A Fuzzy Logic Classifier for the Three Dimensional Bin Packing Problem Deriving From Package Delivery Companies Application

A Fuzzy Logic Classifier for the Three Dimensional Bin Packing Problem Deriving From Package Delivery Companies Application

Paula Hernández Hernández (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico), Norberto Castillo-García (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico), Edilberto Rodríguez Larkins (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico), Jorge Gilberto Guerrero Ruiz (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico), Selene Valeria Morales Díaz (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico) and Erick Sobrevilla Resendiz (National Institute of Technology of Mexico, Mexico & Instituto Tecnológico Altamira, Mexico)
DOI: 10.4018/978-1-5225-8131-4.ch025

Abstract

One of the most common operations in warehouses of package delivery companies (e.g., UPS or FedEx) is to pack the products in trucks in order to locally deliver them to the customers. The products are generally packed in rectangular boxes of different dimensions. An efficient assignment of boxes to delivery trucks must consider the minimization of the number of trucks required. Thus, a considerable amount of fuel is saved, and hence, the delivery time and pollution are reduced. This efficient assignment can be viewed as an application of the well-known three-dimensional bin packing problem (3D-BPP). In this chapter, the authors propose a methodology based on fuzzy logic classification (FLC) to solve 3D-BPP. The FLC assigns a class to each box to be delivered according to their relative proximity. The goal is to contiguously assign the boxes whose destinations are as close as possible.
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Fuzzy Logic Classifier

Classification of Pair of Boxes

The classification of each pair of boxes according to their relative proximity is performed by a fuzzy logic classifier. We use fuzzy logic since it can model real-life situations in a more natural way and it does not require any mathematical formulation to model the phenomenon. Thus, for example, fuzzy logic allows us to classify some pair of boxes as “proximate” or “distant”. Our fuzzy logic classifier uses the following five classes:

  • C1 is the first class. It contains all pair of boxes whose geographic distance is very low.

  • C2 is the second class. It contains all pair of boxes whose geographic distance is low.

  • C3 is the third class. It contains all pair of boxes whose geographic distance is medium.

  • C4 is the fourth class. It contains all pair of boxes whose geographic distance is high.

  • C5 is the fifth class. It contains all pair of boxes whose geographic distance is very high.

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