Constraints in container loading - A state-of-the-art review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.

[1]  Anna Sciomachen,et al.  A 3D-BPP approach for optimising stowage plans and terminal productivity , 2007, Eur. J. Oper. Res..

[2]  Gleb Belov,et al.  Conservative scales in packing problems , 2013, OR Spectr..

[3]  Zhou-Jing Wang,et al.  A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach , 2008, Eur. J. Oper. Res..

[4]  Yoshiko Wakabayashi,et al.  Two- and three-dimensional parametric packing , 2005, Electron. Notes Discret. Math..

[5]  John Y. Cheung,et al.  Hybrid genetic algorithm for container packing in three dimensions , 1993, Proceedings of 9th IEEE Conference on Artificial Intelligence for Applications.

[6]  Yoshiko Wakabayashi,et al.  Three-dimensional packings with rotations , 2009, Comput. Oper. Res..

[7]  Chun-Cheng Lin,et al.  On the Three-Dimensional Container Packing Problem under Home Delivery Service , 2011, Asia Pac. J. Oper. Res..

[8]  Bryan Kok Ann Ngoi,et al.  Applying spatial representation techniques to the container packing problem , 1994 .

[9]  Lei Wu,et al.  A Linear Programming Approach for the Three-Dimensional Bin-Packing Problem , 2010, Electron. Notes Discret. Math..

[10]  E. E. Bischoff,et al.  Three-dimensional packing of items with limited load bearing strength , 2006, Eur. J. Oper. Res..

[11]  Bayram Kahraman THREE DIMENSIONAL CUTTING PROBLEM: AN INTEGER PROGRAMMING APPROACH , 2011 .

[12]  Tetsuo Sawaragi,et al.  A tree search method for the container loading problem with shipment priority , 2011, Eur. J. Oper. Res..

[13]  Michael Eley,et al.  Solving container loading problems by block arrangement , 2002, Eur. J. Oper. Res..

[14]  G. Abdou,et al.  Multi-layer palletisation of multi-size boxes , 1995 .

[15]  Eberhard E. Bischoff,et al.  Allowing for weight considerations in container loading , 1998 .

[16]  Reinaldo Morabito,et al.  MIP-based approaches for the container loading problem with multi-drop constraints , 2012, Ann. Oper. Res..

[17]  Yoshiko Wakabayashi,et al.  Cube packing , 2003, Theor. Comput. Sci..

[18]  Chen-Fu Chien,et al.  An efficient computational procedure for determining the container-loading pattern , 2009, Comput. Ind. Eng..

[19]  Keisuke Ishihara,et al.  A Tree Based Novel Representation for 3D-Block Packing , 2009, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[20]  M.S.W. Ratcliff,et al.  Loading pallets with non-identical items , 1995 .

[21]  Bogumił Kamiński,et al.  Nested vs. Joint Optimization of Vehicle Routing Problems with Three-dimensional Loading Constraints , 2010 .

[22]  Andrew Lim,et al.  A multi-faced buildup algorithm for three-dimensional packing problems , 2003 .

[23]  Loris Faina A global optimization algorithm for the three-dimensional packing problem , 2000, Eur. J. Oper. Res..

[24]  Nancy J. Ivancic An Integer Programming Based Heuristic Approach to the Three Dimensional Packing Problem , 1988 .

[25]  M.-K. Kang,et al.  Heuristics with a new block strategy for the single and multiple containers loading problems , 2010, J. Oper. Res. Soc..

[26]  Chin-Sheng Chen,et al.  An analytical model for the container loading problem , 1995 .

[27]  Daniel Mack,et al.  A heuristic for solving large bin packing problems in two and three dimensions , 2012, Central Eur. J. Oper. Res..

[28]  G. Scheithauer LP‐based bounds for the container and multi‐container loading problem , 1999 .

[29]  Katsuhisa Ohno,et al.  An Efficient Approach for the Three-Dimensional Container Packing Problem with Practical Constraints , 2004, Asia Pac. J. Oper. Res..

[30]  Reinaldo Morabito,et al.  An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container , 2002, Eur. J. Oper. Res..

