Modified Integer Linear Programming Model for Bin-Packing Problems
bin-packing problem, modified branch and bound algorithm, integer linear programming model, matlab software environment
Abstract
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.
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References
P Gilmore, R Gomory (1961) A Linear Programming Approach to the Cutting Stock Problem. 9(2), 849-859.
P Gilmore, R Gomory (1963) A Linear Programming Approach to the Cutting Stock Problem-Part II. 11(6), 863-888.
T Dokeroglu, M Bayir, A Cosar (2014) Integer linear programming solution for the multiple query optimization problem. 51-60.
B Christian, S Verena (2013) Solving the 2D bin packing problem by means of a Hybrid Evolutionary Algorithm. 899-908.
Jakob Puchinger, Günther Raidl, Gabriele Koller (2004) Solving a Real-World Glass Cutting Problem. 165-176.
W Rodrigo, W Daundasekera, A Perera (2012) A Method for Two-Dimensional Cutting Stock Problem with Triangular Shape Items. 3(4), 750-771.
Wnp Rodrigo, W Daundasekera, Aai Perera (2012) Pattern Generation for Two-Dimensional Cutting Stock Problem with Location. 3(2), 354-368.
Sisca Octarina, Vinny Ananda, Evi Yuliza (2019) Gilmore and gomory model on two dimensional multiple stock size cutting stock problem. 1282(1), 012015.
L Fern´andez, L Fern´andez, C Pola (2010) Integer Solutions to Cutting Stock Problems.
N Jatinder, Johnny Gupta (1999) A new heuristic algorithm for the onedimensional bin-packing problem. 10(6), 598-603.
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2020-12-15
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