One-Dimensional Bin-Packing Problems with Branch and Bound Algorithm

In this paper, our objective is to develop a mathematical formulation of solving the Bin Packing Problem (BPP) with different sizes of box. It has become one of the most important mathematical applications throughout the time. In our study, Modified Branch and Bound Algorithm (MBBA) is developed to generate all the feasible packing patterns of given boxes to required containers for One-Dimensional BPP. Further development of algorithms was made to ascertain the locations of each box within the containers by using Cartesian coordinate system. Developed algorithms are coded and programmed in the Python programming environment to generate feasible packing patterns.