[31]  Way Kuo,et al.  THREE DIMENSIONAL PALLETIZATION OF MIXED BOX SIZES , 1993 .

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

[33]  Tetsuo Sawaragi,et al.  A TOC-based heuristic algorithm for solving a two-row pattern container loading problem , 2007 .

[34]  Teodor Gabriel Crainic,et al.  Extreme Point-Based Heuristics for Three-Dimensional Bin Packing , 2008, INFORMS J. Comput..

[35]  Chen-Fu Chien,et al.  A container packing support system for determining and visualizing container packing patterns , 2004, Decis. Support Syst..

[36]  Jiamin Liu,et al.  A novel hybrid tabu search approach to container loading , 2011, Comput. Oper. Res..

[37]  Yuriy Stoyan,et al.  Packing congruent hyperspheres into a hypersphere , 2012, J. Glob. Optim..

[38]  Mhand Hifi,et al.  Approximate algorithms for the container loading problem , 2002 .

[39]  Marco A. Boschetti New lower bounds for the three-dimensional finite bin packing problem , 2004, Discret. Appl. Math..

[40]  Kin Keung Lai,et al.  Container packing in a multi-customer delivering operation , 1998 .

[41]  Uta Sommerweiß,et al.  Modeling of practical requirements of the distributers packing problem , 1996 .

[42]  Kun He,et al.  Solving the single-container loading problem by a fast heuristic method , 2010, Optim. Methods Softw..

[43]  José Fernando Oliveira,et al.  Cylinder packing by simulated annealing , 2000 .

[44]  Eberhard E. Bischoff,et al.  Weight distribution considerations in container loading , 1999, Eur. J. Oper. Res..

[45]  Leah Epstein,et al.  Dynamic multi-dimensional bin packing , 2010, J. Discrete Algorithms.

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

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

[48]  Graham Kendall,et al.  Automating the Packing Heuristic Design Process with Genetic Programming , 2012, Evolutionary Computation.

[49]  Pius J. Egbelu,et al.  A heuristic approach to the three-dimensional cargo-loading problem , 1989 .

[50]  Nelson Maculan,et al.  A greedy search for the three‐dimensional bin packing problem: the packing static stability case , 2003 .

[51]  Hermann Gehring,et al.  Zur Behandlung von Restriktionen bei der Stauraumoptimierung am Beispiel eines genetischen Algorithmus für das Containerbeladeproblem , 1999 .

[52]  Klaus Jansen,et al.  An asymptotic approximation algorithm for 3D-strip packing , 2006, SODA '06.

[53]  Daniele Vigo,et al.  The Three-Dimensional Bin Packing Problem , 2000, Oper. Res..

[54]  W. Dowsland Three-dimensional packing—solution approaches and heuristic development , 1991 .

[55]  Ramón Alvarez-Valdés,et al.  Neighborhood structures for the container loading problem: a VNS implementation , 2010, J. Heuristics.

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

[57]  Ramón Alvarez-Valdés,et al.  A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing , 2010, Ann. Oper. Res..

[58]  Jens Egeblad,et al.  Heuristics for container loading of furniture , 2010, Eur. J. Oper. Res..

[59]  Ramzi A. Haraty,et al.  Smart container loading , 2010, J. Comput. Methods Sci. Eng..

[60]  Hermann Gehring,et al.  A hybrid genetic algorithm for the container loading problem , 2001, Eur. J. Oper. Res..

[61]  A. Moura,et al.  A GRASP approach to the container-loading problem , 2005, IEEE Intelligent Systems.

[62]  Türkay Dereli,et al.  A HYBRID SIMULATED ANNEALING ALGORITHM FOR SOLVING MULTI-OBJECTIVE CONTAINER-LOADING PROBLEMS , 2010, Appl. Artif. Intell..

[63]  Mhand Hifi Exact algorithms for unconstrained three-dimensional cutting problems: a comparative study , 2004, Comput. Oper. Res..

[64]  Yoshiko Wakabayashi,et al.  Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing , 2012, Comput. Oper. Res..

