One-Dimensional Cutting Stock Optimisation by Suborders

This paper introduces a method for solving a one-dimensional cutting stock problem by suborders. The method is used for large orders that for technological and logistical reasons cannot be filled in a single order, but only in several successive suborders. The method has two stages. In the first stage, the suborders are generated and in the second the trim-loss is minimised. All leftovers longer than D are returned to stock and reused. Shorter leftovers are treated as trim-loss and discarded. A detailed description of the method is provided by using a practical case. The method is tested by solving 108 randomly generated problem instances

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

Solving a Real Problem in Plastic Industry: A Case in Trim-loss Problem

In this paper, a cutting plane model is presented for solving a problem in a cast polypropylene (CPP) plastic film manufacturer. The company produces plastic rolls from plastic pellets with widths ranging from 3 050 mm to 3 250 mm. The plastic rolls are trimmed according to customer’s orders. In prior to the trimming process, the production planning and inventory control (PPIC) department scheduled the machines and arranged the plastic trim compositions manually. In this work, the plastic trimming problem is solved by applying the trim loss model. Since trimmed loss problem is an NP-hard problem. In this case, the permutations are selected in advance so that the total length is feasible to the machine length. The computation is carried out using visual basic for application (VBA). The model outcomes are then used for optimizing the machine scheduling process. Modified earliest due date is proposed to schedule in which machines customer’s orders should be done. The machines scheduling represents the company conditions and the cutting production can be scheduled for daily basis. Keywords: cutting plane; cutting stock; earliest due date; machine scheduling; non-polinomial-hard problem

Linear Programming for a Cutting Problem in the Wood Processing Industry – A Case Study

In this paper the authors present a case study from the wood-processing industry. It focuses on a cutting process in which material from stock is cut down in order to provide the items required by the customers in the desired qualities, sizes, and quantities. In particular, two aspects make this cutting process special. Firstly, the cutting process is strongly interdependent with a preceding handling process, which, consequently, cannot be planned independently. Secondly, if the trim loss is of a certain minimum size, it can be returned into stock and used as input to subsequent cutting processes. In order to reduce the cost of the cutting process, a decision support tool has been developed which incorporates a linear programming model as a central feature. The model is described in detail, and experience from the application of the tool is reported.one-dimensional cutting, linear programming, wood-processing industry

Exact and Heuristic Hybrid Approaches for Scheduling and Clustering Problems

This thesis deals with the design of exact and heuristic algorithms for scheduling and clustering combinatorial optimization problems. All the works are linked by the fact that all the presented methods arebasically hybrid algorithms, that mix techniques used in the world of combinatorial optimization. The algorithms are all efficient in practice, but the one presented in Chapter 4, that has mostly theoretical interest. Chapter 2 presents practical solution algorithms based on an ILP model for an energy scheduling combinatorial problem that arises in a smart building context. Chapter 3 presents a new cutting stock problem and introduce a mathematical formulation and a heuristic solution approach based on a heuristic column generation scheme. Chapter 4 provides an exact exponential algorithm, whose importance is only theoretical so far, for a classical scheduling problem: the Single Machine Total Tardiness Problem. The relevant aspect is that the designed algorithm has the best worst case complexity for the problem, that has been studied for several decades. Furthermore, such result is based on a new technique, called Branch and Merge, that avoids the solution of several equivalent sub-problems in a branching algorithm that requires polynomial space. As a consequence, such technique embeds in a branching algorithm ideas coming from other traditional computer science techniques such as dynamic programming and memorization, but keeping the space requirement polynomial. Chapter 5 provides an exact approach based on semidefinite programming and a matheuristic approach based on a quadratic solver for a fractional clustering combinatorial optimization problem, called Max-Mean Dispersion Problem. The matheuristic approach has the peculiarity of using a non-linear MIP solver. The proposed exact approach uses a general semidefinite programming relaxation and it is likely to be extended to other combinatorial problems with a fractional formulation. Chapter 6 proposes practical solution methods for a real world clustering problem arising in a smart city context. The solution algorithm is based on the solution of a Set Cover model via a commercial ILP solver. As a conclusion, the main contribution of this thesis is given by several approaches of practical or theoretical interest, for two classes of important combinatorial problems: clustering and scheduling. All the practical methods presented in the thesis are validated by extensive computational experiments, that compare the proposed methods with the ones available in the state of the art

Pattern Generation for Three Dimensional Cutting Stock Problem

We consider the problem of three-dimensional cutting of a large block that is to be cut into some small block pieces, each with a specific size and request. Pattern generation is an algorithm that has been used to determine cutting patterns in one-dimensional and two-dimensional problems. The purpose of this study is to modify the pattern generation algorithm so that it can be used in three-dimensional problems, and can determine the cutting pattern with the minimum possible cutting residue. The large block will be cut based on the length, width, and height. The rest of the cuts will be cut back if possible to minimize the rest. For three-dimensional problems, we consider the variant in which orthogonal rotation is allowed. By allowing the remainder of the initial cut to be rotated, the dimensions will have six permutations. The result of the calculation using the pattern generation algorithm for three-dimensional problems is that all possible cutting patterns are obtained but there are repetitive patterns because they suggest the same number of cuts.

A Cutting Plan of One-Dimensional Construction Materials to Reduce Loss in Construction Projects.

ได้รับทุนอุดหนุนการวิจัยจากมหาวิทยาลัยเทคโนโลยีสุรนาร