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Packing cylinders and rectangular parallelepipeds with distances between them into a given region

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  • Stoyan, Yu.
  • Chugay, A.

Abstract

This paper considers the problem of packing cylinders and parallelepipeds into a given region so that the height of the occupied part of the region is minimal and the distances between each pair of items, and the distance between each packed item and the frontier of the region must be greater than or equal to given distances. A mathematical model of the problem is built and some characteristics of the mathematical model are investigated. Methods for fast construction of starting points, searching for local minima, and a special non-exhaustive search of local minima to obtain good approximations to a global minimum are offered. A numerical example is given. Runtimes to obtain starting points, local minima and approximations to a global minimum are adduced.

Suggested Citation

  • Stoyan, Yu. & Chugay, A., 2009. "Packing cylinders and rectangular parallelepipeds with distances between them into a given region," European Journal of Operational Research, Elsevier, vol. 197(2), pages 446-455, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:446-455
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    References listed on IDEAS

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    1. Birgin, E. G. & Martinez, J. M. & Ronconi, D. P., 2005. "Optimizing the packing of cylinders into a rectangular container: A nonlinear approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 19-33, January.
    2. Gehring, H. & Menschner, K. & Meyer, M., 1990. "A computer-based heuristic for packing pooled shipment containers," European Journal of Operational Research, Elsevier, vol. 44(2), pages 277-288, January.
    3. Bischoff, E. E. & Janetz, F. & Ratcliff, M. S. W., 1995. "Loading pallets with non-identical items," European Journal of Operational Research, Elsevier, vol. 84(3), pages 681-692, August.
    4. Jie Wang, 1999. "Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 453-463, December.
    5. W Q Huang & Y Li & H Akeb & C M Li, 2005. "Greedy algorithms for packing unequal circles into a rectangular container," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 539-548, May.
    6. A. Sutou & Y. Dai, 2002. "Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 671-694, September.
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    Cited by:

    1. Yuriy Stoyan & Georgiy Yaskov, 2012. "Packing congruent hyperspheres into a hypersphere," Journal of Global Optimization, Springer, vol. 52(4), pages 855-868, April.

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