[65]  Sándor P. Fekete,et al.  An Exact Algorithm for Higher-Dimensional Orthogonal Packing , 2006, Oper. Res..

[66]  Wallace Kit-Sang Tang,et al.  A hybrid genetic approach for container loading in logistics industry , 2005, IEEE Transactions on Industrial Electronics.

[67]  Kun He,et al.  A caving degree based flake arrangement approach for the container loading problem , 2010, Comput. Ind. Eng..

[68]  Manuel Iori,et al.  Rejoinder on: Routing problems with loading constraints , 2010 .

[69]  Daniel Mack,et al.  A heuristic for the three-dimensional strip packing problem , 2007, Eur. J. Oper. Res..

[70]  Andrew Lim,et al.  Two Natural Heuristics for 3D Packing with Practical Loading Constraints , 2010, PRICAI.

[71]  Hermann Gehring,et al.  Greedy Algorithms for Packing Unequal Spheres into a Cuboidal Strip or a Cuboid , 2011, Asia Pac. J. Oper. Res..

[72]  Yang Dai,et al.  Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D , 2002 .

[73]  Guntram Scheithauer Algorithms for the Container Loading Problem , 1992 .

[74]  V. Armentano,et al.  A multi-start random constructive heuristic for the container loading problem , 2007 .

[75]  Anulark Techanitisawad,et al.  A GA-based Heuristic for the Interrelated Container Selection Loading Problems , 2004 .

[76]  Jan Riehme,et al.  An efficient approach for the multi-pallet loading problem , 2000, Eur. J. Oper. Res..

[77]  Daniele Vigo,et al.  Heuristic algorithms for the three-dimensional bin packing problem , 2002, Eur. J. Oper. Res..

[78]  Daniele Vigo,et al.  Erratum to "The Three-Dimensional Bin Packing Problem": Robot-Packable and Orthogonal Variants of Packing Problems , 2005, Oper. Res..

[79]  Henrik I. Christensen,et al.  Using Simulation to Assess the Effectiveness of Pallet Stacking Methods , 2010, SIMPAR.

[80]  Kevin W. Li,et al.  Layer-layout-based heuristics for loading homogeneous items into a single container , 2007 .

[81]  Sara Ceschia,et al.  Local search for a multi-drop multi-container loading problem , 2013, J. Heuristics.

[82]  Jong Mau Yeh,et al.  Applying genetic algorithms and neural networks to the container loading problem , 2003 .

[83]  David Pisinger,et al.  Heuristics for the container loading problem , 2002, Eur. J. Oper. Res..

[84]  Ana Moura,et al.  An integrated approach to the vehicle routing and container loading problems , 2009, OR Spectr..

[85]  E. E. Bischoff,et al.  Issues in the development of approaches to container loading , 1995 .

[86]  Yoshiko Wakabayashi,et al.  Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem , 1999, SIAM J. Comput..

[87]  J.-F. Tsai,et al.  A distributed global optimization method for packing problems , 2003, J. Oper. Res. Soc..

[88]  Yoshiko Wakabayashi,et al.  An algorithm for the three-dimensional packing problem with asymptotic performance analysis , 1997, Algorithmica.

[89]  Andrew Lim,et al.  3-D Container Packing Heuristics , 2005, Applied Intelligence.

[90]  G. Abdou,et al.  3D random stacking of weakly heterogeneous palletization problems , 1999 .

[91]  Kun He,et al.  An efficient placement heuristic for three-dimensional rectangular packing , 2011, Comput. Oper. Res..

[92]  Eberhard E. Bischoff,et al.  A comparative evaluation of heuristics for container loading , 1990 .

[93]  Manoj Kumar Tiwari,et al.  Development of a decision support system for air-cargo pallets loading problem: A case study , 2006, Expert Syst. Appl..

[94]  E. E. Bischoff,et al.  Loading Multiple Pallets , 1995 .

[95]  Hamish J. Fraser,et al.  Integrated container loading software for pulp and paper industry , 1994 .

[96]  Michael Eley A bottleneck assignment approach to the multiple container loading problem , 2003 .

