Abstract
Problem statement: Cutting and packing (C and P) problems are optimization problems that are concerned in finding a good arrangement of multiple small items into one or more larger objects. Bin packing problem is a type of C AND P problems. Bin packing problem is an important industrial problem where the general objective is to reduce the production costs by maximizing the utilization of the larger objects and minimizing the material used. Approach: In this study, we considered both oriented and non-oriented cases of Two-Dimensional Bin Packing Problem (2DBPP) where a given set of small rectangles (items), was packed without overlaps into a minimum number of identical large rectangles (bins). We proposed heuristic placement routines called the Improved Lowest Gap Fill, LGFi and LGFiOF for solving non-oriented and oriented cases of 2DBPP respectively. Extensive computational experiments using benchmark data sets collected from the literature were conducted to assess the effectiveness of the proposed routines. Results: The computational results were compared with some well known heuristic placement routines. The results showed that the LGFi and LGFiOF are competitive when compared with other heuristic placement routines. Conclusion: Both LGFi and LGFiOF produced better packing quality compared to other heuristic placement routines.
Highlights
Cutting and Packing (C and P) Problems can be summarized as follows[10]:“Given two sets of elements, namely, a set of large objects and a set of small items which are defined in one, two, or an even larger number of geometric dimensions
The objective of this study is to develop an improved version of the Lowest Gap Fill (LGF) routine proposed by Lee[7] for 2DBPP
Heuristic placement routine for oriented case: We propose a new heuristic called, LGFiOF which is a modified version of LGFi to solve the oriented case of 2DBPP
Summary
Cutting and Packing (C and P) Problems can be summarized as follows[10]:. “Given two sets of elements, namely, a set of large objects (input, supply) and a set of small items (output, demand) which are defined in one, two, or an even larger number of geometric dimensions. The non-oriented case of 2DBPP can be found in metal industry, where the pieces of the metal as the bins (larger objects) while the different dimension of layouts that needed to be cut out from the pieces of metal are the items. The aim of this problem is to find a good. The oriented case of 2DBPP non-increasing heights and L (lower bound) bins are can contributes in newspaper paging process where the initialized by packing on their bottoms a subset of the pieces of pages in newspaper are the bins and the news rectangles, following best-fit decreasing policy.
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