One-dimensional Cutting Stock Problem Research Articles

Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost

• We propose a two-stage approach for the one-dimensional cutting stock problem. • Many patterns are generated in the first stage by a sequential grouping procedure. • An integer programming model is solved to select the patterns in the solution. • The sequential grouping procedure is efficient for pattern reduction. • Solving the integer programming model can significantly reduce the total cost. The primary objective in the one-dimensional cutting stock problem is to minimize material cost. In real applications it is often necessary to consider auxiliary objectives, one of which is to reduce the number of different cutting patterns (setups). This paper first presents an integer linear programming model to minimize the sum of material and setup costs over a given pattern set, and then describes a sequential grouping procedure to generate the patterns in the set. Two sets of benchmark instances are used in the computational test. The results indicate that the approach is efficient in improving the solution quality.

A GENETIC ALGORITHM FOR THE ONE-DIMENSIONAL CUTTING STOCK PROBLEM WITH SETUPS

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature.

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

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.

Minimal Proper Non-IRUP Instances of the One-Dimensional Cutting Stock Problem

Minimal Proper Non-IRUP Instances of the One-Dimensional Cutting Stock Problem

Parallelized sequential value correction procedure for the one-dimensional cutting stock problem with multiple stock lengths

A heuristic approach with parallel computation is presented for the one-dimensional cutting stock problem with multiple stock lengths. The algorithm is based on the sequential heuristic procedure that generates each pattern to produce some items and repeats until all the required items are fulfilled. A recursion is used to solve the bounded knapsack problem heuristically in the pattern generation process to reduce running time. The item values are adjusted after the generation of each pattern using a value correction formula. The computational results show that the algorithm is more effective than a recently published evolutionary heuristic in improving solution quality, and can reduce computational time because of the efficient parallel implementation.

An Efficient Algorithm Design for the One-Dimensional Cutting-Stock Problem

A Two-level method is proposed to solve the one-dimensional cutting-stock problem during the production process in this paper. First, nested layer cycle is designed to enumerate all the feasible cutting patterns, then a integer linear programming model is established with quantity demands as the constraint. The best cutting scheme is obtained finally according to the branch and bound method. The effectiveness of the proposed method is proved through a real world example, the calculations demonstrate that scheme obviously improves the utilization rate of stock

Solving an one-dimensional cutting stock problem by simulated annealing and tabu search

A cutting stock problem is one of the main and classical problems in operations research that is modeled as LP problem. Because of its NP-hard nature, finding an optimal solution in reasonable time is extremely difficult and at least non-economical. In this paper, two meta-heuristic algorithms, namely simulated annealing (SA) and tabu search (TS), are proposed and developed for this type of the complex and large-sized problem. To evaluate the efficiency of these proposed approaches, several problems are solved using SA and TS, and then the related results are compared. The results show that the proposed SA gives good results in terms of objective function values rather than TS.

Two-stage segment optimal packing of single size rectangles

A two-stage approach was proposed which can solve the optimal packing of single size rectangles effectively.The best cutting patterns of standard sub-segment were solved and the problem was transformed into one-dimensional cutting stock problems in the first stage.In the second stage the best ideal solution was found with different methods for the one-dimensional cutting stock problems.With this method,an optimal packing of single size rectangles system was developed.The system not only can solve the segment layout of single size rectangles but also can solve other kinds of optimal packing of single size rectangles.Enterprise applications show that this method is an effective solution to the problem of single size rectangles packing.

A hybrid algorithm for one-dimensional cutting stock problem with multiple stock sizes

A hybrid algorithm for one-dimensional cutting stock problem with multiple stock sizes

A CAM system for one-dimensional stock cutting

This paper considers the one-dimensional cutting stock problem in which m types of items are cut from stock bars of multiple sizes such that the bar cost is minimized. A solution to this problem is a cutting plan consisting of a set of cutting patterns with specified frequency. A CAM system based on a sequential heuristic procedure is developed for generating cutting plans. The algorithm takes the reduction of bar cost as the primary objective, and considers two secondary objectives - pattern reduction and shorter stocks reduction. The system provides a set of non-dominated cutting plans so that the most appropriate one can be selected according to the specified circumstance. Computational results indicate that the algorithm can generate solutions comparable to or better than those of previously published algorithms that consider pattern reduction.

A GENERALIZED APPROACH TO THE SOLUTION OF ONE-DIMENSIONAL STOCK-CUTTING PROBLEM FOR SMALL SHIPYARDS

A generalized approach is introduced for the optimization of one-dimensional cutting stock problem (1D-CSP), which occurs in wide variety of engineering manufacturing processes especially in ship building industry, Instead of making preliminary specifications and accordingly ignoring many alternative arrangements, the suggested optimization technique selectively considers feasible arrangements by eliminating majority of the possible but inefficient arrangements thus rendering the problem solvable for practical applications. The introduced approach, which minimizes the piece arrangement plans and trim losses in the material, achieves the ideal solution implied by the analytical methods. Another important advantage of the present method is its ability to produce integer results, which usually cannot be obtained by means of analytical methods used in linear programming. Overall, the solution of the problem has been drastically simplified even to allow hand calculations instead of long computer runs. Thus the introduced approach can be very functional for small shipyards and single boat builders. The introduced approach is evaluated by two numerical examples.