[97]  Kam-Hoi Cheng,et al.  On Three-Dimensional Packing , 1990, SIAM J. Comput..

[98]  James T. Moore,et al.  The Distributer's Three-Dimensional Pallet-Packing Problem: A Human Intelligence-Based Heuristic Approach , 2012 .

[99]  Ernesto G. Birgin,et al.  Minimizing the object dimensions in circle and sphere packing problems , 2008, Comput. Oper. Res..

[100]  Chen-Fu Chien,et al.  A framework of modularized heuristics for determining the container loading patterns , 1999 .

[101]  Andrew Lim,et al.  A Heuristic for the Multiple Container Loading Cost Minimization Problem , 2011, IEA/AIE.

[102]  Shih-Wei Huang,et al.  A Hybrid Meta-Heuristic for the Container Loading Problem , 2007 .

[103]  Guochuan Zhang,et al.  Harmonic algorithm for 3-dimensional strip packing problem , 2007, SODA '07.

[104]  Michel Gendreau,et al.  A Tabu Search Algorithm for a Routing and Container Loading Problem , 2006, Transp. Sci..

[105]  Hermann Gehring,et al.  A Parallel Genetic Algorithm for Solving the Container Loading Problem , 2002 .

[106]  G. Abdou,et al.  Interactive ILP procedures for stacking optimization for the 3D palletization problem , 1997 .

[107]  Roger L. Wainwright,et al.  A genetic algorithm for packing in three dimensions , 1992, SAC '92.

[108]  Reinaldo Morabito,et al.  An AND/OR-graph Approach to the Container Loading Problem , 1994 .

[109]  Reinaldo Morabito,et al.  Three-dimensional container loading models with cargo stability and load bearing constraints , 2012, Comput. Oper. Res..

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

[111]  Ramón Alvarez-Valdés,et al.  A Maximal-Space Algorithm for the Container Loading Problem , 2008, INFORMS J. Comput..

[112]  Jens Egeblad,et al.  Heuristic approaches for the two- and three-dimensional knapsack packing problem , 2009, Comput. Oper. Res..

[113]  Emmanouil E. Zachariadis,et al.  A Hybrid Metaheuristic Algorithm for the Integrated Vehicle Routing and Three-Dimensional Container-Loading Problem , 2009, IEEE Transactions on Intelligent Transportation Systems.

[114]  Andrew Lim,et al.  The multiple container loading cost minimization problem , 2011, Eur. J. Oper. Res..

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

[116]  Lazaros G. Papageorgiou,et al.  A problem formulation for optimal mixed-sized box packing , 2005 .

[117]  Jens Egeblad,et al.  Fast neighborhood search for two- and three-dimensional nesting problems , 2007, Eur. J. Oper. Res..

[118]  J. A. George,et al.  A Method for Solving Container Packing for a Single Size of Box , 1992 .

[119]  Guenther Fuellerer,et al.  Metaheuristics for vehicle routing problems with three-dimensional loading constraints , 2010, Eur. J. Oper. Res..

[120]  Daniele Vigo,et al.  TSpack: A Unified Tabu Search Code for Multi-Dimensional Bin Packing Problems , 2004, Ann. Oper. Res..

[121]  Jie Wang,et al.  Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning , 1999, J. Comb. Optim..

[122]  Teodor Gabriel Crainic,et al.  TS2PACK: A two-level tabu search for the three-dimensional bin packing problem , 2009, Eur. J. Oper. Res..

[123]  Kam-Hoi Cheng,et al.  Heuristic Algorithms for On-Line Packing in Three Dimensions , 1992, J. Algorithms.

[124]  Kun He,et al.  A caving degree approach for the single container loading problem , 2009, Eur. J. Oper. Res..

[125]  Søren Gram Christensen,et al.  Container loading with multi-drop constraints , 2009, Int. Trans. Oper. Res..

[126]  Marisa B. Figueiredo,et al.  A particular approach for the Three-dimensional Packing Problem with additional constraints , 2010, Comput. Oper. Res..

[127]  Sándor P. Fekete,et al.  A New Exact Algorithm for General Orthogonal D-Dimensional Knapsack Problems , 1997, ESA.

