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 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.

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.

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 An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

OR Spectrum ◽  
2021 ◽  
Author(s):  
Adejuyigbe O. Fajemisin ◽  
Laura Climent ◽  
Steven D. Prestwich
Keyword(s):  
Real Life ◽  
Forest Harvesting ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Decomposition Approach ◽  
New Class ◽  
Bilevel Problem ◽  
Programming Techniques ◽  
Bilevel Problems ◽  
Better Than

AbstractThis paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

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