## Packing problems.(English)Zbl 0825.90355

### MSC:

 90B06 Transportation, logistics and supply chain management 90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 90C27 Combinatorial optimization 90C90 Applications of mathematical programming 90C39 Dynamic programming
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### References:

 [1] Adamowicz, M.; Albano, A., A two-stage solution of the cutting-stock problem, Information Processing, 71, 1086-1091 (1972) [2] Adamowicz, M.; Albano, A., A solution of the rectangular cutting-stock, IEEE Transactions on Systems, Man and Cybernetics, 6/4, 302-310 (1976) · Zbl 0322.90018 [3] Adamowicz, M.; Albano, A., Nesting two-dimensional shapes in rectangular modules, Computer Aided Design, 8, 27-33 (1976) [4] Albano, A.; Orsini, R., A heuristic solution of the rectangular cutting stock problem, The Computer Journal, 23, 338-343 (1978) [5] Albano, A.; Sapuppo, G., Optimal allocation of two-dimensional irregular shapes using heuristic search methods, IEEE Transactions on Systems, Man and Cybernetics, 10/5, 242-248 (1980) [6] Art, R. C., An approach to the two dimensional, irregular cutting stock problem, IBM Cambridge Centre Report, 36.Y08 (1966) [7] Baker, B. S.; Coffman, E. G.; Rivest, R. L., Orthogonal packings in two dimensions, SIAM Journal on Computing, 9, 846-855 (1980) · Zbl 0447.68080 [8] Baker, B. S.; Coffman, E. G., A tight asymptotic bound for next-fit-decreasing bin-packing, SIAM Journal on Algebraic and Discrete Methods, 2, 147-152 (1981) · Zbl 0496.68049 [9] Baker, B. S.; Calderbank, E. G.; Coffman, J. R.; Lagarias, J. C., Approximation algorithms for maximizing the number of squares packed into a rectangle, SIAM Journal on Algebraic and Discrete Methods, 4, 383-397 (1983) · Zbl 0558.05002 [10] Baker, B. S.; Schwarz, J. S., Shelf algorithms for two-dimensional packing problems, SIAM Journal on Computing, 12, 508-525 (1983) · Zbl 0521.68084 [11] Barnes, F. W., Packing the maximum number of $$m$$ × $$n$$ tiles in a large $$p$$ × $$q$$ rectangle, Discrete Mathematics, 26, 93-100 (1979) · Zbl 0397.05015 [12] Barnett, S.; Kynch, G. J., Exact solution of a simple cutting problem, Operations Research, 15, 1051-1056 (1967) [13] Bartholdi, J.; Vate, J.; Zhang, J., Expected performance of the shelf heuristic for 2P packing, Operations Research Letters, 8, 11-16 (1989) · Zbl 0673.90072 [14] Beasley, J. E., An exact two-dimensional non-guillotine cutting tree search procedure, Operations Research, 33, 49-64 (1985) · Zbl 0569.90038 [15] Beasley, J. E., Bounds for two dimensional cutting, Journal of the Operational Research Society, 36, 71-74 (1985) · Zbl 0557.90046 [16] Beasley, J. E., Algorithms for unconstrained two-dimensional guillotine cutting, Journal of the Operational Research Society, 36, 297-306 (1985) · Zbl 0589.90040 [17] Bengtsson, B. E., Packing rectangular pieces - A heuristic approach, The Computer Journal, 25, 353-357 (1982) [18] Biro, M.; Boros, E., Network flows and non-guillotine cutting patterns, European Journal of Operational Research, 16, 215-221 (1984) · Zbl 0542.05054 [19] Bischoff, E. E., Stability aspects of packing problems, (Presented at IFORS 90. Presented at IFORS 90, Athens (1990)), June · Zbl 1083.90033 [20] Bischoff, E. E.; Dowsland, W. B., An application of the micro to product design and distribution, Journal of the Operational Research Society, 33, 271-281 (1982) [21] Bischoff, E. E.; Marriott, M. D., A comparative evaluation of heuristics for container loading, European Journal of Operational Research, 44, 267-276 (1990) · Zbl 0684.90083 [22] Böhme, D.; Graham, A., Practical experiences with semiautomatic, and automatic partnesting methods, (Kuo, C., Computer Applications in the Automation of Shipyard Operation and design (1979), III North-Holland: III North-Holland Amsterdam), 213-220 [23] Brooks, R. L.; Smith, C. A.B.; Stone, A. H.; Tutte, W. T., The dissection of rectangles into squares, Duke Mathematical Journal, 7, 312-340 (1940) · Zbl 0024.16501 [24] Brown, D. J., An improved BL lower bound, Information Processing Letters, 11/1, 37-39 (1979) · Zbl 0444.68062 [25] Carpenter, H.; Dowsland, W. B., Practical considerations of the pallet loading problem, Journal of the Operational Research Society, 36, 489-497 (1985) · Zbl 0566.90052 [26] Christofides, N., Optimal cutting of two-dimensional rectangular plates, (CAD74 Proceedings (1974)), 1-10 [27] Christofides, N.; Whitlock, C., An algorithm for two-dimensional cutting problems, Operations Research, 25, 31-44 (1977) · Zbl 0369.90059 [28] Christofides, N.; Mingozzi, A.; Toth, P., Loading problems, (Christofides, N., Combinatorial Optimisation (1979), Wiley: Wiley New York), 339-369 [29] Chung, F. R.H.; Garey, M. R.; Johnson, D. S., On packing two-dimensional bins, SIAM Journal on Algebraic and Discrete Methods, 3, 66-76 (1982) · Zbl 0495.05016 [30] Cochard, D. D.; Yost, K. A., Improving utilisation of air force cargo aircraft, Interfaces, 15, 53-68 (1985) [31] Coffman, E. G.; Leung, J. Y.T.; Ting, D. W., Bin packing: maximizing the number of pieces packed, Acta Informatica, 9, 263-271 (1978) · Zbl 0421.68065 [32] Coffman, E. G.; Garey, M. R.; Johnson, D. S., Approximation algorithms for bin packing - an updated survey, (Ausiello, G.; Lucertini, N.; Serafini, P., Algorithm Design for Computer Systems Design (1984), Springer: Springer Vienna), 49-106 · Zbl 0558.68062 [33] Coffman, E. G.; Gilbert, E. N., Dynamic, first fit packings in two or more dimensions, Information and Control, 61, 1-14 (1984) · Zbl 0591.68074 [34] Coffman, E. G.; Lueker, G. S.; Rinnooy Han, A. H.G., Asymptotic methods in the probabilistic analysis of sequencing and packing heuristics, Management Science, 34, 266-290 (1988) · Zbl 0638.90054 [35] Coffman, E. G.; Lagarias, J. C., Algorithms for packing squares: a probabilistic analysis, SIAM Journal of Computing, 18, 166-185 (1989) · Zbl 0671.68014 [36] Coffman, E. G.; Shor, P. W., Average-case analysis of cutting and packing in two dimensions, European Journal of Operational Research, 44, 134-145 (1990) · Zbl 0689.90059 [37] Conway, J. H., Mrs. Perkins’s quilt, (Proceedings of the Cambridge Philosophical Society, 60 (1964)), 363-368 · Zbl 0134.27404 [38] Dagli, C. H., Knowledge-based systems for cutting stock problems, Journal of Operational Research Society, 44, 160-166 (1990) · Zbl 0684.90075 [39] Daniels, J.; Ghandforoush, P., An improved algorithm for the non-guillotine-constrained cutting-stock problem, Journal of the Operational Research Society, 41, 141-150 (1990) · Zbl 0693.90043 [40] De Cani, P., A note on the two-dimensional rectangular cutting-stock problem, Journal of the Operational Research Society, 29, 703-706 (1978) · Zbl 0384.90062 [41] De Cani, P., Packing Problems in Theory and Practice, (Ph.D. Thesis (1979), University of Birmingham: University of Birmingham U.K) [42] De Wit, J. R.; Rinnooy Han, A. H.G.; Wijmenga, R. T., Nonorthogonal twodimensional cutting patterns, Management Science, 33, 341-345 (1987) · Zbl 0629.90044 [43] Dori, D.; Ben-Bassat, M., Efficient nesting on congruent convex figures, Communications of the ACM, 27, 228-235 (1984) [44] Dowsland, K. A., The three-dimensional