Showing papers by "Rolf H. Möhring published in 2011"

Characterizing the Existence of Potential Functions in Weighted Congestion Games

Abstract: Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let $\mathcal{C}$ be an arbitrary set of locally bounded functions and let $\mathcal{G}(\mathcal{C})$ be the set of weighted congestion games with cost functions in $\mathcal{C}$. We show that every weighted congestion game $G\in\mathcal{G}(\mathcal{C})$ admits an exact potential if and only if $\mathcal{C}$ contains only affine functions. We also give a similar characterization for w-potentials with the difference that here $\mathcal{C}$ consists either of affine functions or of certain exponential functions. We finally extend our characterizations to weighted congestion games with facility-dependent demands and elastic demands, respectively.

Decision Support and Optimization in Shutdown and Turnaround Scheduling

Abstract: Large-scale maintenance in industrial plants requires the entire shutdown of production units for disassembly, comprehensive inspection, and renewal. We derive models and algorithms for this so-called turnaround scheduling that include different features such as time-cost trade-off, precedence constraints, external resource units, resource leveling, different working shifts, and risk analysis. We propose a framework for decision support that consists of two phases. The first phase supports the manager in finding a good makespan for the turnaround. It computes an approximate project time-cost trade-off curve together with a stochastic evaluation. Our risk measures are the expected tardiness at time t and the probability of completing the turnaround within time t. In the second phase, we solve the actual scheduling optimization problem for the makespan chosen in the first phase heuristically and compute a detailed schedule that respects all side constraints. Again, we complement this by computing upper bounds for the same two risk measures. Our experimental results show that our methods solve large real-world instances from chemical manufacturing plants quickly and yield an excellent resource utilization. A comparison with solutions of a mixed-integer program on smaller instances proves the high quality of the schedules that our algorithms produce within a few minutes.

Integrated Sequencing and Scheduling in Coil Coating

Abstract: We consider a complex planning problem in integrated steel production. A sequence of coils of sheet metal needs to be color coated in consecutive stages. Different coil geometries and changes of colors necessitate time-consuming setup work. In most coating stages one can choose between two parallel color tanks. This can either reduce the number of setups needed or enable setups concurrent with production. A production plan comprises the sequencing of coils and the scheduling of color tanks and setup work. The aim is to minimize the makespan for a given set of coils. We present an optimization model for this integrated sequencing and scheduling problem. A core component is a graph theoretical model for concurrent setup scheduling. It is instrumental for building a fast heuristic that is embedded into a genetic algorithm to solve the sequencing problem. The quality of our solutions is evaluated via an integer program based on a combinatorial relaxation, showing that our solutions are within 10% of the optimum. Our algorithm is implemented at Salzgitter Flachstahl GmbH, a major German steel producer. This has led to an average reduction in makespan by over 13% and has greatly exceeded expectations. This paper was accepted by Dimitris Bertsimas, optimization.

Sequencing and scheduling for filling lines in dairy production

Abstract: We consider an integrated sequencing and scheduling problem arising at filling lines in dairy industry. Even when a processing sequence is decided, still a scheduling problem has to be solved for the sequence. This incorporates typical side constraints as they occur also in other sequencing problems in practice. Previously, we proposed a framework for general sequencing and scheduling problems: A genetic algorithm is utilized for the sequencing, incorporating a problem specific algorithm for the fixed-sequence scheduling. In this paper, we investigate how this approach performs for filling lines. Based on insights into structural properties of the problem, we propose different scheduling algorithms. In cooperation with Sachsenmilch GmbH, the algorithm was implemented for their bottleneck filling line, and evaluated in an extensive computational study. For the real data from production, our algorithm computes almost optimal solutions. However, as a surprising result, our simple greedy algorithms outperform the more elaborate ones in many aspects, showing interesting directions for future research.