Rank-Cluster-and-Prune: An algorithm for generating clusters in complex set partitioning problems

Naval Research Logistics

Volumn 56, Issue 3, 2009, Pages 215-225

  Cohn, Amy ^a   Magazine, Michael ^b   Polak, George ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF CINCINNATI   (United States)

^c WRIGHT STATE UNIVERSITY   (United States)

Author keywords

Branch and bound; Branch and price; Delayed column generation; Set partitioning

Indexed keywords

BRANCH-AND-BOUND; BRANCH-AND-PRICE; CLUSTERING PROBLEMS; COMPUTATIONAL RESULTS; DELAYED COLUMN GENERATION; INTEGER PROGRAMS; NON-LINEAR; NON-LINEAR COST FUNCTIONS; PRICING PROBLEMS; REAL-WORLD PROBLEMS; SEARCH-BASED ALGORITHMS; SET PARTITIONING; SET PARTITIONING PROBLEMS;

CLUSTERING ALGORITHMS; COST FUNCTIONS; COSTS; INTEGER PROGRAMMING; PRINTED CIRCUIT MANUFACTURE;

PRINTED CIRCUIT BOARDS;

EID: 63449142641     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.20343     Document Type: Article

References (31)

1. E. Balas and M. Padberg, Set partitioning: A survey, SIAM Rev 18 (1976), 710-760.
2. M.O. Ball and MJ. Magazine, Sequencing of insertions in printed circuit board assembly, Oper Res 36 (1988), 192-201.
3. C. Barnhart, E. Johnson, G. Nemhauser, M. Savelsbergh, and P. Vance, Branch-and-price: Column generation for solving huge integer programs, Oper Res 46 (1998), 316-329.
4. C. Barnhart, C. Hane, and P. Vance, Using branch-and-priee- and-cut to solve origin-destination integer multicommodity flow problems, Oper Res 48 (2000), 318-326.
5. C. Barnhart, A. Cohn, E. Johnson, D. Klabjan, G. Nemhauser, and P. Vance, Handbook of transportation science, 2nd ed., Kluwer's International Series, 2003.
6. P. Bergey, C. Ragsdale, and M. Hoskote, A decision support system for the electrical power redistricting problem, Decision Support Syst 36 (2003), 1-17.
7. M. Blais, S. Lapierre, and G. Laporte, Solving a home-care districting problem in an urban setting, J Oper Res Soc 54 (2003), 1141-1147.
8. B. Bozkaya, E. Erkut, and G. Laporte, A tabu search heuristic and adaptive memory procedure for political districting, Eur J Oper Res 144 (2003), 12-26.
9. F. Caro, T. Shirabe, M. Guignard, and A. Weintraub, School redistricting: Embedding GIS tools with integerprogramming, J Oper Res Soc 55 (2004), 836-849.
10. D. Cattrysse, M. Salomon, R. Kuik, and L. Van Wassenhove, A dual ascent and column generation heuristic for the discrete lot-sizing and scheduling problem with setup times, Management Sci 39 (1993), 477-486.
11. Y. Crama, J. van de Klundert, and F.C.R. Spieksma, Production planning problems in printed circuit board assembly, GEMME 9925, University of Liege, Liege, Belgium, 1999.
12. S. D'Amico, S. Wang, R. Batta, and C. Rump, A simulated annealing approach to police district design, Comput Oper Res 29 (2002), 667-684.
13. G. Dantzig and P. Wolfe, The decomposition principle for linear programs, Oper Res 8 (1960), 101-111.
14. G. Desaulniers, J. Desrosiers, I. Ioachim, M. Solomon, F. Soumis, and D. Villeneuve, A unified framework for deterministic time constrained vehicle routing and crew scheduling problems, Fleet Management and Logistics, T. Crainic and G. Laporte (Editors), Kluwer, Boston, 1998, pp. 57-94.
15. J. Desrosiers, N. Mladenovic, and D. Villeneuve, Design of balanced MBA student teams, J Oper Res Soc 56 (2005), 60-66.
16. T. Fahle, U. Junker, S. Karisch, N. Kohl, M. Sellmann, and B. Vaaben, Constraint programming based column generation for crew assignment, J Heuristics 8 (2002), 59-81.
17. P. Gilmore and R. Gomory, A linear programming approach to the cutting stock problem, Oper Res 11 (1963), 863-888.
18. H.O. Günther, M. Grunow, and C. Schorling, Workload planning in small lot printed circuit board assembly, OR Spektrum 19(1997), 147-157.
19. G. Hardy, J. Littlewood, and G. Polya, Inequalities, 2nd ed., Oxford University Press, 1952.
20. S. Hess and J. Weaver, Nonpartisan political redistricting by computer, Oper Res 13 (1965), 998-1006.
21. M.J. Magazine and G.G. Polak, Job release policy and printed circuit board assembly, IIE Trans 35 (2003), 379-387.
22. M.J. Magazine and G.G. Polak, Optimal machine setup and product clustering for printed circuit board manufacturing, Raj Soin College of Business Working Paper 02-006, Wright State University, Dayton, Ohio.
23. M.J. Magazine, G.G. Polak, and D. Sharma, A multi-exchange neighborhood search heuristic for an integrated clustering and machine setup model for PCB manufacturing, J Electron Manuf 11(2002), 107-119.
24. S.K. Norman, Heuristic approaches to batching jobs in printed circuit board assembly, Ph.D. dissertation, QAOM Department, University of Cincinnati, 2001.
25. C.C. Ribeiro, M. Minoux, and M. Penne, An optimal column-generation-with- ranking algorithm for very large scale set partitioning problems in traffic assignment, Eur J Oper Res 41(1989), 232-239.
26. D. Ryan, The solution of massive generalized set partitioning problems in aircrew rostering, J Oper Res Soc 43 (1992), 459-67.
27. D. Ryan and B. Foster, An integer programming approach to scheduling, Comput Sched Public Transport, A. Wren (Editor), North-Holland, Amsterdam, 1981, pp. 269-280.
28. M. Savelsbergh, A branch-and-price algorithm for the generalized assignment problem, Oper Res 45 (1997), 831-841.
29. C. Tang and E. Denardo, Models arising from a flexible manufacturing machine. II: Minimization of the number of switching instants, Oper Res 36 (1988), 778-784.
30. F. Vanderbeck, On dantzig-wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm, Oper Res 48 (2000), 111-128.
31. F. Vanderbeck and L. Wolsey, An exact algorithm for IP column generation, Oper Res Lett 19 (1996), 151-159.