1,161 research outputs found
Set-Monotonicity Implies Kelly-Strategyproofness
This paper studies the strategic manipulation of set-valued social choice
functions according to Kelly's preference extension, which prescribes that one
set of alternatives is preferred to another if and only if all elements of the
former are preferred to all elements of the latter. It is shown that
set-monotonicity---a new variant of Maskin-monotonicity---implies
Kelly-strategyproofness in comprehensive subdomains of the linear domain.
Interestingly, there are a handful of appealing Condorcet extensions---such as
the top cycle, the minimal covering set, and the bipartisan set---that satisfy
set-monotonicity even in the unrestricted linear domain, thereby answering
questions raised independently by Barber\`a (1977) and Kelly (1977).Comment: 14 page
On Iterated Dominance, Matrix Elimination, and Matched Paths
We study computational problems arising from the iterated removal of weakly
dominated actions in anonymous games. Our main result shows that it is
NP-complete to decide whether an anonymous game with three actions can be
solved via iterated weak dominance. The two-action case can be reformulated as
a natural elimination problem on a matrix, the complexity of which turns out to
be surprisingly difficult to characterize and ultimately remains open. We
however establish connections to a matching problem along paths in a directed
graph, which is computationally hard in general but can also be used to
identify tractable cases of matrix elimination. We finally identify different
classes of anonymous games where iterated dominance is in P and NP-complete,
respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical
Aspects of Computer Science (STACS
A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins
The main result of this paper is a bijective proof showing that the
generating function for partitions with bounded differences between largest and
smallest part is a rational function. This result is similar to the closely
related case of partitions with fixed differences between largest and smallest
parts which has recently been studied through analytic methods by Andrews,
Beck, and Robbins. Our approach is geometric: We model partitions with bounded
differences as lattice points in an infinite union of polyhedral cones.
Surprisingly, this infinite union tiles a single simplicial cone. This
construction then leads to a bijection that can be interpreted on a purely
combinatorial level.Comment: 12 pages, 5 figure
The Impossibility of Extending Random Dictatorship to Weak Preferences
Random dictatorship has been characterized as the only social decision scheme
that satisfies efficiency and strategyproofness when individual preferences are
strict. We show that no extension of random dictatorship to weak preferences
satisfies these properties, even when significantly weakening the required
degree of strategyproofness
Welfare Maximization Entices Participation
We consider randomized mechanisms with optional participation. Preferences
over lotteries are modeled using skew-symmetric bilinear (SSB) utility
functions, a generalization of classic von Neumann-Morgenstern utility
functions. We show that every welfare-maximizing mechanism entices
participation and that the converse holds under additional assumptions. Two
important corollaries of our results are characterizations of an attractive
randomized voting rule that satisfies Condorcet-consistency and entices
participation. This stands in contrast to a well-known result by Moulin (1988),
who proves that no deterministic voting rule can satisfy both properties
simultaneously
Consistent Probabilistic Social Choice
Two fundamental axioms in social choice theory are consistency with respect
to a variable electorate and consistency with respect to components of similar
alternatives. In the context of traditional non-probabilistic social choice,
these axioms are incompatible with each other. We show that in the context of
probabilistic social choice, these axioms uniquely characterize a function
proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's
function returns so-called maximal lotteries, i.e., lotteries that correspond
to optimal mixed strategies of the underlying plurality game. Maximal lotteries
are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always
unique, and can be efficiently computed using linear programming
The Air Cargo Load Planning Problem
A major operational planning problem in the air cargo industry is how to arrange cargo
in an aircraft to fly safely and profitably. Therefore, a challenging planning puzzle has to
be solved for each flight. Besides its complexity, the planning is mostly done manually
today, which is a time consuming process with uncertain solution quality. The literature
on loading problems in an air cargo context is scarce and the term is used ambiguously for
different subproblems like selecting containers, packing items into containers, or loading
containers into aircraft. All of the presented models only focus on certain aspects of what
is in practice a larger planning problem. Additionally, some practical aspects have not
been covered in the literature.
In this work, we provide a comprehensive overview of the air cargo load planning problem
as seen in the operational practice of our industrial partner. We formalize its requirements
and the objectives of the respective stakeholders. Furthermore, we develop and
evaluate suitable solution approaches. Therefore, we decompose the problem into four
steps: aircraft configuration, build-up scheduling, air cargo palletization, and weight and
balance. We solve these steps by employing mainly mixed-integer linear programming.
Two subproblems are further decomposed by adding a rolling horizon planning approach
and a Logic-based Benders Decomposition (LBBD). The actual three-dimensional packing
problem is solved as a constraint program in the subproblem of the LBBD.
We evaluated our approaches on instances containing 513 real and synthetic flights. The
numerical results show that the developed approaches are suitable to automatically generate
load plans for cargo flights. Compared to load plans from practice, we could achieve
a 20 percent higher packing density and significantly reduce the handling effort in the air
cargo terminal. The achieved costs of additional fuel burn due to aircraft imbalances and
reloading operations at stop-over airports are almost negligible. The required runtimes
range between 13 and 38 minutes per flight on standard hardware, which is acceptable
for non-interactive planning.
Cargo airlines can significantly profit from employing the developed approaches in their
operational practice. More and especially the profitable last-minute cargo can be transported.
Furthermore, the costs of load planning, handling effort, and aircraft operations
can be significantly reduced
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