Application of local search methods for solving a quadratic assignment problem: A case study


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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

  1. 1. 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 University Orhanlı, Tuzla 34956 Istanbul, Turkey
  2. 2. Introduction <ul><li>Application of local search methods </li></ul><ul><li>Real-life application at a steel cord manufacturing plant </li></ul><ul><li>Layout problem that can be represented as a Quadratic Assignment Problem (QAP) </li></ul><ul><li>Implement the well-known local search methods, 2-opt, 3-opt and tabu search. </li></ul><ul><li>Compare to solution of NEOS </li></ul>
  3. 3. Steel Cord <ul><li>T ypically used as the main reinforcement material in manufacturing steel radial tires. </li></ul><ul><li>S trengthens the tire to provide fuel savings, long mileage, safety and comfort. </li></ul><ul><li>C ontinuous processes, where wire semi-products are stored on discrete inventory units, namely “spools” </li></ul>
  4. 5. Literature on Steel Cord Manufacturing <ul><li>V ery specialized type of manufacturin g. </li></ul><ul><li>S ystems required are produced and installed by only a handful of companies in the world. </li></ul>
  5. 6. Literature on Steel Cord Manufacturing <ul><li>Thomas et al. (2002) : I mprovement of operations in a steel cord manufacturing company using simulation </li></ul><ul><li>Mercankaya (2003) : D evelop ment of an optimization-based decision support system </li></ul><ul><li>Türkseven and Ertek (2003) : D etermin ation of optimal spool lengths under certain constraints . </li></ul>
  6. 7. Steel Cord Manufacturing Processes <ul><li>I ncoming 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 . </li></ul><ul><li>The first phase of the production is carried out by machines that are fixed to their locations. </li></ul><ul><li>The focus of our research is the second phase of production, which starts with wet wire drawing and ends with spiraling. </li></ul>
  7. 8. 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 RESEARCH FOCUS RESEARCH FOCUS
  8. 9. Steel Cord Manufacturing Processes <ul><li>M achine types MT01, MT02 and MT03, have to be located in the neighborhood of a lubricant pool. </li></ul><ul><li>These machines use the lubricant liquid, which is supplied to the machines by an underground pipeline system. </li></ul><ul><li>We assign ed a high flow volume between these machine types and the lubricant cells . </li></ul>
  9. 10. Mathematical Model <ul><li>We assume that the flow from an area of machine type i to another area of machine type j is equally distributed . </li></ul>
  10. 11. 1 2 1 2 3 1 1 1 1 1 1 Machine type i Machine type j
  11. 13. <ul><li>Very s imilar to the Quadratic Assignment Problem (QAP) problem . </li></ul>
  12. 14. Solution Approaches <ul><li>GAMS Model </li></ul><ul><li>The model required specification of the rectilinear distances between areas </li></ul><ul><li>W e implement a “model generator” program to generate the model automatically based on input data using the Java programming language. </li></ul>
  13. 15. Model Generator GAMS Model Machine types K i F ij NEOS
  14. 16. http://www- /
  15. 17. <ul><li>Visualization done by a Java program </li></ul><ul><li>2-opt and 3-opt algorithms terminated without finding any improved solutions. </li></ul>
  16. 18. Solution Approaches <ul><li>Tabu search heuristic developed by Taillard (1991) </li></ul><ul><li>http:// / </li></ul><ul><li>We tried 5 different starting solutions, and observed that all these solutions had the objective function value of 6,953,483 . </li></ul><ul><li>T abu search heuristic is very much applicable for the problem that we have presented . </li></ul>
  17. 19. Future Research <ul><li>How to assign the flows from each area of machine type i to each area of machine type j . </li></ul><ul><li>An embedded network flow problem: </li></ul><ul><li>Given a layout, each flow assignment is a possible solution. </li></ul><ul><li>Given a flow assignment each layout choice is a possible solution. </li></ul><ul><li>There is a need to develop algorithms that can solve these two interrelated problems simultaneously. </li></ul>
  18. 20. 1 2 1 2 3 2 1 2 1 Machine type i Machine type j