<?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>Fri, 22 Mar 2013 10:23:35 +0100</pubDate>
    <lastBuildDate>Fri, 22 Mar 2013 10:23:35 +0100</lastBuildDate>
    <item>
      <title>Integrated size and price optimization for a fashion retailer</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/1124</link>
      <description>This thesis is the result of a collaboration with a German fashion retailer which lasted&#13;
for several years. The aim was the development of a decision-support system for the&#13;
supply of the about 1300 branches in Germany.&#13;
&#13;
There are some specialties about the situation at our industrial partner: The branches&#13;
are supplied by prepackaged size-assortments of a product which we call lot-types.&#13;
With the objective to economize handling cost, these lot-types are already composed&#13;
at the respective low-wage country where the article is also produced. The expense at&#13;
the German central warehouse is further reduced by allowing only four or five different lot-types for the delivery of one product. Moreover, each branch is supplied by a&#13;
certain quantity of a single lot-type.&#13;
&#13;
For the most fashion articles replenishment is not possible. The sales success of&#13;
a product is a priori unknown. Historical sales data can only be used on a higher&#13;
aggregation level, e.g., the average historical demand on the commodity group level.&#13;
Demand estimation is therefore very vague. Under- and oversupplies are unavoidable.&#13;
Influence over the sales process is possible by marking down prices. To compensate&#13;
for an oversupply of a product, weekly the price can be reduced to predefined price&#13;
steps which depend on the starting price of the product. Mark-downs for an article are&#13;
performed simultaneously for all branches and sizes.&#13;
&#13;
Within the cooperation mathematical problem formulations with the aim to minimize measures for the deviation of supply from estimated demand had been developed.&#13;
In these measures the selling process is not or only very vaguely regarded.&#13;
&#13;
Now we include the possibility of marking down prices during the selling time&#13;
already when deciding on the supply. The result is the two-stage stochastic program&#13;
ISPO: The so-called first stage decision is the determination of a supply policy. The&#13;
second stage decision, or recourse, is the decision on mark-downs during the selling&#13;
time. ISPO yields an expected revenue maximizing supply strategy and corresponding&#13;
optimal mark-down strategies for the considered scenarios.&#13;
&#13;
ISPO it too complex to solve it via standard approaches. Customized methods had&#13;
to be devised to solve ISPO. On the one side we present an exact solver for benchmarking. On the other side a fast heuristic was developed for practical use at our partner.&#13;
The basic idea of our exact solver is to enumerate all possible mark-down strategies.&#13;
With this it is possible to reduce ISPO to a former formulation for the optimization of&#13;
supply, which can be solved via standard approaches.&#13;
&#13;
In practice enumeration of all valid mark-down strategies for the purpose of solving&#13;
ISPO is for reasons of time impossible. Therefore the idea is extended to a customized&#13;
Branch&amp;Bound approach. In this context we derived dual bounds for general two-stage stochastic programs which are based on the so-called wait-and-see solution from&#13;
stochastic programming. We show that in general our bounds are tighter.&#13;
&#13;
The heuristic, beginning with a valid second stage decision, determines an optimal&#13;
first stage decision and alternates between solving the first stage and the second stage&#13;
until convergence is reached. The optimality gap is small enough to justify a practical&#13;
use at the industrial partner.&#13;
&#13;
In practice the by ISPO proposed mark-down strategies are not applied; instead&#13;
latest sales figures are exploited. According to these and an updated demand estimation&#13;
weekly a new optimal mark-down strategy for the remaining selling time of the product&#13;
is determined. For this purpose we propose an algorithm which relies on dynamic&#13;
programming and tries to exclude non-optimal solutions a priori by dominance checks.&#13;
&#13;
ISPO, more precisely our heuristic approach, together with the weekly adaption of&#13;
the mark-down strategy forms our decision support system for integrated size and price&#13;
optimization DISPO.&#13;
&#13;
We tested DISPO in a five-month field study, performed as a statistical experiment,&#13;
at our partner where pairs of similar branches were compared. At one branch of each&#13;
pair, the test branch, supply and mark-down decisions came from ISPO. With respect&#13;
to latest sales figures the mark-down decisions were weekly updated via our dynamic&#13;
programming approach. At the other branch, the control branch, these decisions were&#13;
not integrated: Supply was determined according to a strategy resulting from a former&#13;
model that disregarded the selling process and mark-downs were handled manually by&#13;
our partner. For the branches at which the decisions of ISPO were implemented an&#13;
average raise of 1.5 percentage points of relative revenue was observed.</description>
      <author>Miriam Kießling</author>
      <category>doctoralthesis</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/1124</guid>
      <pubDate>Fri, 22 Mar 2013 10:23:35 +0100</pubDate>
    </item>
    <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>
  </channel>
</rss>
