- English (13) (remove)
- A survey of the higher Stasheff-Tamari orders (2012)
- The Tamari lattice, thought as a poset on the set of triangulations of a convex polygon with n vertices, generalizes to the higher Stasheff-Tamari orders on the set of triangulations of a cyclic d-dimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them.
- 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.
- Computational Bounds for Elevator Control Policies by Large Scale Linear Programming (2013)
- We computationally assess policies for the elevator control problem by a new column-generation approach for the linear programming method for discounted infinite-horizon Markov decision problems. By analyzing the optimality of given actions in given states, we were able to provably improve the well-known nearest-neighbor policy. Moreover, with the method we could identify an optimal parking policy. This approach can be used to detect and resolve weaknesses in particular policies for Markov decision problems.
- Demand forecasting for companies with many branches, low sales numbers per product, and non-recurring orderings (2006)
- 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.
- Exploiting combinatorial relaxations to solve a routing & scheduling problem in car body manufacturing (2010)
- Motivated by the laser sharing problem (LSP) in car body manufacturing, we define the new general routing and scheduling problem (RSP). In the RSP, multiple servers have to visit and process jobs; renewable resources are shared among them. The goal is to find a makespan-minimal scheduled dispatch. We present complexity results as well as a branch-and-bound algorithm for the RSP. This is the first algorithm that is able to solve the LSP for industrially relevant problem scales.
- 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.
- 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.
- 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.
- On the benefits of using NP-hard problems in Branch & Bound (2008)
- We present a Brand-and-Bound (B&B) method using combinatorial bounds for solving makespan minimization problems with sequence dependent setup costs. As an application we present a laser source sharing problem arising in car manufacturing.
- 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.