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Ertek, G., Aksu, B., Birbil, S. E., İkikat, M. C., Yıldırmaz, C. (2005). “Application of local search methods for solving a quadratic assignment problem: A case study”, Proceedings of Computers and Industrial Engineering Conference, 2005. Istanbul, Turkey.
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APPLICATION OF LOCAL SEARCH METHODS FOR SOLVING A QUADRATIC ASSIGNMENT
PROBLEM: A CASE STUDY
Gürdal Ertek, Burak Aksu, Ş. İlker Birbil, Murat Cihan İkikat, Can Yıldırmaz
Sabancı UniversityOrhanlı, Tuzla 34956
Istanbul, Turkey
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Introduction
• Application of local search methods • Real-life application at a steel cord
manufacturing plant• Layout problem that can be represented
as a Quadratic Assignment Problem (QAP)
• Implement the well-known local search methods, 2-opt, 3-opt and tabu search.
• Compare to solution of NEOS
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Steel Cord
• Typically used as the main reinforcement material in manufacturing steel radial tires.
• Strengthens the tire to provide fuel savings, long mileage, safety and comfort.
• Continuous processes, where wire semi-products are stored on discrete inventory units, namely “spools”
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Literature on Steel Cord Manufacturing
• Very specialized type of manufacturing.
• Systems required are produced and installed by only a handful of companies in the world.
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Literature on Steel Cord Manufacturing
• Thomas et al. (2002): Improvement of operations in a steel cord manufacturing company using simulation
• Mercankaya (2003): Development of an optimization-based decision support system
• Türkseven and Ertek (2003): Determination of optimal spool lengths under certain constraints.
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Steel Cord Manufacturing Processes
• Incoming raw material, the “steel rod wire”, is thinned by dry and wet drawing into “filaments” that are used in successive bunching operations to construct the “steel cord” final products.
• The first phase of the production is carried out by machines that are fixed to their locations.
• The focus of our research is the second phase of production, which starts with wet wire drawing and ends with spiraling.
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Dry drawing I & II
Annealing
Cold air bath
Cold water bath
Acidic solution
Basic solution
Spiraling
Bunching
Wet drawing
Copper plating
Zinc plating
Packaging
to Copper plating
Steel wire rod
Filament
Steel cord
Begin Production
End production
RE
SEA
RC
H F
OC
US
RE
SEA
RC
H F
OC
US
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Steel Cord Manufacturing Processes
• Machine types MT01, MT02 and MT03, have to be located in the neighborhood of a lubricant pool.
• These machines use the lubricant liquid, which is supplied to the machines by an underground pipeline system.
• We assigned a high flow volume between these machine types and the lubricant cells.
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Mathematical Model
• We assume that the flow from an area of machine type i to another area of machine type j is equally distributed.
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1
1
1
1
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Machine type i Machine type j
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• Very similar to the Quadratic Assignment Problem (QAP) problem.
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Solution Approaches
• GAMS Model
• The model required specification of the rectilinear distances between areas
• We implement a “model generator” program to generate the model automatically based on input data using the Java programming language.
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Model Generator
GAMSModel
Machine typesKi
Fij
NEOS
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http://www-neos.mcs.anl.gov/neos/
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•Visualization done by a Java program•2-opt and 3-opt algorithms terminated without finding any improved solutions.
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Solution Approaches
• Tabu search heuristic developed by Taillard (1991)
• http://ina.eivd.ch/collaborateurs/etd/ • We tried 5 different starting solutions, and
observed that all these solutions had the objective function value of 6,953,483.
• Tabu search heuristic is very much applicable for the problem that we have presented.
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Future Research
• How to assign the flows from each area of machine type i to each area of machine type j.
• An embedded network flow problem:• Given a layout, each flow assignment is a
possible solution.• Given a flow assignment each layout choice is a
possible solution. • There is a need to develop algorithms that can
solve these two interrelated problems simultaneously.
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Machine type i Machine type j