pallet chart: An analysis of the factors affecting the set of feasible layouts for a class two-dimensional packing problems, Journal of the Operational Research Society, 35, 895-905 (1984) · Zbl 0546.90052 [45] Dowsland, K. A., Determining an upper bound for a class of rectangular packing problems, Computers and Operations Research, 12, 201-205 (1985) · Zbl 0608.90080 [46] Dowsland, K. A., A graph-theoretic approach to the pallet loading problem, New Zealand Operational Research, 13, 77-86 (1985) [47] Dowsland, K. A., An exact algorithm for the pallet loading problem, European Journal of Operational Research, 31, 78-85 (1987) · Zbl 0614.90084 [48] Dowsland, K. A., A combined database and algorithmic approach to the pallet loading problem, Journal of the Operational Research Society, 38, 341-345 (1987) · Zbl 0608.90077 [49] Dowsland, K. A., Efficient automated pallet loading, European Journal of Operational Research, 44, 232-238 (1990) · Zbl 0684.90078 [50] Dowsland, W. B., The computer as an aid to physical distribution management, European Journal of Operational Research, 15, 160-168 (1984) · Zbl 0527.90040 [51] Dowsland, W. B., Two and three dimensional packing problems and solution methods, New Zealand Operational Research, 13, 1-17 (1985) · Zbl 0588.90061 [52] Dyckhoff, H., A typology of cutting and packing problems, European Journal of Operational Research, 44, 145-160 (1990) · Zbl 0684.90076 [53] Dyckhoff, H.; Kruse, H. J.; Abel, D.; Gal, T., Trim loss and related problems, OMEGA, 13, 59-72 (1985) [54] Eilon, E., Optimising the shearing of steel bars, Journal of Mechanical Engineering Science, 2, 129-142 (1960) [55] Eilon, S.; Christofides, N., The loading problem, Management Science, 17, 259-268 (1971) · Zbl 0208.45701 [56] Fowler, R. J.; Paterson, M. S.; Tanimoto, S. L., Optimal packing and covering in the plane are NP-complete, Information Processing Letters, 12, 133-137 (1981) · Zbl 0469.68053 [57] Freeman, H.; Shapira, A., Determining the minimum-area encasing rectangle for an arbitratry closed curve, Communications of ACM, 18, 409-413 (1975) · Zbl 0308.68084 [58] Friesen, D. K.; Langston, M. A., Variable sized bin packing, SIAM Journal on Computing, 15, 222-231 (1986) · Zbl 0589.68036 [59] Gehring, H.; Menschner, H.; Meyer, M., A computer-based heuristic for packing pooled shipment containers, European Journal of Operational Research, 44, 277-289 (1990) · Zbl 0684.90084 [60] George, J. A.; Robinson, D. F., A heuristic for packing boxes into a container, Computers and Operations Research, 7, 147-156 (1980) [61] Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting-stock problem (Part 1), Operations Research, 9, 849-859 (1961) · Zbl 0096.35501 [62] Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting-stock problem (Part 2), Operations Research, 11, 863-888 (1963) · Zbl 0124.36307 [63] Gilmore, P. C.; Gomory, R. E., Multistage cutting stock problems of two and more dimensions, Operations Research, 13, 94-120 (1965) · Zbl 0128.39601 [64] Gilmore, P. C.; Gomory, R. E., The theory and computation of knapsack functions, Operations Research, 14, 1045-1074 (1966) · Zbl 0173.21502 [65] Golan, I., Performance bounds for orthogonal oriented two-dimensional packing algorithms, SIAM Journal on Computing, 10, 571-582 (1981) · Zbl 0461.68076 [66] Golden, B. L., Approaches to the cutting stock problem, AIIE Transactions, 8, 265-274 (1976) [67] Golomb, S., Polyominoes (1966), Allen and Unwin: Allen and Unwin London · Zbl 0143.44202 [68] Gurel, O., Additional considerations on market layout problem via graph theory, (IBM Scientific