C-Sets-based sequential heuristic procedure for the one-dimensional cutting stock problem with pattern reduction

This paper presents a sequential heuristic procedure (SHP) for the 1D cutting stock problem with pattern reduction, where a set of items are cut from stock bars of the same length to minimize the bar cost, with a secondary objective being to reduce the pattern count of the cutting plan. The SHP generates the current pattern to produce some items, and continues until all items are fulfilled. The algorithm uses two candidate sets (C-Sets). The first is the set of the candidate items for generating the current pattern. The second is the set of candidate patterns from which the current pattern is selected. The algorithm generates candidate patterns using the candidate items, determines the estimated cutting-plan cost (ECP-cost) of each pattern using a look-ahead strategy, and selects the pattern of the minimum ECP-cost as the current pattern. The computational results indicate that the algorithm is efficient.

Application of Genetic Algorithm to Minimize the Number of Objects Processed and Setup in a One-Dimensional Cutting Stock Problem

This paper presents the application of the one new approach using Genetic Algorithm in solving One-Dimensional Cutting Stock Problems in order to minimize two objectives, usually conflicting, i.e., the number of processed objects and setup while simultaneously treating them as a single goal. The model problem, the objective function, the method denominated SingleGA10 and the steps used to solve the problem are also presented. The obtained results of the SingleGA10 are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio10, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that the proposed method, which only uses a genetic algorithm to solve these two objectives inversely related, provides good results.

One-Dimensional Cutting Stock Optimization with Usable Leftover

This paper describes a method for solving one-dimensional cutting stock problem with usable leftover (CSPUL) in cases where the ratio between the average stock and average order length is less than 3. The proposed method can solve general CSPUL where standard stock lengths, non-standard stock lengths, or a combination of both are cut in the exact required number of pieces. The solutions of sample problems are compared with other methods.

Assessment of stock size to minimize cutting stock production costs

Abstract A method for assessing the optimal stock size for the expected order size for a single-period one-dimensional cutting stock problem is proposed. The stock size is optimal when the expected total costs of trim loss, warehousing, and non-fulfilment are minimum. The stock size is the sum of all bar lengths in the stock, and the order size is the sum of shorter bar lengths in various numbers of pieces. Using simulated test cases, a statistical estimation of optimal stock size is conducted, which in our case is approximately 50% above the expected order. The proposed method can help company choose the appropriate level of stock to minimize their total costs.

An integer programming model for two- and three-stage two-dimensional cutting stock problems

Abstract In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are also addressed, as the rotation of items, the length of the cuts and the value of the remaining plates. The new integer programming model can be seen as an extension of the “one-cut model” proposed by Dyckhoff for the one-dimensional cutting stock problem. In the proposed model, each decision variable is associated with cutting one item from a plate or from a part of a plate resulting from previous cuts (residual plates). Comparative computational results of the proposed model and of models from the literature are presented and discussed.

An evolutionary algorithm for the one-dimensional cutting stock problem

This paper deals with the one-dimensional integer cutting stock problem, which consists of cutting a set of available objects in stock in order to produce ordered smaller items in such a way as to minimize the waste of material. The case in which there are various types of objects available in stock in limited quantities is studied. A new heuristic method based on the evolutionary algorithm concept is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and the results are compared with other methods from the literature.

A software for the one-dimensional cutting stock problem

In this paper, one-dimensional cutting stock problem is taken into consideration and a new heuristic algorithm is proposed to solve the problem. In this proposed algorithm, a new dynamic programming algorithm is applied for packing each of the bins. The algorithm is coded with Delphi and then by computational experiments with the real-life constraint optimization problems, and the obtained results are compared with the other one-dimensional cutting stock commercial packages. The computational experiments show the efficiency of the algorithm.

A heuristic for the one-dimensional cutting stock problem with usable leftover

A heuristic algorithm for the one-dimensional cutting stock problem with usable leftover (residual length) is presented. The algorithm consists of two procedures. The first is a linear programming procedure that fulfills the major portion of the item demand. The second is a sequential heuristic procedure that fulfills the remaining portion of the item demand. The algorithm can balance the cost of the consumed bars, the profit from leftovers and the profit from shorter stocks reduction. The computational results show that the algorithm performs better than a recently published algorithm.

Solving One-Dimensional Cutting Stock Problem with Discrete Demands and Capacitated Planning Objective

Problem statement: One-dimensional cutting stock problem with discret e demands and capacitated planning objective is an NP hard problem. Approach: The mathematical model with column-generation technique by a branch-and-bound procedure and the heuristic b ased on the first fit decreasing method are propose d. Then, both approaches were compared and some characteristics were investigated such as upper-bound value, percent age above lower-bound value, computation time, and number of patterns. Results: The 24 instances were examined. The proposed heuristic provides the upper-bound value a bove the lower-bound around 0-16.78%. All upper-bound values from column-generation and integer programming are better than the proposed heuristic but all c omputation times are higher. Conclusion: The proposed heuristic has consistently high perfo rmance in computation times.