Refine
Document Type
- Preprint (11) (remove)
Keywords
Institute
- Mathematik (11)
- Wirtschaftswissenschaften (1)
-
Zwei auf einen Streich: Optimierte dynamische Einsatzplanung für Gelbe Engel und Lastenaufzüge
(2007)
- Wir modellieren zwei verschiedene dynamische Einsatzplanungsprobleme: die dynamische Einsatzplanung Gelber Engel beim ADAC und die Steuerung von Lastenaufzügen in einem Versandlager der Herlitz PBS AG. Wir benutzen eine Reoptimierungspolitik, die die Steuerung des Systems mit Hilfe der Lösung von statischen Schnappschussproblemen durchführt. Für die auftretenden Schnappschussprobleme vergleichen wir zwei Modellierungsansätze (Flussmodell versus Tourenmodell), von denen nur einer echtzeittauglich ist. Das Verfahren zur dynamischen Einsatzplanung Gelber Engel ist beim ADAC in Betrieb.
-
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
(2008)
- 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.
-
The Stochastic Guaranteed Service Model with Recourse for Multi-Echelon Warehouse Management
(2012)
- The Guaranteed Service Model (GSM) computes optimal order-points in multi-echelon inventory control under the assumptions that delivery times can be guaranteed and the demand is bounded. Our new Stochastic Guaranteed Service Model (SGSM) with Recourse covers also scenarios that violate these assumptions. Simulation experiments on real-world data of a large German car manufacturer show that policies based on the SGSM dominate GSM-policies.
-
The Integrated Size and Price Optimization problem
(2012)
- 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.
-
Stability with uniform bounds for online dial-a-ride problems under reasonable load
(2011)
- In continuously running logistic systems (like in-house pallet transportation systems), finite buffer capacities usually require controls achieving uniformly bounded waiting queues (strong stability). Standard stochastic traffic assumptions (arrival rates below service rates) can, in general, not guarantee these strong stability requirements, no matter which control. Therefore, the worst-case traffic notion of reasonable load was introduced, originally for the analysis of the Online-Dial-a-Ride Problem. A set of requests is reasonable if the requests that are presented in a sufficiently large time period can be served in a time period of at most the same length. The rationale behind this concept is that the occurrence of non-reasonable request sets renders the system overloaded, and capacity should be extended. For reasonable load, there are control policies that can guarantee uniformly bounded flow times, leading to strong stability in many cases. Control policies based on naive eoptimization, however, can in general achieve neither bounded flow times nor strong ability. In this chapter, we review the concept and examples for reasonable load. Moreover, we present new control policies achieving strong stability as well as new elementary examples of request sets where naive reoptimization fails.
-
Lotsize optimization leading to a p-median problem with cardinalities
(2007)
- 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.
-
Local Approximation of Discounted Markov Decision Problems by Mathematical Programming Methods
(2011)
- We develop a method to approximate the value vector of discounted Markov decision problems (MDP) with guaranteed error bounds. It is based on the linear programming characterization of the optimal expected cost. The new idea is to use column generation to dynamically generate only such states that are most relevant for the bounds by incorporating the reduced cost information. The number of states that is sufficient in general and necessary in the worst case to prove such bounds is independent of the cardinality of the state space. Still, in many instances, the column generation algorithm can prove bounds using much fewer states. In this paper, we explain the foundations of the method. Moreover, the method is used to improve the well-known nearest-neighbor policy for the elevator control problem.
-
How to avoid collisions in scheduling industrial robots?
(2010)
- In modern production facilities industrial robots play an important role. When two ore more of them are moving in the same area, care must be taken to avoid collisions between them. Due to expensive equipment costs our approach to handle this is very conservative: Each critical area is modeled as a shared resource where only one robot is allowed to use it at a time. We studied collision avoidance in the context of arc welding robots in car manufacture industry. Here another shared resource comes into place. When using laser welding technology every robot needs to be connected to a laser source supplying it with the necessary energy. Each laser source can be connected to up to six robots but serve only one at a time. An instance of the problem consists of a set of robots, a set of welding task, a number of laser sources, a distance table, collision information and a production cycle time. The goal is to design robot tours covering all task and schedule them resource conflict free such that the makespan does not exceed the cycle time. We propose a general model for integrated routing and scheduling including collision avoidance as well as a branch-and-bound algorithm for it. Computational results on data generated with the robot simulation software KuKa Sim Pro are also provided showing that our algorithm outperforms standard mixed-integer models for our application.
-
Das Optimierungslabor – ein Erfahrungsbericht
(2012)
- Seit mehreren Jahren besuchen uns Schülerinnen und Schüler an der Universität zu Anlässen wie dem Tag der Mathematik, dem Girls’ Day, der MINT-Universität oder einfach auf Initiative ihrer Klassenleitungen. Sie möchten einen Einblick in die Welt der Mathematik über die Schulmathematik hinaus bekommen. Doch wie lässt sich die Brücke vom Schulstoff zu den Inhalten der Universitätsmathematik schlagen? Und: findet man einen Themenschwerpunkt, bei dem ein aktives Mitmachen trotz fehlender Vorkenntnisse in Anbetracht begrenzter Zeit möglich wird? In der diskreten Optimierung lassen sich Problem-Modellierung und Problem-Lösung sehr gut trennen. Selbst forschungsnahe Modelle der ganzzahligen linearen Optimierung (MILP-Modelle) basieren auf sehr elementaren Überlegungen, wie die Entscheidungsmöglichkeiten, Ziele und Restriktionen eines Alltagsproblems in Variablen, Bewertungsfunktionen, Gleichungen und Ungleichungen ausgedrückt werden können. Wie dann optimale Lösungen gefunden werden, erfordert zwar tiefergehende Mathematik, es gibt aber Software dafür, in der das Wissen aus Teilen des Mathematik-Studiums und der mathematischen Forschung kondensiert vorliegt. Unser Vermittlungsziel: Schülerinnen und Schüler wissen nach dem Besuch, dass man verschiedenste Probleme angreifen kann, indem man sie in die Sprache der Mathematik übersetzt, denn in Software gegossenes mathematisches Know-How kann dann diese Probleme lösen, ohne etwas über die Probleme selbst zu wissen. Unsere Idee für eine Maßnahme: Ein Optimierungslabor. Die Schülerinnen und Schüler isolieren in Teamarbeit die wesentlichen logischen Merkmale von Sudokulösen, Rucksackpacken, Routenplanung u.v.a.m. Dann übersetzen sie die Problemstellungen in die Sprache der Mathematik (hier: MILP-Modelle) und lassen sie (unterstützt durch unser Team) von Computerprogrammen lösen (MILP-Löser), die nichts anderes als diese Sprache verstehen. Schließlich übersetzen sie die mathematischen Lösungen wieder in die Sprache der Problemstellung. Erfahrungen mit der Modellierung auf Basis linearer Gleichungssysteme können dabei aus dem Schulunterricht eingebracht werden. In diesem Bericht wollen wir unsere Erfahrungen mit konkreten Details der Umsetzung schildern.
-
An exact column-generation approach for the lot-type design problem
(2012)
- 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.
