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.  

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.

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 balance approach for the one-dimensional multiple stock size cutting stock problem with setup cost

2016 ◽  
Vol 230 (12) ◽  
pp. 2182-2189 ◽  
Author(s):  
Dianjian Wu ◽  
Chunping Yan
Keyword(s):  
Pattern Generation ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Setup Cost ◽  
Stock Size ◽  
One Dimensional ◽  
Setup Costs ◽  
Balance Approach ◽  
The One ◽  
Cutting Plan

A balance approach is presented to solve one-dimensional multiple stock size cutting stock problem with setup cost. The approach first utilizes a sequential pattern generation algorithm to generate a series of cutting plans based on each stock size, respectively. Then, a measure standard of cost balance utilization is used to select a current optimized cutting pattern from a cutting plan corresponding to each stock size. All item demands are dealt by the previous two steps to obtain many optimized cutting plans, and an ideal cutting plan is extracted according to the minimum sum of stock and setup costs at last. The approach is applied to two tests, and the computational results demonstrate that it possesses good cost adaptability and optimization performance.

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