Johannes Hatzl

Review, extensions and computational comparison of MILP formulations for scheduling of batch processes

In this paper we investigate mixed-integer linear programs for minimizing the makespan of batch processes. Thereby it turns out that some additional valid constraints which were originally given for event driven model (EDM) also accelerate the running time for uniform discretization of time model (UDM) considerably. With help of an example for EDM we show that we can store some products in the batches if we prolong the processing times. For this reason EDM differs from the standard model. To achieve the same results as for UDM we introduce the ending times of the batches as additional variables. Moreover we extend the model by considering flexible proportions of output as well. However, computational tests indicate a rise of CPU time for the modified problem although the number of binary variables is smaller compared to UDM. Furthermore we point out that an upper bound on the total number of batchstarts is only possible for some production processes. Extensive computational tests on five benchmark problems proposed in the literature are reported. Thereby new optimal solutions could be found.

A complex time based construction heuristic for batch scheduling problems in the chemical industry

Abstract In this paper we investigate a heuristic for batch processing problems occurring in the chemical industry, where the objective is to minimize the makespan. Usually, this kind of problem is solved using mixed-integer linear programs. However, due to the large number of binary variables good results within a reasonable computational time could only be obtained for small instances. We propose an iterative construction algorithm which alternates between construction and deconstruction phases. Moreover, we suggest diversification and intensification strategies in order to obtain good suboptimal solutions within moderate running times. Computational results show the power of this algorithm.

Median problems on wheels and cactus graphs

SummaryThis paper is dedicated to location problems on graphs. We propose a linear time algorithm for the 1-median problem on wheel graphs. Moreover, some general results for the 1-median problem are summarized and parametric median problems are investigated. These results lead to a solution method for the 2-median problem on cactus graphs, i.e., on graphs where no two cycles have more than one vertex in common. The time complexity of this algorithm is

How hard is it to find extreme Nash equilibria in network congestion games

\mathcal O(n^2)

A parity domination problem in graphs with bounded treewidth and distance-hereditary graphs

, where n is the number of vertices of the graph.

The 1-Median Problem in Rd with the Chebyshev-Norm and its Inverse Problem

This paper concerns the reverse 2-median problem on trees and the reverse 1-median problem on graphs that contain exactly one cycle. It is shown that both models under investigation can be transformed to an equivalent reverse 2-median problem on a path. For this new problem an O(nlogn) algorithm is proposed, where n is the number of vertices of the path. It is also shown that there exists an integral solution if the input data are integral.

A combinatorial algorithm for the 1-median problem in Rd with the Chebyshev norm

We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach while finding a best equilibrium is NP-hard. For a fixed number of users we give a pseudo-polynomial algorithm to find the best equilibrium in series-parallel networks. For general network topologies also finding a worst equilibrium is NP-hard.

How Hard Is It to Find Extreme Nash Equilibria in Network Congestion Games

Abstract In this paper, we consider the 1-median problem in R d with the Chebyshev-norm. We give an optimality criterion for this problem which enables us to solve the following inverse location problem by a combinatorial algorithm in polynomial time: Given n points P 1 , … , P n ∈ R d with non-negative weights w i and a point P 0 the task is to find new non-negative weights w i such that P 0 is a 1-median with respect to the new weights and ‖ w − w ‖ 1 is minimized. In fact, this problem reduces to a 2-balanced flow problem for which an optimal solution can be obtained by solving a fractional b -matching problem.