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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 20 (1998), S. 251-258 
    ISSN: 1436-6304
    Keywords: Mixed integer programming ; Steel production ; Gemischt-ganzzahlige lineare Programmierung ; Stahlproduktion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Stahlproduktion wird zur Kühlung des flüssigen Roheisens Metallschrott hinzugefügt. Dabei wird Schrott mit unterschiedlichem Gehalt an Eisen sowie an Spurenelementen eingesetzt. Abhängig von dieser Zusammensetzung variiert der Einkaufspreis für den Schrott. Für jeden produzierten Stahltyp sind gewisse Grenzwerte für Eisenanteil und den Gehalt an Spurenelementen im Stahl einzuhalten, um die geforderte Qualität zu erreichen. Der Schrott wird in Eisenbahnwaggons gelagert. Dadurch, daß Züge aus diesen Waggons gebildet werden müssen und diese Züge die Werkshalle auf dem vorgegebenen Gleisnetz erreichen bzw. verlassen müssen, entstehen zusätzlich zu den Materialrestriktionen auch noch Transportrestriktionen. Unser Ziel ist es, für jeden Produktionsprozeß die kostengünstigste Schrottzusammenstellung zu finden, so daß alle Material- und Transportrestriktionen eingehalten werden. Wir modellieren das Problem mit Hilfe eines gemischt-ganzzahligen linearen Programms (MIP) und lösen es mit dem kommerziellen MIP-Löser CPLEX. Unsere Rechenergebnisse für reale Produktionsserien zeigen bemerkenswerte Einsparungen gegenüber dem zur Zeit verwendeten Verfahren.
    Notes: Abstract In steel production, scrap metal is used for cooling the enormous quantity of heat produced by blowing oxygen on hot metal. Scrap differs in regard to the content of iron and of some tramp elements. The price of the scrap depends on these attributes. Each melting bath unit of steel has its own material constraints for the amount of iron and tramp elements in order to guarantee the desired quality. In addition, the transportation of scrap is restricted because it needs time and space: the scrap is kept in some railroad cars in the scrap hall; empty cars must leave the hall, filled cars must be taken from several railroad tracks in the scrap yard and assembled to a train before transportation to the hall. There are upper limits for the number of cars in the hall and in the train, also for the number of railroad tracks used for assembly. Our objective is to find a minimum cost scrap combination for each melting bath unit of steel that obeys the material and transportation constraints. We model the problem using a MIP (mixed integer linear programming) approach. Real-life situations are solved with the commercial MIP-solver CPLEX. We present computational results which show significant improvement compared to the strategy applied today.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 20 (1998), S. 251-258 
    ISSN: 1436-6304
    Keywords: Key words:Mixed integer programming – Steel production ; Schlüsselwörter: Gemischt-ganzzahlige lineare Programmierung – Stahlproduktion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In der Stahlproduktion wird zur Kühlung des flüssigen Roheisens Metallschrott hinzugefügt. Dabei wird Schrott mit unterschiedlichem Gehalt an Eisen sowie an Spurenelementen eingesetzt. Abhängig von dieser Zusammensetzung variiert der Einkaufspreis für den Schrott. Für jeden produzierten Stahltyp sind gewisse Grenzwerte für Eisenanteil und den Gehalt an Spurenelementen im Stahl einzuhalten, um die geforderte Qualität zu erreichen. Der Schrott wird in Eisenbahnwaggons gelagert. Dadurch, daß Züge aus diesen Waggons gebildet werden müssen und diese Züge die Werkshalle auf dem vorgegebenen Gleisnetz erreichen bzw. verlassen müssen, entstehen zusätzlich zu den Materialrestriktionen auch noch Transportrestriktionen. Unser Ziel ist es, für jeden Produktionsprozeß die kostengünstigste Schrottzusammenstellung 0zu finden, so daß alle Material- und Transportrestriktionen eingehalten werden. Wir modellieren das Problem mit Hilfe eines gemischt-ganzzahligen linearen Programms (MIP) und lösen es mit dem kommerziellen MIP-Löser CPLEX. Unsere Rechenergebnisse für reale Produktionsserien zeigen bemerkenswerte Einsparungen gegenüber dem zur Zeit verwendeten Verfahren.
    Notes: Abstract. In steel production, scrap metal is used for cooling the enormous quantity of heat produced by blowing oxygen on hot metal. Scrap differs in regard to the content of iron and of some tramp elements. The price of the scrap depends on these attributes. Each melting bath unit of steel has its own material constraints for the amount of iron and tramp elements in order to guarantee the desired quality. In addition, the transportation of scrap is restricted because it needs time and space: the scrap is kept in some railroad cars in the scrap hall; empty cars must leave the hall, filled cars must be taken from several railroad tracks in the scrap yard and assembled to a train before transportation to the hall. There are upper limits for the number of cars in the hall and in the train, also for the number of railroad tracks used for assembly. Our objective is to find a minimum cost scrap combination for each melting bath unit of steel that obeys the material and transportation constraints. We model the problem using a MIP (mixed integer linear programming) approach. Real-life situations are solved with the commercial MIP-solver CPLEX. We present computational results which show significant improvement compared to the strategy applied today.
    Type of Medium: Electronic Resource
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  • 3
    Title: Operations Research Proceedings 2014 /
    Contributer: Lübbecke, Marco , Gesellschaft für Operations-Research
    Publisher: Springer,
    Year of publication: 2016
    Pages: XIV, 659 S. : , Illustrationen, Diagramme
    ISBN: 978-3-319-28697-6 , 978-3-319-28695-2
    Type of Medium: Book
    Language: English
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  • 4
    Publication Date: 2022-03-14
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 5
    Publication Date: 2022-03-11
    Description: The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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  • 7
    Publication Date: 2022-03-14
    Description: We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data.
    Language: English
    Type: article , doc-type:article
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  • 8
    Publication Date: 2020-12-15
    Description: The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
    Publication Date: 2022-03-14
    Description: We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 10
    Publication Date: 2023-02-06
    Description: The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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