Centre Report (1968), IBM: IBM New York), 320-2945 [69] Gurel, O., Market layout problem via graph theory: an attempt for optimal layout of irregular patterns, (IBM Scientific Centre Report 320-2921 (1968), IBM: IBM New York) · Zbl 0188.22903 [70] Gurel, O., Circular graph of market layout, (IBM Scientific Centre Report 320-2965 (1969), IBM: IBM New York) · Zbl 0188.22903 [71] Haessler, R. W., A note on computational modifications to the GilmoreGomory cutting stock algorithm, Operations Research, 10, 1001-1005 (1980) · Zbl 0441.90066 [72] Haessler, R. W.; Talbot, F. B., Load planning for shipments of low density products, European Journal of Operational Research, 44, 289-299 (1990) · Zbl 0684.90085 [73] Hahn, S. G., On the optimal cutting of defective sheets, Operations Research, 16, 1100-1114 (1968) [74] Haims, M. J.; Freeman, H., A multistage solution of the templatelayout problem, IEEE Transactions on Systems Science and Cybernetics, 6/2, 145-151 (1970) · Zbl 0217.26904 [75] Han, C. P.; Knott, K.; Egbelu, P. J., A heuristic approach to the three-dimensional cargo-loading problem, International Journal of Production Research, 27, 757-774 (1989) · Zbl 0667.90075 [76] Herz, J. C., Recursive computational procedure for two-dimensional stock cutting, IBM Journal of Research and Development, 16, 462-469 (1972) · Zbl 0265.90057 [77] Hinxman, A. I., The trim-loss and assortment problems: a survey, European Journal of Operational Research, 5, 8-18 (1980) · Zbl 0442.90072 [78] Hodgson, T. T., A combined approach to the pallet loading problem, IIE Transactions, 14, 175-182 (1982) [79] Hodgson, T. T.; Hughes, D. S.; Martin-Vega, L. A., A note on a combined approach to the pallet loading problem, IIE Transactions, 15, 268-271 (1983) [80] Hofri, M., Two-dimensional packing: Expected performance of simple level algorithms, Information and Control, 45, 1-17 (1980) · Zbl 0443.05033 [81] Ikeda, Y.; Kokan, K. K., The pansy, an advanced interactive parts nesting system, (Kuo, C., Computer Applications in the Automation of Shipyard Operation and Ship Design, III (1979), North Holland: North Holland Amsterdam), 313-321 [82] Isermann, H., Ein Planungssystem zur Optimierung der Palettenbeladung mit kongruenten rechteckigen Versandgebinden, OR Spectrum, 9, 235-249 (1987) [83] Israni, S.; Sanders, J. L., Performance testing of rectangular parts-nesting heuristics, International Journal of Production Research, 23, 437-456 (1985) · Zbl 0571.90029 [84] Kantorovich, L. V., Mathematical methods of organising and planning production, Management Science, 6, 366-422 (1939, 1960) [85] Kämpke, T., Simulated annealing: use of a new tool in bin packing, Annals of Operations Research, 16, 327-332 (1988) · Zbl 0692.90086 [86] Lindgren, H., Geometric Dissections (1964), Van Nostrand Reinhold: Van Nostrand Reinhold New York [87] Liu, N. C.; Chen, L. C., A new algorithm for container loading, (Compsac 81 - 5th International Computer Software and Applications Conference Proceedings (1981), IEEE: IEEE Chicago), 292-299 [88] Mannchen, K., Solution methods for two and three dimensional packing problems, (Dissertation (1989), Karlsruhe: Karlsruhe Germany) [89] Martello, S.; Toth, P., Knapsack problems - algorithms and computer implementations (1990), Wiley: Wiley New York · Zbl 0708.68002 [90] Martin, R. R.; Stephenson, P. C., Putting objects into boxes, Computer Aided Design, 20, 506-514 (1988) [91] Matson, J. O.; White, J. A., Operational research and material handling, European Journal of Operational Research, 11, 309-318 (1982) [92] McRoberts, H., A search model for evaluating