Optimal orthogonal subdivision of rectangular sheets

Journal of Manufacturing Science and Engineering, Transactions of the ASME

Volumn 118, Issue 3, 1996, Pages 281-288

  Shpitalni, M ^a   Manevich, V ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER INTEGRATED MANUFACTURING; CUTTING; FLEXIBLE MANUFACTURING SYSTEMS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; SCRAP METAL;

INTEGER LINEAR PROGRAMMING; NESTING; OBJECTIVE FUNCTIONS; OPTIMAL ORTHOGONAL SUBDIVISION; RECTANGLES; STOCK CUTTING; TWO DIMENSIONAL;

SHEET METAL;

EID: 0030213048     PISSN: 10871357     EISSN: 15288935     Source Type: Journal    
DOI: 10.1115/1.2831027     Document Type: Article

References (24)

1. Brown, A. R., 1971, Optimum Packing and Depletion: The Computer in Space-and Resource-Usage Problems, Macdonald. London & American Elsevier Inc., New York
2. Dagli, C. H., 1990. -Knowlcdgc-Ba^d Systems for Cutting Stock Piob-Icitis,— European Journal of Operational Research, Vol. 44. pp 160-166.
3. Garcy, M. R., and Johnson, D. S., 1979, Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, U.S.A.
4. Coffman, Jr., E. G., Lueker, G. S., and Rinnooy, A. H. G., 1988. -Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics.— Management Science. Vol. 34. pp. 266-290.
5. Dantzig, G. B., 1951. -Maximation of a Linear Function of Variables Subject to Linear Inequalities,— Activity Analysis of Production and Allocation, T. C. Koopmans. ecL, Cowles Commission Monograph. 13. Wiley. New York, pp. 339-347.
6. Kantorovich, L. V., and Zalgallcr, V. A., 1951, OptimaI Calculation for Subdivision in the Material Industry. Leningrad. Lenidat. p 198.
7. Gilmore, P. C., and Gomory, R. E., 1961. -A Linear Programming Approach to the Cutting-Stock Problem,— Operations Research, Vol. 9, pp. 849-859.
8. Gilmore, F. C., and Gomory, R. E., 1963, -A Linear Programming Approach 10 the Cutting-Stock Problem. Pari II.— Operations Research. Vol. 11. pp. 863-888.
9. Gilmore, P. C, and Gomory, R. E., 1965. -’Multistage Cutting Stock Problems of Two and More Dimensions.— Operations Research. Vol. 13, pp. 94-120.
10. Gilmore, P. C., and Gomory, R. E., 1966, -The Theory and Computation of Knapsack Functions.— Operations Research, Vol. 14. pp 1045-1074.
11. Hacsslcr, R. W., 1980, -A Note on Some Computational Modifications to the Gilmore-Gomory Cutting Stock Algorithm.— Operations Research. Vol. 28. pp. 1001-1005.
12. Marinescu, D., 1984, -An Integer Programming Model For Two-Dimen-sional Cutting Stock Problem.— Proc. of the Colloquium on Approximation and Optimization, pp. 269-276.
13. Nee, A. Y. C., Seow, K. W., and long, S. L., 1986, -Designing Algorithm for Nesting Irregular Shapes With and Without Boundary Constraints.— Annals of the CIRP, Vol. 35. No. 1, pp. 107-110.
14. Weishuang, Q., and Sanders, J. L., 1987. “A Nesting Algorithm for Irregular Parts and Factors Affecting Trim Losses,” Int. J. of Prod. Res., Vol. 25, No. 2. pp. 381-307.
15. Ismail, H. S., and Hon, K. K. B., 1992. -New Approaches for the Nesting of Two-Dimensional Shapes for Press Tool Design.— Int J. of Prod. Ret., Vol. 30, No. 4, pp. 825-837.
16. Hen, J. C., 1972, -Recursive Computational Procedure for Two dimensional Stock Cutting,— IRM J. Res. Develop., pp. 462-469.
17. Adamowicz, M., and Albano, A., 1976. -A Solution of the Rectangular Cutting-Stock Problem,— IEEE. Transactions on Systems, Man. and Cybernetics, SMC-6/4. pp. 302-310.
18. DeVries, J., Van Roosraalen, A. A. H. M., Stieppel, A. H., and Kals, H. J J., 1993, -Planning and Nesting in Small Batch Sheet Metal Manufacturing,— 25th CIRP International Seminar on Manufacturing Systems-FMS. April 22-23. Slovenia, pp 77-90.
19. Dyckhoff, H., 1990, -A Typology of Cutting and Packing Problems,— European Journal of Operational Research. Vol. 14. pp. 145-159.
20. Coffman, Jr., E. G., and Shor, P. W., 1990. -Average-Case Analysis of Cutting and Packing in Two Dimensions,— European Journal of Operational Research. Vol. 44. pp. 134-144.
21. Diegel, A., 1988. -Integer l.P Solution for Large Trim Problems,— Fuiro IX, TIMS 28 Joint International Conference, Paris, July 6-8.
22. Berkelaar, M. R. C. M., and Solve, L. P., Eindhoven University of Technology. Design Automation Section. P.O. Box 513. NL-5600 MB Eindhoven. The Netherlands.
23. Saaty, T. L., and Kainen, P. C. 1977, The Four-Color Problem. McGraw Hill International, p. 126.
24. Mcriam, J. L., and Kraigc, L. G., 1987, Engineering Mechanics. Vol. 1-Statistics. John Wiley and Son. p. 212.