003). Dynamic capacity acquisition and assignment under uncertainty. Annals of Operations Research , 124 (1–4), 267–283.
Article Google Scholar
Deĭneko, V. G., & Woeginger, G. J. (2006). On the robust assignment problem under a fixed number of cost scenarios. Operations Research Letters , 34 (2), 175–179.
Hwang, J., & Singh, M. R. (1998). Optimal production polices for multi-stage systems with setup costs and uncertain capacities. Management Sciences , 44 (9), 1279–1294.
Lai, K. K., & Ng, W.-L. (2005). A stochastic approach to hotel revenue optimization. Computers & Operations Research , 32 (5), 1059–1072.
Laguna, M., Lino, P., Pérez, A., Quintanilla, S., & Valls, V. (2000). Minimizing weighted tardiness of jobs with stochastic interruptions in parallel machines. European Journal of Operational Research , 127 (2), 444–457.
Mazzola, J. B., & Neebe, A. W. (1988). Bottleneck generalized assignment problem. Engineering Costs and Production Economics , 14 (1), 61–65.
Mulvey, J. M., Venderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research , 43 (2), 264–281.
Martello, S., & Toth, P. (1995). The bottleneck generalized assignment problem. European Journal of Operational Research , 83 (3), 621–638.
Shrage, L. E. (1997). Optimization modeling with LINDO . Pacific Grove: Duxbury Press.
Google Scholar
Snyder, L. V. (2006). Facility location under uncertainty: A review. IIE Transactions , 38 (7), 547–564.
Yechiali, U. (1968). A stochastic bottleneck assignment problem. Management Science , 14 (11), 732–733.
Yu, C. S., & Li, H. L. (2000). A robust optimization model for stochastic logistic problems. International Journal of Production Economics , 64 (1–3), 385–397.
Download references
Author information
Authors and affiliations.
School of Management, University of Science and Technology of China, Hefei, China
Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong
Yelin Fu & K. K. Lai
School of Management, Hefei University of Technology, Hefei, China
Jianshan Sun
International Business School, Shaanxi Normal University, Xian, China
Department of Marketing, City University of Hong Kong, Kowloon, Hong Kong
John W. K. Leung
You can also search for this author in PubMed Google Scholar
Corresponding author
Correspondence to Jianshan Sun .
Rights and permissions
Reprints and permissions
About this article
Fu, Y., Sun, J., Lai, K.K. et al. A robust optimization solution to bottleneck generalized assignment problem under uncertainty. Ann Oper Res 233 , 123–133 (2015). https://doi.org/10.1007/s10479-014-1631-5
Download citation
Published : 29 May 2014
Issue Date : October 2015
DOI : https://doi.org/10.1007/s10479-014-1631-5
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
- Robust optimization
- Stochastic programming
- Find a journal
- Publish with us
- Track your research
General Bottleneck Assignment Problem and its Algorithm
Ieee account.
- Change Username/Password
- Update Address
Purchase Details
- Payment Options
- Order History
- View Purchased Documents
Profile Information
- Communications Preferences
- Profession and Education
- Technical Interests
- US & Canada: +1 800 678 4333
- Worldwide: +1 732 981 0060
- Contact & Support
- About IEEE Xplore
- Accessibility
- Terms of Use
- Nondiscrimination Policy
- Privacy & Opting Out of Cookies
A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2024 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.
- Help & FAQ
On the bottleneck assignment problem
- Marcus Department of Industrial and Manufacturing Engineering
Research output : Contribution to journal › Article › peer-review
In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is shown that any critical solution yields a global optimum. This theorem is then used as a basis to develop a general method to solve max-min permutation problems.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
Access to Document
- 10.1007/BF00933089
Other files and links
- Link to publication in Scopus
- Link to the citations in Scopus
Fingerprint
- Bottleneck Problem Mathematics 100%
- Assignment Problem Business & Economics 79%
- Permutation Mathematics 53%
- Min-max Mathematics 28%
- Global Optimum Mathematics 16%
- Theorem Mathematics 5%
- Class Mathematics 3%
T1 - On the bottleneck assignment problem
AU - Ravindran, A.
AU - Ramaswami, V.
PY - 1977/4
Y1 - 1977/4
N2 - In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is shown that any critical solution yields a global optimum. This theorem is then used as a basis to develop a general method to solve max-min permutation problems.
AB - In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is shown that any critical solution yields a global optimum. This theorem is then used as a basis to develop a general method to solve max-min permutation problems.
