THREE DIMENSIONAL PALLETIZATION OF MIXED BOX SIZES

The pallet loading problem has historically been addressed in two-dimensions by attempting to maximize the pallet area utilized in each loading layer. This paper investigates a constrained version of three-dimensional pallet loading problem with mixed box sizes. This loading method allows many boxes of various sizes to be placed onto the same pallet. A restriction is placed on the number of boxes of each size that can be loaded. The modeling procedure presented converts the three-dimensional pallet loading problem into a standard mixed 0-1 integer programming model. The solution procedure for the formulated model is also described.

[1]  Linus Schrage,et al.  Subset Coefficient Reduction Cuts for 0/1 Mixed-Integer Programming , 1985, Oper. Res..

[2]  Endre Boros,et al.  Network flows and non-guillotine cutting patterns , 1984 .

[3]  A. Farley,et al.  A note on modifying a two-dimensional trim-loss algorithm to deal with cutting restrictions , 1983 .

[4]  Igal Golan,et al.  Performance Bounds for Orthogonal Oriented Two-Dimensional Packing Algorithms , 1981, SIAM J. Comput..

[5]  P. Y. Wang,et al.  Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems , 1983, Oper. Res..

[6]  W. C. Healy.  Multiple Choice Programming A Procedure for Linear Programming with Zero-One Variables , 1964 .

[7]  A. Farley,et al.  Trim-loss pattern rearrangement and its relevance to the flat-glass industry , 1983 .

[8]  J. Beasley.  Bounds for Two-Dimensional Cutting , 1985 .

[9]  Brenda S. Baker,et al.  A 5/4 Algorithm for Two-Dimensional Packing , 1981, J. Algorithms.

[10]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

[11]  Mary W. Cooper,et al.  A dynamic programming algorithm for multiple-choice constraints , 1984 .

[12]  Naonori Nishida,et al.  A branch-and-bound algorithm for 0-1 parametric mixed integer programming , 1985 .

[13]  Robert E. Tarjan,et al.  Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms , 1980, SIAM J. Comput..

[14]  Harold J. Steudel.  Generating pallet loading patterns with considerations of item stacking on end and side surfaces , 1984 .

[15]  S. A. Roberts.  Application of Heuristic Techniques to the Cutting-Stock Problem for Worktops , 1984 .

[16]  R. G. Jeroslow,et al.  Experimental Results on the New Techniques for Integer Programming Formulations , 1985 .

[17]  Dennis J. Sweeney,et al.  The reduced cost branch and bound algorithm for mixed integer programming , 1985, Comput. Oper. Res..

[18]  Sharat Israni,et al.  Two-dimensional cutting stock problem research: A review and a new rectangular layout algorithm , 1982 .

[19]  Louis A. Martin-Vega,et al.  Micro-IPLS: pallet loading on a microcomputer , 1985 .

[20]  B. Golden.  Approaches to the Cutting Stock Problem , 1976 .

[21]  Gary A. Kochenberger,et al.  A simple, all primal branch and bound approach to pure and mixed integer binary programs , 1982, Oper. Res. Lett..

[22]  David A. Kendrick,et al.  A Branch-and-Bound Algorithm for Zero-One Mixed Integer Programming Problems , 1971, Oper. Res..

[23]  John E. Beasley,et al.  Algorithms for Unconstrained Two-Dimensional Guillotine Cutting , 1985 .

[24]  R. Rutledge,et al.  A simplex method for zero-one mixed integer linear programs , 1967 .

[25]  J. A. George,et al.  A heuristic for packing boxes into a container , 1980, Comput. Oper. Res..

[26]  Louis A. Martin-Vega,et al.  A Note on a Combined Approach to the Pallet Loading Problem , 1983 .

[27]  Thom J. Hodgson,et al.  A Combined Approach to the Pallet Loading Problem , 1982 .

[28]  A. I. Hinxman.  The trim-loss and assortment problems: A survey , 1980 .