Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

A New Exact Algorithm Using the Stair Structure for the Pallet Loading Problem

계단 구조를 이용한 팔레트적재문제의 새로운 해법

  • 지영근 (포디엄시스템 기술연구소) ;
  • 진고환 (우송대학교 IT 경영정보학과)
  • Published : 2009.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The pallet loading problem(PLP) requires the best orthogonal layout that loads the maximum number of identical boxes(small rectangle) onto a pallet(large rectangle). Since the high pallet utilization saves the distribution and storage costs, many heuristic and exact algorithms have been developed so far. Martins and Dell have found the optimal layouts for the all PLPs less than or equal to 100 boxes except for only 5 problems in their recent research. This paper defines the 'stair structure' and proposes a new exact algorithm applying it. In order to show the priority of the proposed algorithm, computational results are compared to previous algorithms and the optimal layouts for the S unsolved problems are given.

Keywords

References

  1. Arenales M. and R. Morabito, 'An AND/ORgraph approach to the solution of two-dimensional non-guillotine cutting problems,' European Journal of Operational Research, Vol.84(1995), pp.599-617 https://doi.org/10.1016/0377-2217(95)00026-M
  2. Barnes F., 'Packing the maximum number of m $\times$ n tiles in a large p $\times$ q rectangle,' Discrete Mathmatics, Vol.26(1979), pp.93-100 https://doi.org/10.1016/0012-365X(79)90115-8
  3. Bhattacharya S., R. Roy, and S. Bhattacharya, 'An exact depth-first algorithm for the pallet loading problem,' European Journal of Operational Research, Vol.110(1998), pp.610-625 https://doi.org/10.1016/S0377-2217(97)00272-5
  4. Dowsland K, 'The Three-dimensional pallet chart : An analysis of the factors affecting the set of feasible layouts for a class of twodimensional packing problems,' Journal of the Operational Research Society, Vol.35(1984), pp.895-905 https://doi.org/10.1057/jors.1984.180
  5. Dowsland K, 'Determining an upper bound for a class of rectangular packing problems,' Computers and Operations Research, Vol.12 (1985), pp.201-205 https://doi.org/10.1016/0305-0548(85)90044-9
  6. Dowsland K, 'An exact algorithm for the pallet loading problem,' European Journal of Opemtional Research, Vol.31(1987), pp.78-84 https://doi.org/10.1016/0377-2217(87)90140-8
  7. G Y.-G. and M-K Kang, 'A fast algorithm for two-dimensional pallet loading problems of large size,' European Journal of Operational Research, Vol.134(2001), pp.193-202 https://doi.org/10.1016/S0377-2217(00)00249-6
  8. G y.-G. and M -K Kang, 'A new Upper bound for unconstrained two-dimensional cutting and packing,' Journal of the Operational Research Society, Vol.53(2002), pp.587-591 https://doi.org/10.1057/palgrave.jors.2601326
  9. Letchford A. and A. Amaral, 'Anlysis of upper bounds for the pallet loading problem,' European Journal of Operational Research, Vol.132(2001), pp.582-593 https://doi.org/10.1016/S0377-2217(00)00163-6
  10. Martins G. and R. Dell, 'The minimum size instance of a pallet loading problem equivalence class,' European Journal of Operational Research, Vol.179(2007), pp.17-26 https://doi.org/10.1016/j.ejor.2006.03.009
  11. Martins G. and R. Dell, 'Solving the pallet loading problem,' European Journal of Operational Research, Vol.184(2008), pp.129-440 https://doi.org/10.1016/j.ejor.2006.11.012
  12. Morabito R. and S. Morales, 'A simple and effective recursive procedure for the manufacturer's pallet loading problem,' Journal of the Operational Research Society, Vol.49(1998), pp.819-828 https://doi.org/10.1057/palgrave.jors.2600588
  13. Neliben J., 'How to use structural constraints to compute an upper bound for the pallet loading problem,' European Journal of Operational Research, Vol.84(1995), pp.662-680 https://doi.org/10.1016/0377-2217(95)00030-T
  14. Scheithauer G. and J. Terno, 'The G4-heuristic for the pallet looding problem,' European Journal of Operational Research, Vol.108(1996), pp.511-522