Bettina Klinz

Perspectives of Monge properties in optimization

Abstract An m × n matrix C is called Monge matrix if c ij + c rs ⩽ c is + c rj for all 1 ⩽ i r ⩽ m , 1 ⩽ j s ⩽ n . In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) fundamental combinatorial properties of Monge structures, (ii) applications of Monge properties to optimization problems and (iii) recognition of Monge properties.

The Quickest Flow Problem

AbstractConsider a network

Minimum Cost Dynamic Flows: The Series-Parallel Case

\mathcal{N}

Permuting matrices to avoid forbidden submatrices

=(G, c, τ) whereG=(N, A) is a directed graph andcij andτij, respectively, denote the capacity and the transmission time of arc (i, j) ∈A. The quickest flow problem is then to determine for a given valueυ the minimum numberT(υ) of time units that are necessary to transmit (send)υ units of flow in

A process scheduling problem arising from chemical production planning

\mathcal{N}

Four point conditions and exponential neighborhoods for symmetric TSP

from a given sources to a given sinks′.In this paper we show that the quickest flow problem is closely related to the maximum dynamic flow problem and to linear fractional programming problems. Based on these relationships we develop several polynomial algorithms and a strongly polynomial algorithm for the quickest flow problem.Finally we report computational results on the practical behaviour of our metholds. It turns out that some of them are practically very efficient and well-suited for solving large problem instances.