<?xml version="1.0" encoding="utf-8"?>
<rss version="2.0">
  <channel>
    <title>OPUS 4 Latest Documents RSS Feed</title>
    <description>Latest documents</description>
    <link>http://opus4.kobv.de/opus4-ubbayreuth/index/index/</link>
    <pubDate>Thu, 15 Nov 2012 13:23:46 +0100</pubDate>
    <lastBuildDate>Thu, 15 Nov 2012 13:23:46 +0100</lastBuildDate>
    <item>
      <title>The Integrated Size and Price Optimization problem</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886</link>
      <description> We present the Integrated Size and Price Optimization Problem (ISPO)&#13;
  for a fashion discounter with many branches.  Based on a two-stage&#13;
  stochastic programming model with recourse, we develop an exact&#13;
  algorithm and a production-compliant heuristic that produces small&#13;
  optimality gaps.  In a field study we show that a distribution of&#13;
  supply over branches and sizes based on ISPO solutions is&#13;
  significantly better than a one-stage optimization of the&#13;
  distribution ignoring the possibility of optimal pricing.&#13;
  </description>
      <author>Miriam  Kießling; Sascha Kurz; Jörg  Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886</guid>
      <pubDate>Thu, 15 Nov 2012 13:23:46 +0100</pubDate>
    </item>
    <item>
      <title>Das Optimierungslabor – ein Erfahrungsbericht</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/838</link>
      <description>Seit mehreren Jahren besuchen uns Schülerinnen und Schüler an der&#13;
Universität zu Anlässen wie dem Tag der Mathematik, dem Girls’ Day,&#13;
der MINT-Universität oder einfach auf Initiative ihrer&#13;
Klassenleitungen. Sie möchten einen Einblick in die Welt der&#13;
Mathematik über die Schulmathematik hinaus bekommen. Doch wie lässt&#13;
sich die Brücke vom Schulstoff zu den Inhalten der&#13;
Universitätsmathematik schlagen? Und: findet man einen&#13;
Themenschwerpunkt, bei dem ein aktives Mitmachen trotz fehlender&#13;
Vorkenntnisse in Anbetracht begrenzter Zeit möglich wird?&#13;
&#13;
In der diskreten Optimierung lassen sich Problem-Modellierung und&#13;
Problem-Lösung sehr gut trennen. Selbst forschungsnahe Modelle der&#13;
ganzzahligen linearen Optimierung (MILP-Modelle) basieren auf sehr&#13;
elementaren Überlegungen, wie die Entscheidungsmöglichkeiten, Ziele&#13;
und Restriktionen eines Alltagsproblems in Variablen,&#13;
Bewertungsfunktionen, Gleichungen und Ungleichungen ausgedrückt werden&#13;
können. Wie dann optimale Lösungen gefunden werden, erfordert zwar&#13;
tiefergehende Mathematik, es gibt aber Software dafür, in der das&#13;
Wissen aus Teilen des Mathematik-Studiums und der mathematischen&#13;
Forschung kondensiert vorliegt.&#13;
&#13;
Unser Vermittlungsziel: Schülerinnen und Schüler wissen nach dem&#13;
Besuch, dass man verschiedenste Probleme angreifen kann, indem man sie&#13;
in die Sprache der Mathematik übersetzt, denn in Software gegossenes&#13;
mathematisches Know-How kann dann diese Probleme lösen, ohne etwas&#13;
über die Probleme selbst zu wissen. Unsere Idee für eine Maßnahme:&#13;
Ein Optimierungslabor. Die Schülerinnen und Schüler isolieren in&#13;
Teamarbeit die wesentlichen logischen Merkmale von Sudokulösen,&#13;
Rucksackpacken, Routenplanung u.v.a.m. Dann übersetzen sie die&#13;
Problemstellungen in die Sprache der Mathematik (hier: MILP-Modelle)&#13;
und lassen sie (unterstützt durch unser Team) von Computerprogrammen&#13;
lösen (MILP-Löser), die nichts anderes als diese Sprache verstehen.&#13;
Schließlich übersetzen sie die mathematischen Lösungen wieder in die&#13;
Sprache der Problemstellung. Erfahrungen mit der Modellierung auf&#13;
Basis linearer Gleichungssysteme können dabei aus dem Schulunterricht&#13;
eingebracht werden.&#13;
&#13;
In diesem Bericht wollen wir unsere Erfahrungen mit konkreten Details&#13;
der Umsetzung schildern.</description>
      <author>Miriam Kießling; Tobias Kreisel; Sascha Kurz; Jörg Rambau; Konrad Schade; Cornelius Schwarz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/838</guid>
      <pubDate>Thu, 11 Oct 2012 10:27:37 +0200</pubDate>
    </item>
    <item>
      <title>An exact column-generation approach for the lot-type design problem</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877</link>
      <description>We consider a fashion discounter distributing its many branches with&#13;
integral multiples from a set of available lot-types. For the problem of&#13;
approximating the branch and size dependent demand using those lots&#13;
we propose a tailored exact column generation approach assisted by fast&#13;
algorithms for intrinsic subproblems, which turns out to be very efficient&#13;
on our real-world instances.&#13;
</description>
      <author>Sascha Kurz; Miriam Kießling; Jörg Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877</guid>
      <pubDate>Mon, 20 Aug 2012 10:11:31 +0200</pubDate>