UR - http://www.scopus.com/inward/record.url?scp=0347497381&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0347497381&partnerID=8YFLogxK
U2 - 10.1007/BF00933089
DO - 10.1007/BF00933089
M3 - Article
AN - SCOPUS:0347497381
SN - 0022-3239
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
Exclusive: Banking bottleneck causing six-month delays for Russia-China payments, sources say
- This content was produced in Russia where the law restricts coverage of Russian military operations in Ukraine
'SERIOUS DELAYS'
LACK OF TRUST?
Get a look at the day ahead in U.S. and global markets with the Morning Bid U.S. newsletter. Sign up here.
Reporting by Reuters in Moscow; additional reporting by Casey Hall in Shanghai; Writing by Alexander Marrow, editing by Emelia Sithole-Matarise
Our Standards: The Thomson Reuters Trust Principles. , opens new tab
Oil falls on renewed push for Middle East ceasefire
Oil prices fell on Monday, ending a multi-session rally after Israel reduced its troops in southern Gaza and began a fresh round of ceasefire talks with Hamas.
An innovation is born: new mom pitches baby bottle monitor on Shark Tank
Veba Baby tracks temperature and expiration of both breastmilk and formula to give parents peace of mind.
By Irene Ferradaz
April 8, 2024 at 11:34am
When Veon Brewster, a computer science Ph.D. student, first became a mom, she quickly realized how demanding and stressful it was to keep her son nourished. She breastfed him but oftentimes had to express her milk via a pump in order to run errands and, a few months later, go back to work full-time as a user experience researcher for Google.
Her new worry: tracking the expiration of that bottled breastmilk to ensure it remained fresh for consumption.
This very real problem inspired Brewster to create Veba Baby , a baby bottle monitor that tracks temperature and expiration in real time. Established in partnership with her husband, Sean, Veba Baby leverages technology and health data to give parents peace of mind regarding their baby’s milk intake.
The only such device on the market, Veba Baby was recently featured on Shark Tank, one of the nation’s best-rated reality TV shows.
Although Brewster didn’t make a deal with the sharks, Veba Baby hopes to benefit from the “Shark Tank Effect” which holds that simply appearing on the show, even without getting an offer, has the potential to significantly boost sales for companies. In fact, some entrepreneurs have reported 10- to 20-fold increases in daily revenue s after the show's airing.
Brewster knew she was taking a risk pitching her product only two weeks after Veba Baby officially launched but, as she says with a laugh, “When Shark Tank comes calling, you don’t say no!”
Being on Shark Tank was not only thrilling, but greatly informative as well.
“Lori really understood and appreciated the Veba Baby monitor,” says Brewster. “She told us it will be a very useful product for first-time parents.”
Mark Cuban also provided solid advice on packaging the monitor and succeeding in the retail space. “We had a great dialogue about it and he learned that moms spend from four to six hours a day pumping!”
One of the most surprising things she realized about her entrepreneurial journey is how far society still needs to go to better understand the realities of new mothers, especially those who simultaneously hold down a job.
“I don’t think many people get how hard it can be to breastfeed a child while working, having to excuse yourself every few hours to pump and the pain we experience when we don’t pump on time,” says Brewster. “During my pitches to investors and venture capital firms, I am confronted with having to explain motherhood to my mostly male audience. Getting them to really understand why my product is such a godsend for new moms can often be a challenge.” It is estimated that between 75 and 85 percent of mothers use a breast pump.
Although Veba Baby is still early in its journey, Brewster is excited for the next steps.
Having officially launched Veba Baby in August 2023, Brewster recently met with StartUP FIU co-founder and director Robert Hacker to learn about federal grants available that will allow her to continue funding research & development and building more of her baby bottle monitors.
“Becoming a new mom inspired Veon to stretch her innovative mind and design a unique, technologically savvy solution that efficiently tracks infant feedings,” says Hacker. “Working with creative and entrepreneurial students like Veon is always a joy.”
IMAGES
VIDEO
COMMENTS
In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem ( LBAP) is similar to the linear assignment problem. [1] In plain words the problem is stated as follows: There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary ...
We briefly describe a simple algorithm which solves the bottleneck assignment problem: Let Π be an assignment over the graph. If there does not exist an assignment consisting of edges with strictly lower weight than Π, then Π is optimal. If there does, replace Π with the found assignment. Repeat until Π is optimal.
We briefly describe a simple algorithm which solves the bottleneck assignment problem: Let Π be an assignment over the graph. If there does not exist an assignment consisting of edges with strictly lower weight than Π, then Π is optimal. If there does, replace Π with the found assignment. Repeat until Π is optimal.
For the bottleneck assignment problem there are many algorithms which provide solution in polynomial time, reviewed in Pentico (2007) and Pferschy (1997). In many applications the weight associated with the assignment of an agent to a task carries with it some uncertainty. Measurement errors, communication delays, or a dynamic environment may ...
