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.

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 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.

scholarly journals Minimizing waste (off-cuts) using cutting stock model: The case of one dimensional cutting stock problem in wood working industry

2016 ◽  
Vol 9 (3) ◽  
pp. 834 ◽  
Author(s):  
Gbemileke A. Ogunranti ◽  
Ayodeji E. Oluleye
Keyword(s):  
Linear Programming ◽  
Real Life ◽  
Cost Savings ◽  
Pattern Generation ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Generation Algorithm ◽  
One Dimensional ◽  
Stock Model ◽  
Total Stock

Purpose: The main objective of this study is to develop a model for solving the one dimensional cutting stock problem in the wood working industry, and develop a program for its implementation.Design/methodology/approach: This study adopts the pattern oriented approach in the formulation of the cutting stock model. A pattern generation algorithm was developed and coded using Visual basic.NET language. The cutting stock model developed is a Linear Programming (LP) Model constrained by numerous feasible patterns. A LP solver was integrated with the pattern generation algorithm program to develop a one - dimensional cutting stock model application named GB Cutting Stock Program.Findings and Originality/value: Applying the model to a real life optimization problem significantly reduces material waste (off-cuts) and minimizes the total stock used. The result yielded about 30.7% cost savings for company-I when the total stock materials used is compared with the former cutting plan. Also, to evaluate the efficiency of the application, Case I problem was solved using two top commercial 1D-cutting stock software.  The results show that the GB program performs better when related results were compared.Research limitations/implications: This study round up the linear programming solution for the number of pattern to cut.Practical implications: From Managerial perspective, implementing optimized cutting plans increases productivity by eliminating calculating errors and drastically reducing operator mistakes. Also, financial benefits that can annually amount to millions in cost savings can be achieved through significant material waste reduction.Originality/value: This paper developed a linear programming one dimensional cutting stock model based on a pattern generation algorithm to minimize waste in the wood working industry. To implement the model, the algorithm was coded using VisualBasic.net and linear programming solver called lpsolvedll (dynamic link library) was integrated to develop a one dimensional cutting stock Program.

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 Least-Loss Algorithm for a Bi-Objective One-Dimensional Cutting-Stock Problem

2019 ◽  
Vol 6 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Hesham K. Alfares ◽  
Omar G. Alsawafy
Keyword(s):  
Real Life ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Benchmark Problems ◽  
Standard Size ◽  
One Dimensional ◽  
Small Item ◽  
Proposed Model ◽  
Trim Loss ◽  
Industrial Problem

This article presents a new model and an efficient solution algorithm for a bi-objective one-dimensional cutting-stock problem. In the cutting-stock—or trim-loss—problem, customer orders of different smaller item sizes are satisfied by cutting a number of larger standard-size objects. After cutting larger objects to satisfy orders for smaller items, the remaining parts are considered as useless or wasted material, which is called “trim-loss.” The two objectives of the proposed model, in the order of priority, are to minimize the total trim loss, and the number of partially cut large objects. To produce near-optimum solutions, a two-stage least-loss algorithm (LLA) is used to determine the combinations of small item sizes that minimize the trim loss quantity. Solving a real-life industrial problem as well as several benchmark problems from the literature, the algorithm demonstrated considerable effectiveness in terms of both objectives, in addition to high computational efficiency.

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