An Analysis of Solutions to the 2D Bin Packing Problem and Additional Complexities

Abstract

The Bin Packing problem in 2 space is an NP-Hard combinatorial problem in optimization of packing and arrangement of objects in a given space. It has a wide variety of applications ranging from logistics in retail industries to resource allocation in cloud computing. In this paper, we discuss the mathematical formulation of this problem. Furthermore, we analyse its time complexity, its NP-Hardness and some of its stochastic solutions with their efficiencies. We then propose additional complexities that would make the problem more fit for industrial use and discuss in depth the domains in which it might prove to be useful. We conclude while suggesting areas of improvement in operations research on this subject.