Solving Logistic-Oriented Bin Packing Problems Through a Hybrid Quantum-Classical Approach

TL;DR

This work resorts to the previously published quantum-classical framework known as Q4RealBPP, and elaborate on the solving of real-world oriented instances of the Bin Packing Problem, and gravitates on the existence of heterogeneous bins.

Abstract

The Bin Packing Problem is a classic problem with wide industrial applicability. In fact, the efficient packing of items into bins is one of the toughest challenges in many logistic corporations and is a critical issue for reducing storage costs or improving vehicle space allocation. In this work, we resort to our previously published quantum-classical framework known as Q4RealBPP, and elaborate on the solving of real-world oriented instances of the Bin Packing Problem. With this purpose, this paper gravitates on the following characteristics: i) the existence of heterogeneous bins, ii) the extension of the framework to solve not only three-dimensional, but also one- and two-dimensional instances of the problem, iii) requirements for item-bin associations, and iv) delivery priorities. All these features have been tested in this paper, as well as the ability of Q4RealBPP to solve real-world oriented instances.

Figures (7)

• Figure 1: Orientations $k\in K_i$ for an item $i$ of dimensions $(l_i,w_i)$.
• Figure 2: Scheme of $b_{i,k,q}$ activated for relative positions $q\in Q$ among items $i,k\in I$. Both are in contact but it is not mandatory.
• Figure 3: Solutions provided by Q4RealBPP for the instances deeming heterogeneous bins.
• Figure 4: Solutions provided by Q4RealBPP for the instances deeming requirements for item-bin associations. Bin ids are {0,1,2}, being id=0 the rightmost one, and id=2 the leftmost one.
• Figure 5: Solutions provided by Q4RealBPP for the instances considering delivery priorities.