Lot sizing problem integrated with cutting stock problem in a paper industry: a multiobjective approach (original) (raw)
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A multiobjective integrated model for lot sizing and cutting stock problems
Journal of the Operational Research Society, 2019
In recent years, researchers have investigated a variety of approaches to integrating lot sizing and cutting stock problems due to their high importance in the manufacturing industry. Although the mono-objective integrated problem has been considered an excellent alternative for minimising global costs, it does not include all the multiple criteria involved in the manufacturing process. Thus, to address this issue, we use a multiobjective approach and explain its importance in providing various answers to the decision maker through the Pareto-optimal solution set. We analyse existing trade-offs and correlations between each cost of the integrated problem and the related decision variables. Several computational tests are performed, which validate the efficacy of our strategy.
The combined cutting stock and lot-sizing problem in industrial processes
European Journal of Operational Research, 2006
Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-optimal solutions for the cutting stock and lot-sizing problems considered separately. The goal here is to minimize the trim loss, the storage and setup costs. With a view to this, we formulate a mathematical model of the combined cutting stock and lot-sizing problem and propose a solution method based on an analogy with the network shortest path problem. Some computational results comparing the combined problem solutions with those obtained by the method generally used in industry-first solve the lot-sizing problem and then solve the cutting stock problem-are presented. These results demonstrate that by combining the problems it is possible to obtain benefits of up to 28% profit. Finally, for small instances we analyze the quality of the solutions obtained by the network shortest path approach compared to the optimal solutions obtained by the commercial package AMPL.
The Integrated Lot Sizing and Cutting Stock Problem in a Furniture Factory
IFAC Proceedings Volumes, 2013
The integrated lot sizing and cutting stock problem is studied in the context of furniture production. The goal is to capture the interdependencies between the determination of the lot size and of the cutting process in order to reduce raw material waste and production and inventory costs. An integrated mathematical model is proposed that includes lot sizing decisions with safety stock level constraints and saw capacity constraints taking into account saw cycles. The model solution is compared to a simulation of the common practice of taking the lot size and the cutting stock decisions separately and sequentially. Given the large number of variables in the model, a column-generation solution method is proposed to solve the problem. An extensive computational study is conducted using instances generated based on data collected at a typical small scale Brazilian factory. It includes an analysis of the performance of the integrated approach against sequential approaches, when varying the costs in the objective function. The integrated approach performs well, both in terms of reducing the total cost of raw materials as well as the inventory costs of pieces. They also indicate that the model can support the main decisions taken and can bring improvements to the factory's production planning.
Mathematical Problems in Engineering, 2014
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 New Decision Model for Reducing Trim Loss and Inventory in the Paper Industry
Journal of Applied Mathematics, 2014
In the paper industry, numerous studies have explored means of optimizing order allocation and cutting trim loss. However, enterprises may not adopt the resulting solutions because some widths of the inventory exceed or are less than those required for acceptable scheduling. To ensure that the results better suit the actual requirements, we present a new decision model based on the adjustment of scheduling and limitation of inventory quantity to differentiate trim loss and inventory distribution data. Differential analysis is used to reduce data filtering and the information is valuable for decision making. A numerical example is presented to illustrate the applicability of the proposed method. The results show that our proposed method outperforms the manual method regarding scheduling quantity and trim loss.
Applied Artificial Intelligence, 2019
This paper addressed an important variant of two-dimensional cutting stock problem. The objective was not only to minimize trim loss, as in traditional cutting stock problems, but rather to minimize the number of machine setups. This additional objective is crucial for the life of the machines and affects both the time and the cost of cutting operations. Since cutting stock problems are well known to be NP-hard, we proposed an approximate method to solve this problem in a reasonable time. This approach differs from the previous works by generating a front with many interesting solutions. By this way, the decision maker or production manager can choose the best one from the set based on other additional constraints. This approach combined a genetic algorithm with a linear programming model to estimate the optimal Pareto front of these two objectives. The effectiveness of this approach was evaluated through a set of instances collected from the literature. The experimental results for different-size problems show that this algorithm provides Pareto fronts very near to the optimal ones.
Solving a combined cutting-stock and lot-sizing problem with a column generating procedure
Computers & Operations Research, 2008
In Nonås and Thorstenson [A combined cutting stock and lot sizing problem. European Journal of Operational Research 120(2) (2000) 327-42] a combined cutting-stock and lot-sizing problem is outlined under static and deterministic conditions. In this paper we suggest a new column generating solution procedure for this problem that works well on both small and large-sized problems. The procedure includes characteristics from both the column generating procedure in Nonås and Thorstenson, which works well on small-sized problems, and from the sequential heuristic due to Haessler [A heuristic programming solution to a nonlinear cutting stock problem, Management Science 17(12) (1971) 793-802], which works well on large-sized problems. Numerical results are presented that show that the new heuristic performs better than both of the earlier procedures. Comparisons with results obtained by other authors indicate that the procedure works well also for the extended cutting-stock problem with only a setup cost for each pattern change. ᭧
Multi-Objective Lot-Sizing and Scheduling Dealing with Perishability Issues
Industrial & Engineering Chemistry Research, 2011
The recent evidence demonstrating the importance of perishables in terms of store choice and shopping experience makes these products a very interesting topic in many different research areas. Nevertheless, the production planning research has not been paying the necessary attention to the complexities of production systems of such items. The evidence that consumers of perishable goods search for visual and other cues of freshness, such as the printed expiry dates, triggered the development of a multiobjective lot-sizing and scheduling model taking this relevant aspect into account by considering it explicitly as an objective function. A hybrid genetic algorithm based on NSGA-II was developed to allow the decision maker a true choice between different trade-offs from the Pareto front. Computational experiments were based on a case study, reported in the literature, concerning a diary company producing yogurt.