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A mixed-integer linear model for the Multiple Heterogeneous Knapsack Problem with realistic container loading constraints and bins’ priority

Deplano, I, Lersteau, C and Nguyen, TT A mixed-integer linear model for the Multiple Heterogeneous Knapsack Problem with realistic container loading constraints and bins’ priority. International Transactions in Operational Research. ISSN 0969-6016 (Accepted)

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Abstract

We propose a mixed-integer linear model that solves the Multiple Heterogeneous Knapsack Problem, minimising the wasted space of the bins, taking into account their priority, and considering the following constraints: non overlapping, boundaries and positioning (both constrained and free), rotations (around the vertical axis), orthogonal displacement, weight limit, static stability, weight distribution in a pyramidal region and load bearing considering items’ arbitrary centre of mass. In the experiments, the priority parameter is set to prioritize smaller bins, but the model is generic to cover other cases. We study the trade-off of adding more constraints to make the problem more realistic and the complexity of finding a solution. We introduce new metrics that facilitate the comparison of datasets used in experiments. These metrics allow the export of theoretical results in the industry. We also propose a constructive heuristic named Weight First Best Fit to handle large scale instances in a reasonable time.

Item Type: Article
Uncontrolled Keywords: 0102 Applied Mathematics, 0806 Information Systems, 1503 Business and Management
Subjects: H Social Sciences > HE Transportation and Communications
T Technology > T Technology (General)
Divisions: Maritime & Mechanical Engineering
Publisher: Wiley
Date Deposited: 14 Oct 2019 09:05
Last Modified: 14 Oct 2019 09:05
URI: http://researchonline.ljmu.ac.uk/id/eprint/11537

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