Cornelius Schwarz

On the benefits of using NP-hard problems in Branch & Bound

We present a Branch-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

Solving a vehicle routing problem with resource conflicts and makespan objective with an application in car body manufacturing

We investigate the problem of dispatching arc welding robots in car body manufacturing. Such arc welding robots receive their energy from expensive laser sources. Laser sources can be shared among the robots. However, this requires that the robots be scheduled because each laser source can only be used by one robot at a time. We want to compute the minimal number of laser sources necessary to perform all welding tasks in a given processing time. To this end, we introduce the laser-sharing problem (LSP): for a given number of laser sources, find collision-free scheduled tours for all robots through all welding jobs so that the makespan is minimized. We propose a branch-and-bound algorithm for the LSP using bounds that stem from optimal solutions to carefully selected NP-hard combinatorial subproblems. This is the first algorithm for the LSP that is able to solve industrially relevant problem scales.

A New Branch and Bound Algorithm for the Clique Partitioning Problem

This paper considers the problem of clustering the vertices of a complete, edge weighted graph. The objective is to maximize the edge weights within the clusters (also called cliques). This so called Clique Partitioning Problem (CPP) is NP-complete, but it has several real life applications such as groupings in exible manufacturing systems, in biology, in flight gate assignment, etc.. Numerous heuristic and exact approaches as well as benchmark tests have been presented in the literature. Most exact methods use branch and bound with branching over edges. We present tighter upper bounds for each search tree node than those known from literature, improve constraint propagation techniques for fixing edges in each node, and present a new branching scheme