[128]  Kamlesh Mathur,et al.  Value considerations in three-dimensional packing -- A heuristic procedure using the fractional knapsack problem , 1994 .

[129]  Kun He,et al.  A new heuristic algorithm for cuboids packing with no orientation constraints , 2009, Comput. Oper. Res..

[130]  Andreas Bortfeldt,et al.  A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints , 2012, Comput. Oper. Res..

[131]  D. Mack,et al.  A parallel hybrid local search algorithm for the container loading problem , 2004 .

[132]  Jens Egeblad,et al.  Translational packing of arbitrary polytopes , 2009, Comput. Geom..

[133]  Chen-Fu Chien,et al.  A recursive computational procedure for container loading , 1998 .

[134]  G. Abdou,et al.  A SYSTEMATIC APPROACH FOR THE THREE-DIMENSIONAL PALLETIZATION PROBLEM , 1994 .

[135]  Graham Kendall,et al.  A hybrid placement strategy for the three-dimensional strip packing problem , 2011, Eur. J. Oper. Res..

[136]  Andreas Bortfeldt,et al.  A Tree Search Algorithm for Solving the Container Loading Problem , 2010, INFORMS J. Comput..

[137]  Guntram Scheithauer A Three-dimensional Bin Packing Algorithm , 1991, J. Inf. Process. Cybern..

[138]  Du-Ming Tsai Modeling and analysis of three-dimensional robotic palletizing systems for mixed carton sizes , 1987 .

[139]  Eberhard Girlich,et al.  Zur Effektivität von Gradientenverfahren für Zuschnittprobleme , 1994 .

[140]  Manuel Iori,et al.  Routing problems with loading constraints , 2010 .

[141]  Manfred W. Padberg,et al.  Packing small boxes into a big box , 2000, Math. Methods Oper. Res..

[142]  David Pisinger,et al.  Guided Local Search for the Three-Dimensional Bin-Packing Problem , 2003, INFORMS J. Comput..

[143]  Robert W. Haessler,et al.  Load planning for shipments of low density products , 1990 .

[144]  Daniele Vigo,et al.  Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem , 2007, TOMS.

[145]  M. Meyer,et al.  A computer-based heuristic for packing pooled shipment containers , 1990 .

[146]  Daniel Mack,et al.  A parallel tabu search algorithm for solving the container loading problem , 2003, Parallel Comput..

[147]  Andrew Lim,et al.  The container loading problem , 2005, SAC '05.

[148]  Jin-Ling Lin,et al.  A Study of Optimal System for Multiple-Constraint Multiple-Container Packing Problems , 2006, IEA/AIE.

[149]  Katsuhisa Ohno,et al.  The Three-Dimensional Bin Packing Problem and Its Practical Algorithm , 2003 .

[150]  Andrew Lim,et al.  Space Defragmentation Heuristic for 2D and 3D Bin Packing Problems , 2011, IJCAI.

[151]  Philippe Grégoire,et al.  A General Purpose Algorithm for Three-Dimensional Packing , 2005, INFORMS J. Comput..

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

[153]  David Pisinger,et al.  Multi-dimensional bin packing problems with guillotine constraints , 2010, Comput. Oper. Res..

[154]  Kun He,et al.  An Efficient Algorithm for Solving the Container Loading Problem , 2007, ESCAPE.

[155]  Tetsuo Sawaragi,et al.  A priority-considering approach for the multiple container loading problem , 2011, Int. J. Metaheuristics.

[156]  Olli Nevalainen,et al.  On-line packing with boxes of different sizes , 1998 .

[157]  Lazaros G. Papageorgiou,et al.  A MILP model for N-dimensional allocation , 2007, Comput. Chem. Eng..

[158]  Chung-Shou Liao,et al.  New Lower Bounds for the Three-dimensional Orthogonal Bin Packing Problem , 2013, CCCG.

[159]  Mauricio G. C. Resende,et al.  A parallel multi-population biased random-key genetic algorithm for a container loading problem , 2012, Comput. Oper. Res..