The pinwheel pattern and its application to the manufacturer's pallet-loading problem

To solve the manufacturer's pallet-loading problem (MPLP), pallet-loading patterns with regular, sound and optimum number layouts should be presented. In this paper, we present a pinwheel pattern as an alternative solution to the pallet-loading problem. The definition, elements, categories, and practical advantages, generating algorithms of the pinwheel patterns, are discussed, and a uniform notation is proposed. With the ranges for all pinwheel instances within an area ratio no more than 76 boxes calculated, the study of geometry shows that each pinwheel pattern has a specific range of box ratio, and it may achieve optimality. The pinwheel pattern can be found for all non-prime numbers of boxes. Further discussions are focused on the dataset, loophole constraint and asymmetric pinwheels. The study suggests that the pinwheel pattern is an advantageous alternative to implement the MPLP.

[1]  Heinrich Exeler,et al.  Das homogene Packproblem in der betriebswirtschaftlichen Logistik , 1988 .

[2]  Mike Wright,et al.  Experiments with a strategic oscillation algorithm for the pallet loading problem , 2001 .

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

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

[5]  Eberhard E. Bischoff.  Stability aspects of pallet loading , 1991 .

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

[7]  William B. Dowsland.  On a Research Bibliography for Cutting and Packing Problems , 1992 .

[8]  Kathryn A. Dowsland,et al.  A family of genetic algorithms for the pallet loading problem , 1996, Ann. Oper. Res..

[9]  Hermann Gehring,et al.  A Genetic Algorithm for Solving the Container Loading Problem , 1997 .

[10]  E. Bischoff,et al.  An Application of the Micro to Product Design and Distribution , 1982 .

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

[12]  M. Arenales,et al.  An AND/OR-graph approach to the solution of two-dimensional non-guillotine cutting problems , 1995 .

[13]  Fuh-Hwa F. Liu,et al.  A three-dimensional pallet loading method for single-size boxes , 1997 .

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

[15]  Reinaldo Morabito,et al.  Loading optimization of palletized products on trucks , 2000 .

[16]  José Mario Martínez,et al.  Optimizing the packing of cylinders into a rectangular container: A nonlinear approach , 2005, Eur. J. Oper. Res..

[17]  Josef Neliβen.  How to use structural constraints to compute an upper bound for the pallet loading problem , 1995 .

[18]  Harold J. Steudel,et al.  Generating Pallet Loading Patterns: A Special Case of the Two-Dimensional Cutting Stock Problem , 1979 .

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

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

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

[22]  Reinaldo Morabito,et al.  A Tight Lagrangean Relaxation Bound for the Manufacturer's Pallet Loading Problem , 2002, Stud. Inform. Univ..

[23]  Adrian Smith,et al.  An Algorithm to Optimize the Layout of Boxes in Pallets , 1980 .

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

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

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

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

[28]  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 .

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

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

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

[32]  Subir Bhattacharya,et al.  An exact depth-first algorithm for the pallet loading problem , 1998, Eur. J. Oper. Res..

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