    </item>
    <item>
      <title>Bounds for the minimum oriented diameter</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378</link>
      <description>We consider the problem of finding an orientation with minimum diameter of a connected bridgeless graph. Fomin et. al. discovered a relation between the minimum oriented diameter an the size of a minimal dominating set. We improve their upper bound.</description>
      <author>Sascha Kurz; Martin Lätsch</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378</guid>
      <pubDate>Tue, 15 Apr 2008 11:09:47 +0200</pubDate>
    </item>
    <item>
      <title>Integral point sets over Z_n^m</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377</link>
      <description>There are many papers studying properties of point sets in the Euclidean space or on integer grids, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the point sets which instead of being integers are elements of Z_n, and study the properties of the resulting combinatorial structures.</description>
      <author>Axel Kohnert; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377</guid>
      <pubDate>Tue, 15 Apr 2008 11:07:00 +0200</pubDate>
    </item>
    <item>
      <title>On the minimum diameter of plane integral point sets</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375</link>
      <description>Since ancient times mathematicians consider geometrical objects with integral side lengths. We consider plane integral point sets P, which are sets of n points in the plane with pairwise integral distances where not all the points are collinear. The largest occurring distance is called its diameter. Naturally the question about the minimum possible diameter d(2,n) of a plane integral point set consisting of n points arises. We give some new exact values and describe state-of-the-art algorithms to obtain them. It turns out that plane integral point sets with minimum diameter consist very likely of subsets with many collinear points. For this special kind of point sets we prove a lower bound for d(2,n) achieving the known upper bound n^{c_2loglog n} up to a constant in the exponent.</description>
      <author>Sascha Kurz; Alfred Wassermann</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375</guid>
      <pubDate>Tue, 15 Apr 2008 11:01:24 +0200</pubDate>
    </item>
    <item>
      <title>The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374</link>
      <description>We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branchs individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.</description>
      <author>Sascha Kurz; Jörg Rambau; Jörg Schlüchtermann; Rainer Wolf</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374</guid>
      <pubDate>Tue, 15 Apr 2008 10:59:29 +0200</pubDate>
    </item>
    <item>
      <title>Lotsize optimization leading to a p-median problem with cardinalities</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373</link>
      <description>We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programming formulation and a primal heuristic for this problem we also consider a more abstract version which we relate to several other classical optimization problems like the p-median problem, the facility location problem or the matching problem.</description>
      <author>Constantin Gaul; Sascha Kurz; Jörg Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373</guid>
      <pubDate>Tue, 15 Apr 2008 10:55:26 +0200</pubDate>
    </item>
    <item>
      <title>Inclusion-maximal integral point sets over finite fields</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372</link>
      <description>We consider integral point sets in affine planes over finite fields. Here an integral point set is a set of points in $GF(q)^2$ where the formally defined Euclidean distance of every pair of points is an element of $GF(q)$. From another point of view we consider point sets over $GF(q)^2$ with few and prescribed directions. So this is related to Redeis work. Another motivation comes from the field of ordinary integral point sets in Euclidean spaces. In this article we study the spectrum of integral point sets over $GF(q)^2$ which are maximal with respect to inclusion. We give some theoretical results, constructions, conjectures, and some numerical data.</description>
      <author>Michael Kiermaier; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372</guid>
      <pubDate>Tue, 15 Apr 2008 10:52:18 +0200</pubDate>
    </item>
    <item>
      <title>Integral point sets over finite fields</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371</link>
