Modified Integer Linear Programming Model for Bin-Packing Problems (Global Journal of Science Frontier Research, 2020)
In this paper, our objective is to compare the solutions obtained from develop mathematical model and general model for Two-Dimensional Bin Packing Problem (BPP) with different sizes of boxes. 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 Two-Dimensional BPP. A computer program is developed using Matlab software package to generate feasible packing patterns and optimum packing plan. As a case study, three different sizes of rectangular shape packing items are selected with given demand in order to pack into two different sizes of pallets. Applying the proposed algorithm, demand is satisfied and total unused area significantly minimized. Accordingly, proposed mathematical model is more appropriate for medium size two dimensional BPP.
Keywords: bin-packing problem; modified branch and bound algorithm; integer linear programming model; matlab software environment