OPUS 4 Latest Documents RSS FeedLatest documents
http://opus4.kobv.de/opus4-ubbayreuth/index/index/
Thu, 15 Nov 2012 13:23:46 +0100Thu, 15 Nov 2012 13:23:46 +0100The Integrated Size and Price Optimization problem
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886
We present the Integrated Size and Price Optimization Problem (ISPO)
for a fashion discounter with many branches. Based on a two-stage
stochastic programming model with recourse, we develop an exact
algorithm and a production-compliant heuristic that produces small
optimality gaps. In a field study we show that a distribution of
supply over branches and sizes based on ISPO solutions is
significantly better than a one-stage optimization of the
distribution ignoring the possibility of optimal pricing.
Miriam Kießling; Sascha Kurz; Jörg Rambaupreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886Thu, 15 Nov 2012 13:23:46 +0100An exact column-generation approach for the lot-type design problem
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877
We consider a fashion discounter distributing its many branches with
integral multiples from a set of available lot-types. For the problem of
approximating the branch and size dependent demand using those lots
we propose a tailored exact column generation approach assisted by fast
algorithms for intrinsic subproblems, which turns out to be very efficient
on our real-world instances.
Sascha Kurz; Miriam Kießling; Jörg Rambaupreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877Mon, 20 Aug 2012 10:11:31 +0200Bounds for the minimum oriented diameter
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378
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.Sascha Kurz; Martin Lätschpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378Tue, 15 Apr 2008 11:09:47 +0200Integral point sets over Z_n^m
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377
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.Axel Kohnert; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377Tue, 15 Apr 2008 11:07:00 +0200On the minimum diameter of plane integral point sets
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375
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.Sascha Kurz; Alfred Wassermannpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375Tue, 15 Apr 2008 11:01:24 +0200The 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
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374
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.Sascha Kurz; Jörg Rambau; Jörg Schlüchtermann; Rainer Wolfpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374Tue, 15 Apr 2008 10:59:29 +0200Lotsize optimization leading to a p-median problem with cardinalities
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373
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.Constantin Gaul; Sascha Kurz; Jörg Rambaupreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373Tue, 15 Apr 2008 10:55:26 +0200Inclusion-maximal integral point sets over finite fields
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372
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.Michael Kiermaier; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372Tue, 15 Apr 2008 10:52:18 +0200Integral point sets over finite fields
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371
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.Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371Tue, 15 Apr 2008 10:50:28 +0200Maximal integral point sets over Z^2
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369
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.Sascha Kurz; Andrey Radoslavov Antonovpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369Tue, 15 Apr 2008 10:45:28 +0200Demand forecasting for companies with many branches, low sales numbers per product, and non-recurring orderings
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/368
We propose the new Top-Dog-Index to quantify the historic deviation of the supply data of many small branches for a commodity group from sales data. On the one hand, the common parametric assumptions on the customer demand distribution in the literature could not at all be supported in our real-world data set. On the other hand, a reasonably-looking non-parametric approach to estimate the demand distribution for the different branches directly from the sales distribution could only provide us with statistically weak and unreliable estimates for the future demand.Sascha Kurz; Jörg Rambauarticlehttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/368Tue, 15 Apr 2008 10:41:39 +0200Enumeration of integral tetrahedra
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/367
We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d<=1000 via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most d in O(d^5) time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integral 4x4 matrices with diameter d fulfilling the triangle inequalities we derive an exact formula.Sascha Kurzworkingpaperhttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/367Tue, 15 Apr 2008 10:37:27 +0200Convex hulls of polyominoes
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245
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 $n$.Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245Thu, 01 Mar 2007 12:38:38 +0100A note on Erdös-Diophantine graphs and Diophantine carpets
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177
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.Axel Kohnert; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177Wed, 07 Dec 2005 14:56:57 +0100On the characteristic of integral point sets in $\mathbb{E}^m$
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175
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.Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175Mon, 05 Dec 2005 10:33:52 +0100A bijection between the d-dimensional simplices with distances in {1,2} and the partitions of d+1
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/141
We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.Christian Haase; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/141Mon, 27 Jun 2005 11:02:39 +0200