scholarly journals Flexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial-Use Paper Production

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Fu-Kwun Wang ◽  
Feng-Tai Liu
Keyword(s):  
Real Data ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Paper Production ◽  
Proposed Model ◽  
Trim Loss ◽  
Production Quantity ◽  
Industrial Use ◽  
Stock Allocation ◽  
Loss Control

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.

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 A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

2020 ◽  
Vol 10 (15) ◽  
pp. 5274
Author(s):  
Razaullah Khan ◽  
Catalin Iulian Pruncu ◽  
Abdul Salam Khan ◽  
Khawar Naeem ◽  
Muhammad Abas ◽  
...  
Keyword(s):  
Programming Model ◽  
Optimization Procedure ◽  
Paper Mill ◽  
Simplex Algorithm ◽  
Cutting Stock ◽  
Environmental Damage ◽  
Constraint Matrix ◽  
Make To Order ◽  
Proposed Model ◽  
Trim Loss

One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

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.

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.

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 DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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