A Mathematical formulation and a lower bound for the three-dimensional multiple-bin-size bin packing problem (MBSBPP): A Tunisian industrial case

Abstract

In our research, we are interested in the three-dimensional multiple-bin-size bin packing problem (MBSBPP). We deal with the real word application of cutting mousse blocks proposed by a Tunisian industrial company. First, we present the general context related to our optimization problem. Second we formulate it as a mathematical problem without considering the guillotine constraint, and then we tested it on small instances taken from the industry. Thereafter, we propose and test a lower bound for large instances from the same industrial company. Finally, some computational results are presented.

An Efficient Constructive Heuristic for the Cutting Stock Problem Applied in a Foam Mattress Industry

“…The feasible solution of the MILP able to provide an upper bound for the problem, but the attained results are only presented for properly small size instances compared with the company demand. Baazaoui et al (2014) also proposed a lower bound. They used these two bounds to restrict the optimum value between two values and get it for some small instances.…”