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Sequencing and Scheduling in Coil Coating with Shuttles

Wiebke Höhn(hoehn***at***math.tu-berlin.de)
Felix G. König(fkoenig***at***math.tu-berlin.de)
Marco E. Lübbecke(luebbecke***at***mathematik.tu-darmstadt.de)
Rolf H. Möhring(rolf.moehring***at***tu-berlin.de)

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. Di erent coil geometries and changes of coatings may necessitate time-consuming setup work. In most coating stages one can choose between two parallel color tanks in order to reduce setup times. As a complicating consequence, setup times for a coil may depend on the whole sequence of predecessors. 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 scheduling. It is instrumental for building a fast heuristic which 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.

Keywords: sequencing, scheduling, integrated steel production, coil coating, 2-union-graphs, independent set, branch-and-price

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Combinatorial Optimization (Graphs and Matroids )

Citation: TU Berlin, Institut für Mathematik, Preprint 2009/1

Download: [PDF]

Entry Submitted: 03/18/2010
Entry Accepted: 03/19/2010
Entry Last Modified: 03/18/2010

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