combinatorially explosive problems, Operations Research, 6, 1331-1349 (1971) · Zbl 0228.90021 [93] Metzger, R., Stock slitting, (Elementary Mathematical Programming (1958), Wiley: Wiley New York), Chapter 8 [94] Oliveira, J. F.; Ferreira, J. S., An improved version of Wang’s algorithm for two-dimensional cutting problems, European Journal of Operational Research, 44, 256-266 (1990) · Zbl 0684.90073 [95] Paull, A.; Walter, J., The trim problem: an application of linear programming to the manufacture of newsprint paper, (Proceedings of Annual Econometric Meeting. Proceedings of Annual Econometric Meeting, Montreal, Sept. 10th-13th (1954)) [96] Peleg, K., Computerised pallet stacking, Packaging Technology, September, 18-25 (1971) [97] Peleg, K.; Peleg, E., Container dimensions for optimal utilization of storage and transportation space, Computer Aided Design, 8, 775-781 (1976) [98] Puls, F. N.; Tanchoco, J. M.A., Robotic implementation of pallet loading patterns, International Journal of Production Research, 24, 635-645 (1986) [99] Sculli, D.; Hui, C. F., Three dimensional stacking of containers, OMEGA, 16, 585-594 (1988) [100] Short, P. J., Optimal batch execution on a multiprocessing computer - a 2D packing problem, (M.Sc. Thesis (1973), University of London) [101] Smith, A.; De Cani, P., An algorithm to optimize the layout of boxes in pallets, Journal of the Operational Research Society, 31, 573-578 (1980) [102] Sperling, B., Nesting is more than a layout problem, (Kuo, C., Computer Applications in the Automation of Shipyard Operation and Ship Design, III (1979), North Holland: North Holland Amsterdam), 287-294 [103] Steudel, H. J., Generating pallet loading patterns: a special case of the two-dimensional cutting stock problem, Management Science, 25, 997-1004 (1979) · Zbl 0465.90051 [104] Steudel, H. J., Generating pallet loading patterns with considerations of item stacking on end and side surfaces, Journal of Manufacturing Systems, 3, 135-143 (1984) [105] Stone, D. C.; Moore, M. C., How to determine existence of acceptable pallet patterns, Package Development, September/October, 20-27 (1971) [106] Stoyan, Y. G., Mathematical methods for geometry design, (Ellis, T.; Siemenkov, O., Advances in CAD/CAM (1983), North Holland: North Holland Amsterdam), 67-86, IFIP 83 [107] Sweeney, P. E.; Ridenour, E. L., Cutting and packing problems: A categorized, application-oriented research bibliography, (Working Paper 610 (1989), School of Business Administration, University of Michigan) · Zbl 0757.90055 [108] Tinarelli, G. U.; Addonizio, M., Un problema di caricamento di containers, (Proceedings AIRO (1978)), 217-231 [109] Tsai, R. D.; Malstrom, E. M.; Meeks, H. D., A two-dimensional palletizing procedure for warehouse loading operations, IIE Transactions, 20, 418-423 (1988) [110] Van Delft, P.; Botermans, J., Creative Puzzles of the World (1978), Cassell: Cassell London [111] Vasko, F. J., A computational improvement to Wang’s two-dimensional cutting stock algorithm, Computers in Industrial Engineering, 16, 109-115 (1989) [112] Wang, P. Y., Two algorithms for constrained two-dimensional cutting stock problems, Operations Research, 31, 573-586 (1983) · Zbl 0517.90093 [113] Wright, P. G., There may be a better pack for you, Australian Lithographer, 12, 33-34 (1973) [114] Wright, P. G., A systems approach to packaging design, Australian Packaging, June, 27-33 (1973) [115] Wright, P. G., Pallet loading configurations for optimum storage and shipping, Paperboard Packaging, December, 46-49 (1974)
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