Lexicographic bottleneck problems
References (2)
Some partial orders related to Boolean optimization and the Greedy algorithm
Ann. of Discrete Math.
(1977)- et al.
Inequalities: Theory of Majorization and its Applications
(1979)
Cited by (69)
A lexicographic approach for solving bi-criteria bottleneck assignment problems
2024, Decision Analytics JournalSolving simultaneous target assignment and path planning efficiently with time-independent execution
2023, Artificial IntelligenceA solution technique for capacitated two-level hierarchical time minimization transportation problem
2023, Computers and Operations ResearchCitation Excerpt :For example, Hammer (1969) firstly addressed TMTP. Burkard and Franz (1991) and Arora and Puri (1997) investigated lexicographic TMTP. However, most researches on TP assume that transportation only happens in one phase, and such assumption is unreasonable in certain conditions (Kaur et al., 2016; Jain et al., 2020), e.g., transporting military equipments to battlefields during wars and delivering perishable goods to areas hurt by natural disasters (Geng et al., 2017), and so on.
Sensitivity analysis for bottleneck assignment problems
2022, European Journal of Operational ResearchCitation Excerpt :We discuss Problem 2 first as the theoretical tools are better motivated and easier to derive in the context of bottleneck edge sensitivity, and will be central in the analysis of bottleneck assignment sensitivity. The problem of assessing the sensitivity of a bottleneck edge is directly comparable to the sensitivity of the bottleneck assignment for the lexicographic assignment, see Burkard & Rendl (1991), and the solution of Problem 2 is a conservative estimate of the sensitivity from Problem 1. Exclusive Set
A greedy and distributable approach to the Lexicographic Bottleneck Assignment Problem with conditions on exactness
2022, AutomaticaCitation Excerpt :This motivates the derivation of an algorithm that solves the SeqBAP. Existing algorithms for solving the LexBAP, e.g., in Burkard et al. (2009) and Burkard and Rendl (1991), are not amenable to a distributed implementation. In this paper, we develop an approach to solve the SeqBAP that can be implemented with distributed computation and provides certificates when the resulting assignment is also a solution to the LexBAP.
Balanced flows for transshipment problems
2021, Discrete Applied Mathematics