Facility location and related problems

PRINTAUSGABE IN HAUPTBIBLIOTHEK NICHT EINGELANGT! -- Bei Standortoptimierungsproblemen geht es um eine strategisch günstige Auswahl von Orten unter den Gesichtspunkten des Nutzens und der Aufwände, die mit den Standort-entscheidungen einhergehen. Beispielsweise können in der Planung die lageabhängigen Betriebskosten und die Errichtungskosten gegeneinander aufgewogen werden. Der zentrale Beitrag der vorliegenden Arbeit sind zwei Erweiterungen von Standortproblemen die durch einen Überblick klassischer Modelle eingefasst werden. Die eine Erweiterung behandelt ein dynamisches Warehouse-Location Problem in einem stochastischen Umfeld: Während mehrerer Perioden können Standorte geöffnet und geschlossen werden. Ziel ist die Minimierung der erwarteten Kosten die sich aus Betriebskosten, Produktionskosten, Transportkosten, Lagerhaltungskosten und Strafkosten bei Fehlmengen zusammensetzen. Ein exaktes und ein heuristisches Lösungsverfahren werden vorgestellt. Die zweite Erweiterung kann man als doppeltes Set-Cover Problem verstehen. Es sollen Kunden mit zwei Dienstleistungen bedient werden, die an Zentren gebunden sind. Jeder Kunde muss von mindestens einem Zentrum eines jeden Dienstleistungstyps erreichbar sein. Gleichzeitig ist darauf zu achten, dass die Anzahl verwendeter Zentren beschränkt ist und dass die Zentren höchstens einer Dienstleistung zugeordnet sind. Es werden verschiedene Anwendungen vorgestellt, und durch Einschränkungen wird versucht die Grenze zwischen Problemen mit polynomiellem Aufwand und NP-schweren Problemen zu ziehen. Im Rahmen einer bioinformatischen Anwendung wird eine Ant-Colony Metaheuristik eingesetzt.Facility location treats the problem of choosing locations while respecting effort and utility. E.g.: we can think of balancing the maintenance and setup costs for a facility. The central contribution of this work are two extensions of classical location models that get enclosed into the presentation of standard facility location models. One of the extensions is a dynamic warehouse location problem in a stochastic environment. Within a planning horizon of given number of periods we are able to open and close facilities and the aim is to minimize the expected costs. The costs consist of operating costs, production costs, inventory costs and penalty costs for shortages. We present an exact method and a heuristic approach. The second extension can be regarded as a double Set Cover Problem. We have to maintain two services by allocating corresponding sites and each customer has to be reachable by at least one of the centers and each service type. Simultaneously we have to respect that the number of used locations is limited, while no location is assigned to two services. We present different applications and by restricting the problem we draw the line between polynomially solvable problems and intractable ones. In the context of an application in bio-informatics we develop an ACO heuristic

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Knowledge of knots: shapes in action

Logic is to natural language what knot theory is to natural knots. Logic is concerned with some cognitive performances; in particular, some natural language inferences are captured by various types of calculi (propositional, predicate, modal, deontic, quantum, probabilistic, etc.), which in turn may generate inferences that are arguably beyond natural logic abilities, or non-well synchronized therewith (eg. ex falso quodlibet, material implication). Mathematical knot theory accounts for some abilities - such as recognizing sameness or differences of some knots, and in turn generates a formalism for distinctions that common sense is blind to. Logic has proven useful in linguistics and in accounting for some aspects of reasoning, but which knotting performaces are there, over and beyond some intuitive discriminating abilities, that may require extensions or restrictions of the normative calculus of knots? Are they amenable to mathematical treatment? And what role is played in the game by mental representations? I shall draw from a corpus of techniques and practices to show to what extent compositionality, lexical and normative elements are present in natural knots, with the prospect of formally exploring an area of human competence that interfaces thought, perception and action in a complex fabric