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Updated: Nov 21, 2025

Design and Optimization Strategies of a High-Performance Vented Box

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Published on: June 9, 2023

Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology.

Nestor M Cid-Garcia¹, Yasmin A Rios-Solis²

¹Laboratorio Nacional de Geointeligencia, CONACYT-Centro de Investigación en Ciencias de Información Geoespacial, Aguascalientes, Aguascalientes, Mexico.

|January 14, 2021

Summary

This study introduces an exact method for the 2D strip packing problem, finding optimal solutions for packing rectangular items to minimize strip height. The Positions and Covering methodology proves effective for various instance sizes.

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Area of Science:

Operations Research
Combinatorial Optimization

Background:

The two-dimensional, non-guillotine restricted, strip packing problem is a classical NP-hard problem.
Objective is to minimize the height of a strip with fixed width and infinite height, given a set of rectangular items.

Purpose of the Study:

To develop an exact methodology for solving the 2D strip packing problem.
To obtain optimal solutions for instances where the optimal solution was previously unknown.

Main Methods:

The Positions and Covering methodology, a two-stage procedure.
Stage 1: Pseudo-polynomial generation of valid item positions.
Stage 2: Set-covering formulation to select the optimal item configuration.

Main Results:

The methodology yields exact solutions for the strip packing problem.
Experimental results validate the quality and effectiveness for small to medium-sized instances.
Optimal solutions were found for previously unsolved literature instances.

Conclusions:

The Positions and Covering methodology is a powerful approach for the 2D strip packing problem.
This method advances the field by providing optimal solutions for challenging instances.
The approach demonstrates effectiveness and potential for practical applications.