scholarly journals 3-Phase Matheuristic Model in Two-Dimensional Cutting Stock Problem of Triangular Shape Items

2020 ◽  
Vol 5 (1) ◽  
pp. 23
Author(s):  
Putra Bahtera Jaya Bangun ◽  
Sisca Octarina ◽  
Sisca Puspita Sepriliani ◽  
Laila Hanum ◽  
Endro Sastro Cahyono
Keyword(s):  
Branch And Bound ◽  
Consumer Demand ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Triangular Shape ◽  
Optimum Cutting ◽  
Trim Loss ◽  
Cutting Pattern ◽  
Optimum Solution

Cutting Stock Problem (CSP) is a problem of cutting stocks with certain cutting rules. This study used the data of rectangular stocks, which cut into triangular shape items with various order sizes. The Modified Branch and Bound Algorithm (MBBA) was used to determine the optimum cutting pattern then formulated it into the 3-Phase Matheuristic model which consisted of constructive phase, improvement phase, and compaction phase. Based on the results, it showed that the MBBA produces three optimum cutting patterns, which was used six times, eight times, and four times respectively to fulfill the consumer demand. Then the cutting patterns were formulated into the 3-Phase Matheuristic model whereas the optimum solution was the minimum trim loss for the first, second and third patterns.

A Hybrid Genetic Algorithm for Optimization of Two-Dimensional Cutting-Stock Problem

2012 ◽  
pp. 56-71
Author(s):  
Ahmed Mellouli ◽  
Faouzi Masmoudi ◽  
Imed Kacem ◽  
Mohamed Haddar
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Production Cost ◽  
Programming Model ◽  
Hybrid Genetic Algorithm ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Genetic Approach ◽  
Cutting Pattern

In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfill the customer orders with minimal production cost. The effectiveness of the hybrid genetic approach has been evaluated through a set of instances which are both randomly generated and collected from the literature.

A Hybrid Genetic Algorithm for Optimization of Two-dimensional Cutting-Stock Problem

2010 ◽  
Vol 1 (2) ◽  
pp. 34-49 ◽  
Author(s):  
Ahmed Mellouli ◽  
Faouzi Masmoudi ◽  
Imed Kacem ◽  
Mohamed Haddar
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Production Cost ◽  
Programming Model ◽  
Hybrid Genetic Algorithm ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Genetic Approach ◽  
Cutting Pattern

In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfil the customer orders with minimal production cost. The effectiveness of the hybrid genetic approach has been evaluated through a set of instances which are both randomly generated and collected from the literature.

scholarly journals Column Generation Model in Capacitated Multi-Periods Cutting Stock Problem with Pattern Set-Up Cost

2021 ◽  
Vol 6 (1) ◽  
pp. 8
Author(s):  
Putra Bahtera Jaya Bangun ◽  
Sisca Octarina ◽  
Laila Hanum ◽  
Ranti Sawitri ◽  
Endro Sastro Cahyono
Keyword(s):  
Column Generation ◽  
Pattern Generation ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Generation Model ◽  
Generation Algorithm ◽  
Second Stage ◽  
Trim Loss ◽  
Cutting Pattern ◽  
Set Up

Cutting Stock Problem (CSP) determines the cutting of stocks with standard length and width to meet the item’s demand. The optimal cutting pattern will minimize the usage of stocks and trim loss. This research implemented the pattern generation algorithm to form the Gilmore-Gomory and Column Generation model in two-dimensional CSP. The CSP in this research had three periods of cutting with different capacities in each period. The Column Generation model added the pattern set-up cost as the constraint. The Gilmore-Gomory model ensured that the first stage’s strips were used in the second stage and met the item’s demand. Based on the Column Generation model’s solution, the 1st period used the 2nd, 4th, and 5th patterns, the 2nd period used 4th and 5th patterns, and the 3rd period did not use any patterns. The first and second periods fulfilled all of the demands.

The Nesting of Two-Dimensional Shapes Using Genetic Algorithms

1995 ◽  
Vol 209 (2) ◽  
pp. 115-124 ◽  
Author(s):  
H S Ismail ◽  
K K B Hon
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spatial Constraints ◽  
Global Optimal ◽  
Optimum Solution ◽  
Rapid Conversion

The general two-dimensional cutting stock problem is concerned with the optimum layout and arrangement of two-dimensional shapes within the spatial constraints imposed by the cutting stock. The main objective is to maximize the utilization of the cutting stock material. This paper presents some of the results obtained from applying a combination of genetic algorithms and heuristic approaches to the nesting of dissimilar shapes. Genetic algorithms are stochastically based optimization approaches which mimic nature's evolutionary process in finding global optimal solutions in a large search space. The paper discusses the method by which the problem is defined and represented for analysis and introduces a number of new problem-specific genetic algorithm operators that aid in the rapid conversion to an optimum solution.

scholarly journals Set Covering Model in Solving Multiple Cutting Stock Problem

2020 ◽  
Vol 5 (4) ◽  
pp. 121
Author(s):  
Sisca Octarina ◽  
Devi Gusmalia Juita ◽  
Ning Eliyati ◽  
Putra Bahtera Jaya Bangun
Keyword(s):  
Column Generation ◽  
Pattern Generation ◽  
Cutting Stock Problem ◽  
Set Covering ◽  
Cutting Stock ◽  
Second Stage ◽  
Generation Technique ◽  
Cutting Pattern ◽  
Covering Model

Cutting Stock Problem (CSP) is the determination of how to cut stocks into items with certain cutting rules. A diverse set of stocks is called multiple stock CSP. This study used Pattern Generation (PG) algorithm to determine cutting pattern, then formulated it into a Gilmore and Gomory model and solved by using Column Generation Technique (CGT). Set Covering model was generated from Gilmore and Gomory model. Based on the results, selected cutting patterns in the first stage can be used in the second stage. The combination of patterns generated from Gilmore and Gomory model showed that the use of stocks was more effective than Set Covering model.  

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