The minimum size instance of a Pallet Loading Problem equivalence class

Solving the pallet loading problem

“…The time required to find relaxed classes is proportional to the number of efficient partitions and to the time required to find the MSI of a class (Martins and Dell, 2007). The procedure increases each efficient partition by one unit, of a or b, depending on the case, and computes the MSI of the resulting relaxed class, if feasible.…”

“…Performance of selected heuristics and easily computed bounds Martins and Dell (2007) show the set of all PLP instances with an area ratio (pallet area divided by box area) less than 101 boxes can be represented by 3,080,730 equivalent classes. For each equivalence class, we compute the MP, MAR, and Barnes bound.…”

“…Dowsland (1984) establishes that PLP instances can be divided into classes with the same optimal placement pattern. Martins and Dell (2007) one MSI, and then enumerate all 3,080,730 equivalence classes with an area ratio (pallet area divided by box area) smaller than 101 boxes. The complete set of instances can be accessed at http://www.palletloading.org.…”

An improved best-first branch and bound algorithm for the pallet-loading problem using a staircase structure

“…Beasley (1985) proposed an exact algorithm using a 0-1 mathematical model, Dowsland (1987) solved the PLP using graph theory, Bhattacharya, Roy, and Bhattacharya (1998) proposed the maximal breadth filling sequence depth-first algorithm, and Alvarez-Valdes, Parreno, and Tamarit (2005) proposed a branch-and-cut algorithm, and Lau et al (2009) proposed a hybrid approach for the multi-pallet loading operations. Martins and Dell (2007) reported the set of all PLP instances with an area ratio (pallet area divided by box area) of less than 101 boxes, which is represented by 3,080,730 classes. Martins and Dell (2008) proposed an exact algorithm using HVZ coding (H, V, Z represent horizontal box, vertical box and zero, respectively.…”

Pallet Consolidation Problems in Distribution Centers

“…They exploit the specific structure of the PLP to define the solution graph and develop efficient separation procedures. Martins and Dell (2007) define the Minimum Size Instance (MSI) of an equivalence class of PLP and present an algorithm for MSI. Martins and Dell (2008) present new bounds, heuristics, and an exact algorithm for the MPL The set of all PLP instances with an area ratio (pallet area divided by box area) less than 101 boxes can be represented by 3,080,730 equivalent classes.…”