A min-max theorem for the minimum fleet-size problem
نویسندگان
چکیده
A retrospective fleet-sizing problem can be solved via bipartite matching, where a maximum cardinality matching corresponds to the minimum number of vehicles needed cover all trips. We prove min-max theorem on this fleet-size problem: pairwise incompatible trips is equal fleet size needed.
منابع مشابه
The Duality Theorem for Min-max Functions
The set of min-max functions F : R → R is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an inf...
متن کاملThe Duality Theorem for Min - Max Functionsst
The set of min-max functions F : R n ! R n is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an...
متن کاملA Min Flow Max Cut Theorem
Consider a network of pipes joining a set of intakes (the source) to a separate set of outlets (the e n sink), so that liquid flows from the intakes, through the network, to the outlets. A cross-section of th etwork, separating the intakes on one side from the outlets on the other, is called a cut. A minimal t c cut is one that, roughly speaking, slices through a set of pipes whose combined cap...
متن کاملOn a Min-max Theorem of Cacti
A simple proof is presented for the min-max theorem of Lovv asz on cacti. Instead of using the result of Lovv asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem.
متن کاملApplications of the Gaussian Min-Max theorem
We show how the Gaussian min-max theorem provides direct proofs of several famous results in asymptotic geometric analysis, such as, the Dvoretzky theorem, the Johnson-Lindenstrauss Lemma, Gluskin’s theorem on embedding in `1 , and others.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operations Research Letters
سال: 2023
ISSN: ['0167-6377', '1872-7468']
DOI: https://doi.org/10.1016/j.orl.2023.03.013