A fast algorithm for identifying minimum size instances of the equivalence classes of the Pallet Loading Problem

In this paper, a novel and fast algorithm for identifying the Minimum Size Instance (MSI) of the equivalence class of the Pallet Loading Problem (PLP) is presented. The new algorithm is based on the fact that the PLP instances of the same equivalence class have the property that the aspect ratios of their items belong to an open interval of real numbers. This interval characterises the PLP equivalence classes and is referred to as the Equivalence Ratio Interval (ERI) by authors of this paper. The time complexity of the new algorithm is two polynomial orders lower than that of the best known algorithm. The authors of this paper also suggest that the concept of MSI and its identifying algorithm can be used to transform the non-integer PLP into its equivalent integer MSI.

[1]  Reinaldo Morabito,et al.  An effective recursive partitioning approach for the packing of identical rectangles in a rectangle , 2010, J. Oper. Res. Soc..

[2]  Ramón Alvarez-Valdés,et al.  A branch-and-cut algorithm for the pallet loading problem , 2005, Comput. Oper. Res..

[3]  Kathryn A. Dowsland.  Determining an upper bound for a class of rectangular packing problems , 1985, Comput. Oper. Res..

[4]  Gustavo H. A. Martins.  Packing in two and three dimensions , 2003 .

[5]  J. Nelissen.  New approaches to the pallet loading problem , 1993 .

[6]  Robert F. Dell,et al.  The minimum size instance of a Pallet Loading Problem equivalence class , 2007, Eur. J. Oper. Res..

[7]  Adam N. Letchford,et al.  Analysis of upper bounds for the Pallet Loading Problem , 2001, Eur. J. Oper. Res..

[8]  W. B. Dowsland,et al.  Practical Considerations of the Pallet-Loading Problem , 1985 .

[9]  Kathryn A. Dowsland,et al.  The Three-Dimensional Pallet Chart: An Analysis of the Factors Affecting the Set of Feasible Layouts for a Class of Two-Dimensional Packing Problems , 1984 .

[10]  K. Dowsland.  An exact algorithm for the pallet loading problem , 1987 .

[11]  Reinaldo Morabito,et al.  A simple and effective recursive procedure for the manufacturer's pallet loading problem , 1998, J. Oper. Res. Soc..

[12]  Reinaldo Morabito,et al.  Some experiments with a simple tabu search algorithm for the manufacturer's pallet loading problem , 2006, Comput. Oper. Res..

[13]  Robert F. Dell,et al.  Solving the pallet loading problem , 2008, Eur. J. Oper. Res..

[14]  Guntram Scheithauer,et al.  The G4-Heuristic for the Pallet Loading Problem , 1996 .

[15]  Glaydston Mattos Ribeiro,et al.  Lagrangean relaxation with clusters and column generation for the manufacturer's pallet loading problem , 2007, Comput. Oper. Res..

[16]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[17]  Gerhard Wäscher,et al.  An improved typology of cutting and packing problems , 2007, Eur. J. Oper. Res..

[18]  Andreas Bortfeldt,et al.  Constraints in container loading - A state-of-the-art review , 2013, Eur. J. Oper. Res..

[19]  Reinaldo Morabito,et al.  An L-approach for packing (ℓ, w)-rectangles into rectangular and L-shaped pieces , 2003, J. Oper. Res. Soc..

[20]  Reinaldo Morabito,et al.  A note on an L-approach for solving the manufacturer's pallet loading problem , 2005, J. Oper. Res. Soc..

[21]  Maing-Kyu Kang,et al.  A fast algorithm for two-dimensional pallet loading problems of large size , 2001, Eur. J. Oper. Res..

[22]  Kathryn A. Dowsland.  A Combined Data-Base and Algorithmic Approach to the Pallet-Loading Problem , 1987 .

[23]  Kenneth Holmström,et al.  Computing stable loads for pallets , 2010, Eur. J. Oper. Res..

[24]  B. Ram.  The pallet loading problem: A survey , 1992 .