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Minmax-Regret k-Sink Location on a Dynamic Tree Network with Uniform Capacities [article]

Mordecai J. Golin, Sai Sandeep
2018 arXiv   pre-print
Similarly, the Minmax-Regret k-center problem on trees is polynomial solvable in n and k.  ...  The Minmax-Regret k-Sink Location on a Dynamic Path Networks with uniform capacities is polynomial solvable in n and k.  ...  This is known as the minmax-regret problem. minmax-regret optimization has been extensively studied for the k-median [11, 8, 44] and k-center problems [4, 36, 9, 44] ([10] is a recent example) and  ... 
arXiv:1806.03814v1 fatcat:5l3kxbwhsreenllvu2463trbzu

Dynamic Pricing Through Sampling Based Optimization

Ruben Lobel, Georgia Perakis
2010 Social Science Research Network  
The main contribution of this paper is the exploration of closed-loop pricing policies for different robust objectives, such as MaxMin, MinMax Regret and MaxMin Ratio.  ...  We introduce a sampling based optimization approach that can solve this problem in a tractable way, with a confidence level and a robustness level based on the number of samples used.  ...  the participants of  ... 
doi:10.2139/ssrn.1748426 fatcat:vle6z6vfnrbtjowat6prfme7kq

Facility location problems with uncertainty on the plane

Igor Averbakh, Sergei Bereg
2005 Discrete Optimization  
We present an O(n 2 log 2 n) algorithm for the interval data minmax regret rectilinear 1-median problem and an O(n log n) algorithm for the interval data minmax regret rectilinear weighted 1-center problem  ...  We discuss possibilities of solving approximately the minmax regret Euclidean 1-median problem, and present an O(n 2 2 (n) log 2 n) algorithm for solving the minmax regret Euclidean weighted 1-center problem  ...  Minmax regret center location problems on networks have also been studied in the literature.  ... 
doi:10.1016/j.disopt.2004.12.001 fatcat:2mqgwwthpjgirif5d76kasuxgi

Hub location under uncertainty: a minimax regret model for the capacitated problem with multiple allocations

Iman Kazemian, Samin Aref
2017 International Journal of Supply Chain and Inventory Management  
In this paper the capacitated hub location problem is formulated by a minimax regret model, which takes into account uncertain setup cost and demand.  ...  We focus on hub location with multiple allocations as a strategic problem requiring one definite solution.  ...  Acknowledgment The authors thank Mark C. Wilson and Golbon Zakeri for their valuable comments.  ... 
doi:10.1504/ijscim.2017.086371 fatcat:zr6ty7iiirgl5bsvhcy4wt4vfy

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Alfredo Candia-Véjar, Eduardo Álvarez-Miranda, Nelson Maculan
2011 Reserche operationelle  
This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty  ...  In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the  ...  an exact O mn 2 log n algorithm for the 1-median problem on a general network with interval-uncertain node weights, where m is the number of edges and n the number of nodes.  ... 
doi:10.1051/ro/2011111 fatcat:bp3m2pn55rcy5fmn2pjojfpesq

An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks

Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, Michael Wagner
2018 International Symposium on Algorithms and Computation  
We want to minimize the aggregate evacuation time to an evacuation center (called a sink) on a path network with uniform edge capacities.  ...  Under this assumption, we compute a sink location that minimizes the maximum "regret." We present the first sub-cubic time algorithm in n to solve this problem, where n is the number of vertices.  ...  Divide the problem in two subproblems: minmax regret sink is (i) on an edge, and (ii) at a vertex. Compare the two solutions and pick the one with the smaller cost.  ... 
doi:10.4230/lipics.isaac.2018.14 dblp:conf/isaac/BhattacharyaHKK18 fatcat:p6y7fskgerdo3bxpils6zc53u4

Interval Travel Times for More Reliable Routing in City Logistics

Patrick-Oliver Groß, Michael Geisinger, Jan Fabian Ehmke, Dirk Christian Mattfeld
2016 Transportation Research Procedia  
ITT define an expected range of travel times, which can be derived with relatively low effort by CLSP.  ...  To ensure cost-efficient routing while satisfying promised delivery dates, information on expected travel times between customers needs to be exploited.  ...  One can easily recognize that applying the minmax regret criterion to a routing problem with interval data leads to high computational complexity, as every possible scenario of cost realizations has to  ... 
doi:10.1016/j.trpro.2016.02.062 fatcat:qha25aefgnartadpe72ho3obzi

