2D knapsack: Packing squares

Lan, Yan; Dósa, György; Han, Xin; Zhou, Chenyang; Benko, Attila

doi:10.1016/j.tcs.2012.07.035

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…The 2D-KP problem is one of the most classical problems in the combinatorial optimization field and has a lot of applications in the real world [28]. In the 2D-KP problem, each item has a corresponding profit, and one needs to select a subset of items to be packed in a single bin to maximize the total profit of selected items [22].…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In addition, the parameter λ is defined to determine the number of vehicles to be packed |I | based on the assumption 3), where λ is an arbitrary real number in (0, 1] in order to ensure that there are sufficient vehicles to be packed. Given a value of the parameter λ, there is a unique that meets inequalities (28) and (29) at the same time. The smaller the λ value, the larger |I | is.…”

Section: Computational Study a Experimental Designmentioning

confidence: 99%

See 1 more Smart Citation

A Two-Phase Stowage Approach for Passenger-Cargo RoRo Ship Based on 2D-KP: Coping With Complex Rotation and Safe Navigation Constraints

Hong-wei

et al. 2020

IEEE Access

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The passenger-cargo Roll on/Roll off ship stowage (PRSS) is the core step of passengercargo Roll on/Roll off (RoRo) transportation. The layout of vehicles in the cabin is directly related to the space utilization of the cabin and the efficiency of stowage operations, which in turn affects the economic benefits of the port. In this paper, we address the PRSS problem in the context of passenger-cargo RoRo transportation in the Qiongzhou Strait of China. By focusing on the utilization ratio of the cabin area, the PRSS problem can be viewed as a special version of a two-dimensional knapsack packing (2D-KP) problem with additional constraints, such as two-phase, complex rotation and safe navigation constraints. Then we present a mixed integer linear programming (MILP) mathematical model and an algorithm framework to tackle the PRSS problem. In the algorithm framework, a novel multi-phase heuristic stowage method is proposed to improve the current manual stowage decision-making state which completely depends on operational experience. Finally, several instances are generated based on the realistic date of Qiongzhou Strait to verify the effectiveness of the model and stowage method. Computational results show that the proposed model and stowage method are well suited to solve the PRSS problem and the algorithm framework has a strong robustness in large-scale application experiments. INDEX TERMS Maritime transportation, ship stowage planning, passenger-cargo roll-on/roll-off, twodimensional knapsack packing, multi-phase heuristic.

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Section: Problem Descriptionmentioning

confidence: 99%

Section: Computational Study a Experimental Designmentioning

confidence: 99%