fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

Abstract

The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimization problems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting in relaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.

Conscious Exploration of Alpha-Cuts in the Parametric Solution of the School Bus Routing Problem with Fuzzy Walking Distance

“…Authors who use the parametric approach to solve fuzzy problems usually use a uniform method to establish the aforementioned alpha-cuts, such is the case of [ 7 , 9 , 31 ]. On the other hand, in [ 16 ], an adaptive method is proposed where the alpha-cuts are calculated similarly to a binary search.…”

“…Thus, certain levels of uncertainty need to be introduced [ 6 ]. Numerous authors have employed fuzzy elements to model optimization problems [ 7 – 11 ]. In particular, there are several engaging solutions to transportation planning problems, like the numerous variants of the Vehicle Routing Problem (VRP) [ 12 – 14 ].…”