Dynamic Pricing Through Data Sampling

Maxime C. Cohen, Ruben Lobel, Georgia Perakis
2013 Social Science Research Network  
Furthermore, we provide theoretical performance guarantees for this sampling-based solution, based on the number of samples used.  ...  In this paper we study a dynamic pricing problem, where a firm offers a product to be sold over a fixed time horizon.  ...  In this paper we will explore three different types of robust models: the MaxMin, the MinMax Regret (or alternatively MinMax Absolute Regret) and the MaxMin Ratio (or alternatively MaxMin Relative Regret  ... 
doi:10.2139/ssrn.2376667 fatcat:wz373sydjbg3ffn4w3icqrhljm

Combinatorial two-stage minmax regret problems under interval uncertainty

Marc Goerigk, Adam Kasperski, Paweł Zieliński
2020 Annals of Operations Research  
In order to choose a solution, the minmax regret criterion is used.  ...  Some general properties of the problem are established and results for two particular problems, namely the shortest path and the selection problem, are shown.  ...  Acknowledgements The second and third author were supported by the National Science Centre, Poland, Grant 2017/25/B/ST6/00486.  ... 
doi:10.1007/s10479-020-03863-7 fatcat:m7vunruignbdtpqmosaug6c3ay

Pseudo-centroid clustering

Fred Glover
2016 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
We formulate a K-PC algorithm analogous to a K-Means algorithm and focus on two key types of pseudo-centroids, MinMax-centroids and (weighted) MinSum-centroids, and describe how they, respectively, give  ...  We also introduce a regret-threshold PC algorithm that modifies the K-PC algorithm together with an associated diversification method and a new criterion for evaluating the quality of a collection of clusters  ...  The K-MinMedian problem is not to be confused with the K-median problem, which is based on a different concept relying on coordinate vectors.  ... 
doi:10.1007/s00500-016-2369-6 fatcat:wbgxarr6ljdj7hdsuazdaw6wxi

Minmax Regret 1-Sink for Aggregate Evacuation Time on Path Networks [article]

Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh
2018 arXiv   pre-print
The aim of this paper is to optimize the aggregate evacuation time in the simplest case, where the network is a path and only one evacuation center (called a sink) is to be introduced.  ...  Under this assumption, we compute the sink location that minimizes the maximum "regret."  ...  Note that O(n 2 ) regret functions have O(n 3 ) linear segments. Future research topics include solving the minmax regret problem for aggregate time sink for more general networks such as trees.  ... 
arXiv:1806.00814v1 fatcat:dscjujbi6zaj7ngipbcfhslxjy

A Polynomial Time Algorithm for Minimax-Regret Evacuation on a Dynamic Path [article]

Guru Prakash Arumugam, John Augustine, Mordecai J. Golin, Prashanth Srikanthan
2014 arXiv   pre-print
The previously best known algorithms for the minmax regret version problem ran in time exponential in k.  ...  The basic problem is to place k sinks on the line, with an associated evacuation strategy, so as to minimize the total time needed to evacuate everyone.  ...  [4] provides an O(n log 2 n) algorithm for the 1-sink minmax-regret problem on a uniform capacity tree.  ... 
arXiv:1404.5448v1 fatcat:7sdbmpgh75bufpalwjjl7ynw5i

A modeling framework for facility location of medical services for large-scale emergencies

Hongzhong Jia, Fernando Ordóñez, Maged Dessouky
2007 IIE Transactions  
Research on facility location is abundant.  ...  This general facility location model can be cast as a covering model, a P-median model or a P-center model, each suited for different needs in a large-scale emergency.  ...  Also the authors wish to thank Richard Larson, Harry Bowman, and Terry O'Sullivan for their valuable input and comments for the improvement of this paper.  ... 
doi:10.1080/07408170500539113 fatcat:c42gvi7bnfeyrndykvkpkmplle

A multi-objective heuristic approach for the casualty collection points location problem

T Drezner, Z Drezner, S Salhi
2006 Journal of the Operational Research Society  
Our pm we have /, idea of minimum regret, also known as minmax, is widely used in the literature but our implementation in_ this particular location problem is, to our knowledge, new.  ...  While this descent algorithm performed quite well on the p-median problem (see Table 2), it was not as effective for the other objectives.  ... 
doi:10.1057/palgrave.jors.2602047 fatcat:fxt6semsvjhjvkjb5nqcseklfm

Combinatorial Optimization Problems with Balanced Regret [article]

Marc Goerigk, Michael Hartisch
2021 arXiv   pre-print
We then consider a type of selection problem in more detail and show that, while the classic regret setting with budgeted uncertainty sets can be solved in polynomial time, the balanced regret problem  ...  In computational experiments using random and real-world data, we show that balanced regret solutions provide a useful trade-off for the performance in classic performance measures.  ...  Due to the computational challenge that min-max regret problems pose, algorithms have been developed for specific problems, such as knapsack [FIMY15] , spanning tree [KMZ12] , network optimization [  ... 
arXiv:2111.12470v1 fatcat:jjl4ep5c3vfb3ezgxxxpyvamuu
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