scholarly journals Implementation of arc flow model incapacitated multi-period cutting stock problem with the pattern set up cost to minimize the trim loss

2021 ◽  
Vol 1940 (1) ◽  
pp. 012018
Author(s):  
S Octarina ◽  
D Septimiranti ◽  
E Yuliza
Keyword(s):  
Flow Model ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Trim Loss ◽  
Set Up

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 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.

scholarly journals Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry

2016 ◽  
Vol 17 (3) ◽  
pp. 305 ◽  
Author(s):  
Sônia Cristina Poltroniere ◽  
Silvio Alexandre Araujo ◽  
Kelly Cristina Poldi
Keyword(s):  
Lower Bounds ◽  
Production Scheduling ◽  
Optimization Problems ◽  
Lot Sizing ◽  
Paper Industry ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Lot Sizing Problem ◽  
Different Types ◽  
Trim Loss

Two important optimization problems occur in the planning and production scheduling in paper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon.These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and in- ventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed. 

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.

Arc-flow model for the two-dimensional guillotine cutting stock problem

2010 ◽  
Vol 37 (6) ◽  
pp. 991-1001 ◽  
Author(s):  
Rita Macedo ◽  
Cláudio Alves ◽  
J.M. Valério de Carvalho
Keyword(s):  
Flow Model ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Guillotine Cutting

scholarly journals Optimasi Trim Loss menggunakan Integer Linear Programming pada Cutting Stock Problem untuk industri meubel (Studi Kasus pada UD. Flybers)

AKSIOMA ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 80-108
Author(s):  
Ismail Djakaria ◽  
Fenly B Mohamad ◽  
Djihad Wungguli
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Stock Cutting ◽  
Trim Loss

Trim loss merupakan kerugian yang timbul dari hasil pemotongan yang tidak optimal. Trim loss dipengaruhi beberapa faktor salah satunya yaitu peletakan pola pemotongan yang kurang tepat. Trim loss dapat diselesaikan dengan beberapa metode salah satunya menggunakan metode cutting stock. cutting stock digunakan pada pengoptimalan pemotongan sisa material yang tidak dapat digunakan lagi. Pada cutting stock dipengaruhi oleh masalah pola pemotongan disebut cutting stock problem(CSP). CSP dapat diselesaikan dengan menggunakan pendekatan integer linear programming (ILP). ILP adalah salah satu model dalam program linear yang variabel keputusannya berbentuk bilangan positif atau nol.

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