On the Impact of Fuzzy Constraints in the Variable Size and Cost Bin Packing Problem

The Variable Size and Cost Bin Packing Problem (VSCBPP) consists of minimizing the cost of all bins used to pack a set of items without exceeding the bins capacities. It is a well known NP-Hard problem with many practical applications. In this contribution we assume that the capacity of a bin can be understood in a flexible way (so it may allow some overload) thus leading to a fuzzy version of the VSCBPP with fuzzy constraints. We solve the proposed fuzzy VSCBPP by using the parametric approach based on [Formula: see text]-cuts, thus defining a set of related crisp problems. By using three different solving algorithms and several instances, we explore the impact of different degrees of relaxation not only in terms of cost, but also in the structure of the solutions.