A Linear Programming Approach for the Three-Dimensional Bin-Packing Problem

Local branching-based algorithms for the disjunctively constrained knapsack problem

“…The use of ILP is a natural approach for formulating several problems where it is necessary to optimize the system characterizing the constraints, the integrality constraints and the objective. Such ILP models play a central role for solving a wide range of combinatorial optimization problems, including cutting and packing (cf., Hifi, Negre Kacem, & Wu, 2010), vehicle routing (cf., Baldacci, Toth, & Vigo, 2010;Iori, Salazar González, & Vigo, 2007), knapsacks (cf., Cherfi & Hifi, 2010;Puchinger, Raidl, & Pferschy, 2010) and other operations research problems. Furthermore, several of these combinatorial optimization problems cannot be solved exactly within a reasonable amount of time.…”

Hybrid greedy heuristics based on linear programming for the three‐dimensional single bin‐size bin packing problem

“…We propose to approximately solve the problem by considering the mathematical model already presented in Hifi et al. (). In fact, the mathematical model was proposed especially for computing a new lower bound, that is, a value obtained by injecting successive valid constraints.…”

“…Indeed, as considered in Hifi et al. (), several valid constraints have been introduced to an ILP for increasing the quality of the provided lower bound (i.e., the continuous bound). Herein, we try to exploit such a lower bound, by combining mathematical models and greedy procedures, in order to approximately solve the problem.…”

Estivagem de unidades de celulose via modelo de corte e empacotamento.

“…Nesse contexto, Hifi et al (2010) foram alguns dos autores que desenvolveram modelos com conceitos similares ao trabalho citado anteriormente. Hifi et al (2010) abordaram o problema do Bin Packing em três dimensões (3 − ). Nesse tipo de problema busca-se minimizar o número total de bins utilizados para alocar todos os itens disponíveis.…”

“…Nesse tipo de problema busca-se minimizar o número total de bins utilizados para alocar todos os itens disponíveis. Apesar das diferenças entre o problema tratado pelos autores e o problema abordado pelo presente trabalho (PEUC), o modelo de Hifi et al (2010) pode ser adaptado para o caso do Problema de Estivagem de Unidades de Celulose. Sendo assim, faz-se necessário apresentar de forma mais detalhada o modelo de Hifi et al (2010).…”