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain conditions the structure of the BAP can be exploited such that subgroups of tasks are assigned separately with lower complexity and then merged to form a combined assignment.
This problem is known as the multi-level bottleneck assignment problem (MBAP). The MBAP with m = 2 is a special case of the classical bottleneck assignment problem and belongs to a class of high dimensional (axial) generalization of the well-known assignment problem, see Burkard et al. (2009). Therefore, MBAP is a hypergraph version of ...
Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as ...
Download PDF Abstract: In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous ...
and we want to minimize the time at which the last task is completed, then we have a bottleneck assignment problem. Formally, the bottleneck assignment problem is defined as follows, where c;. is the cost of assigning resource i to task j: For a summary of major results on and algorithms for solving the bottleneck assignment problem, see §6.2 ...
We consider two versions of bottleneck (or min-max) generalized assignment problem (BGAP) under capacity uncertainty: Task-BGAP and Agent-BGAP. A robust optimization approach is employed to study this issue. The decision maker's degree of risk aversion and the penalty weighting parameter are incorporated into the objective function. A state-of-the-art linearization method is introduced ...
For the 1-2 Dim bottleneck problems, some researcher had got results. Based on these work, we discussed a general bottleneck assignment problem in this paper. For this problem, we present a dynamic algorithm with threshold.
A simple algorithm for solving either of two different bottleneck assignment problems, which requires finding an assignment of men to machines in a serial production line to maximize the rate of flow through the line. Expand. 75. Save. Knapsack Problems: Algorithms and Computer Implementations. S. Martello P. Toth.
In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is shown that any critical solution yields a global optimum.
A variety of well-known facility location and location-allocation models are shown to be equivalent to, and therefore solvable as, generalized assignment problems GAP's and it is shown how certain types of constraints limiting the site and capacity combinations allowed can be incorporated into these models through their treatment as GAPs.
We discuss bottleneck (or minimax) versions of the generalized assignment problem. The basic problem involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. Two versions of the bottleneck generalized assignment problem (BGAP ...
1. T he bottleneck assignment problem is an interesting problem in combinatorial optimization. It has many variants and is as well a variant of the assignment problem. In general, the problem is defined based on a set of agents that must be assigned to a set of tasks while ensuring that each task is done by one agent.
A simple algorithm for solving either of two different bottleneck assignment problems, which requires finding an assignment of men to machines in a serial production line to maximize the rate of flow through the line. Abstract : A simple algorithm for solving either of two different bottleneck assignment problems is described in this paper. The one problem requires finding an assignment of men ...
N2 - In this paper, a new approach for solving the bottleneck assignment problem is presented. The problem is treated as a special class of permutation problems which we call max-min permutation problems. By defining a suitable neighborhood system in the space of permutations and designating certain permutations as critical solutions, it is ...
The bottleneck generalized assignment problem. The min-max version of the generalized assignment problem is considered. We introduce relaxations and show that they produce, as sub-problems, min-max versions of the multiple-choice knapsack problem and of the 0-1 knapsack problem. It is proved that such problems can be solved exactly in ...
But the major problem is that only VTB has a fully functioning Chinese branch, which opened in 2008. Dominant Russian lender Sberbank (SBER.MM) , opens new tab had planned to open a branch by end ...
Mobile robots play an important role in smart factories, though efficient task assignment and path planning for these robots still present challenges. In this paper, we propose an integrated task- and path-planning approach with precedence constrains in smart factories to solve the problem of reassigning tasks or replanning paths when they are handled separately. Compared to our previous work ...
A new simple but faster algorithm for solving linear bottleneck assignment problems, so that in such emergent situation efficient and faster decision taking could be make possible. Linear bottleneck assignment problems have wide range of applications in emergency situation like call for fire fighters, ambulances etc. This paper presents a new simple but faster algorithm for solving linear ...
Then the multiple bottleneck assignment problem (MBAP) is defined as MBAP: f ∗ = def min f (π): π∈Π = def f (π ∗ ). This model has been studied in the literature by several authors 1, 2, 3. Unlike the sum and bottleneck assignment problems, MBAP is strongly NP-hard [4]. It is therefore essential to obtain sharp bounds to solve the ...
This very real problem inspired Brewster to create Veba Baby, a baby bottle monitor that tracks temperature and expiration in real time. Established in partnership with her husband, Sean, Veba Baby leverages technology and health data to give parents peace of mind regarding their baby's milk intake.
The results improve on the previous best-known expression for the expected value of a random bottleneck assignment problem, yield the first results on moments other than the expectedvalue, and produce the firstresults on the moments for the time to first complete matching in a random bipartite graph process. One of the most important variants of the standard linear assignment problem is the ...