Two heuristics for the label printing problem

Abstract

The label printing problem (LPP) arises in the printing industry, where we have a set of labels that require printing. Each one has different demands and must be printed using a single template. The number of labels we can allocate in a template is a fixed one, and the number of templates varies in a small range of different sizes. The goal of the LPP is to design templates to meet the demands for the labels while minimizing the percentage of material wasted. In each grid, the need for each printed cover must be met to facilitate label management. To deal with LPP, we used two known metaheuristics: a threshold accepting and a tabu search. These heuristics, with the aid of a Hill climbing double neighborhood, improved the results significantly.

An integer linear programming model for the label printing problem

“…One thus has mn quadratic terms in such a model. In another research, Alonso-Pecina et al (2022) propose a nonlinear model based on 2 m binary vectors. The number of quadratic terms in their model is (2m + 1)2 m .…”

“…The demands of the next four labels are 3850, 1400, 2700, and 1400, respectively. Alonso-Pecina et al (2022) propose five sets of instances, namely L001, L002, R001, R002, and R003. For the instances in L001 and L002, the value of n also ranges in {4, 5, 6}.…”

“…In a recent paper, Alonso-Pecina et al ( 2022) collect six sets of benchmark instances from the literature and propose five other ones. For the convenience of description, we shall adopt and extend the notation used in Alonso-Pecina et al (2022) to describe these 11 sets of benchmark instances. The extended notation is of the form set_name (m, t, n), where set_name is the name of the set while m, t, n are those just defined.…”

Preparation and properties of alcohol‐resistant thermal transfer printing inks for multifunctional label printing via physical blending of resins

“…Among them, the application of nanoparticles in thermal transfer printing has received widespread attention. [10][11][12] Thermal transfer technology is a printing method based on gravure printing 13,14 ; this particular technique offers excellent pattern fidelity with regard to resolution and print speed and can print clearly on a variety of different types of labels. [15][16][17][18] And thermal transfer technology is easy to use as a simple operation.…”

“…For a few decades, chemical synthesis of nanomaterials and composite nanomaterials have been observed and performed in numerous applications, including energy storage, 1,2 environmental remediation, 3,4 catalysis, 5–7 medicine and therapy, 8,9 etc. Among them, the application of nanoparticles in thermal transfer printing has received widespread attention 10–12 . Thermal transfer technology is a printing method based on gravure printing 13,14 ; this particular technique offers excellent pattern fidelity with regard to resolution and print speed and can print clearly on a variety of different types of labels 15–18 .…”