      <description>We consider point sets in the affine plane GF(q)^2 where each Euclidean distance of two points is an element of GF(q). These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces. We determine their maximal cardinality I(GF(q),2). For arbitrary commutative rings R instead of GF(q) or for further restrictions as no three points on a line or no four points on a circle we give partial results. Additionally we study the geometric structure of the examples with maximum cardinality.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371</guid>
      <pubDate>Tue, 15 Apr 2008 10:50:28 +0200</pubDate>
    </item>
    <item>
      <title>Enumeration of generalized polyominoes</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/370</link>
      <description>Wir verallgemeinern den Begriff von Polyominoes (Tetrisbausteine) und betrachten Seite-an-Seite benachbarte überschneidungsfreie Vereinigungen von regelmäßigen k-Ecken. Für n&lt;=4 geben wir Formeln für die Anzahl a_k(n) von verallgemeinerten Polyominoes, bestehend aus n regelmäßigen k-Ecken, an. Für weitere kleine Werte von k und n tabellieren wir durch computerunterstützte Enumeration gewonnene Anzahlen. Zum Abschluss erwähnen wir ein paar ungelöste Probleme für verallgemeinerte Polyominoes.</description>
      <author>Matthias Koch; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/370</guid>
      <pubDate>Tue, 15 Apr 2008 10:48:06 +0200</pubDate>
    </item>
    <item>
      <title>Maximal integral point sets over Z^2</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369</link>
      <description>Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a set P={p(1),...,p(n)} in Z^2 a maximal integral point set over Z^2 if all pairwise distances are integral and every additional point p(n+1) destroys this property. Here we consider such sets for a given cardinality and with minimum possible diameter. We determine some exact values via exhaustive search and give several constructions for arbitrary cardinalities. Since we cannot guarantee the maximality in these cases we describe an algorithm to prove or disprove the maximality of a given integral point set. We additionally consider restrictions as no three points on a line and no four points on a circle.</description>
      <author>Sascha Kurz; Andrey Radoslavov Antonov</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369</guid>
      <pubDate>Tue, 15 Apr 2008 10:45:28 +0200</pubDate>
    </item>
    <item>
      <title>Convex hulls of polyominoes</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245</link>
      <description>In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of $n$ unit hypercubes in $mathbb{R}^d$. For $d=2$ we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each $n$.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245</guid>
      <pubDate>Thu, 01 Mar 2007 12:38:38 +0100</pubDate>
    </item>
    <item>
      <title>A note on Erdös-Diophantine graphs and Diophantine carpets</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</link>
      <description>A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in $\mathbb{Z}^{2}$ (the coordinates)and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diophantine graphs are equivalent if they only differ by translation or rotation of vertices. Due to a famous theorem of Erdös and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdös-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdös-Diophantine graphs and characterize the chromatic number of Diophantine carpets.</description>
      <author>Axel Kohnert; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</guid>
      <pubDate>Wed, 07 Dec 2005 14:56:57 +0100</pubDate>
    </item>
    <item>
      <title>On the characteristic of integral point sets in $\mathbb{E}^m$</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175</link>
      <description>We generalise the definition of the characteristic of an integral triangle to integral simplices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral point sets. Using this algorithm we are able to provide new exact values for the minimum diameter of integral point sets.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175</guid>
      <pubDate>Mon, 05 Dec 2005 10:33:52 +0100</pubDate>
    </item>
    <item>
      <title>Counting polyominoes with minimum perimeter</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/142</link>
      <description>Es wird die Anzahl der wesentlich verschiedenen Polyominoes der Ordnung n mit minimalem Umfang p(n) bestimmt.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/142</guid>
      <pubDate>Mon, 27 Jun 2005 13:48:50 +0200</pubDate>
    </item>
    <item>
      <title>A bijection between the d-dimensional simplices with distances in {1,2} and the partitions of d+1</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/141</link>
      <description>We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.</description>
      <author>Christian Haase; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/141</guid>
      <pubDate>Mon, 27 Jun 2005 11:02:39 +0200</pubDate>
    </item>
  </channel>
</rss>
