Get this from a library! Métodos y modelos de investigación de operaciones. vol. 2, Modelos estocásticos. [Juan Prawda Witenberg]. Métodos y modelos de investigación de operaciones, Volume 1. By Juan Prawda Witenberg. About this book · Get Textbooks on Google Play. Rent and save. Métodos y modelos de investigación de operaciones: Modelos determinísticos, Volume 1. Front Cover. Juan Prawda Witenberg. Limusa, – pages.

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Skip to main content. Log In Sign Up. Francisco Zaragoza Huerta E-mail: This method contains every constraint necessary in order to provide effectiveness regarding the cutting planning process and diminishing its time.

The model delivers solutions in real and polynomial time, and the cost of solving it is low since the demo version of the software can be used. This tool could be useful to any other organization from the same industry or with a similar cutting process. Also, it is expected that the analyzed company will make total use of this tool in no longer than three months.

This causes a lot of monetary losses due to material. This is the reason why it has been considered that the process has to be optimized. The reduction of waste is one of the most important objectives of any company. The application of the optimization takes place in a factory dedicated to the design and manufacture of custom furniture, each project involves a unique design, inspired by the tastes and needs of the customer.

However, the factory is dedicated to authentic projects where almost everything is majorly handmade, so every project is constantly exposed to human decision making that involves common mistakes and almost always leads to monetary losses, generated by the lack of use of resources in an optimal manner. Initially, it was intended to use the cutting-stock algorithm, but this algorithm only covers linear cuts.

A new algorithm was created, which presents a logical argumentation, where the parts that will be cut, are arranged in such way that the material is fully used. The algorithm allows to make superficial cuts. It is way more efficient respecting of the The Cutting-Stock offers a greater simplicity on exploitation of resources, since it is not produced the interpretation of the analysis of sensibility.

The algorithm results to be more comprehensible In the of superficial cutting algorithm, the for the people who do not have sufficient technical variables could increase considerably as knowledge of Operational Research. Advantages Cutting Stock Disadvantages Superficial Algorithm Problem The cutting-stock is done with the In the superficial cutting algorithm exist as minimum number of iterations.

The analysis of sensibility has a The interpretation of the variables is a simple interpretation. Nevertheless, it is important to take into account the scope of it. The created algorithm processes just known pieces with rectangular dimensions. Since the most important aspect of this algorithm is the interpretation of the results, the company most have employees capable to manage the software in use in this case GAMS.

The reason why the optimization software GAMS was used, is because its various advantages, as offering the facility to change to more complex versions, being that the format that the PC program offers is similar to the software of a parallel supercomputer. GAMS offers the possibility to solve multiple versions of one same model of linear programming, non linear programming, mix programming and nonlinear mix programming.


Unlike other softwares, GAMS can solve complex programs, than Lingo or Lindo, because the software allows to deposit parameters, which simplifies the solving of matricial problems.

Moreover, the way to deposit data reduces the capturing time, also GAMS can be used as demo for unlimited time. Using the superficial cutting algorithm, the cutting process will be standardized, optimizing this procedure for the reduction of wastage. This will allow the company to have a better and more competitive price and to win more clients, aspiring to the diversification of their product, the professionalization of the company and better methods.

Metodos Y Modelos De Investigacion De Operaciones Ii pdf

However, the main intention of this model is for it to be replicated with any type of furniture, from any material, in any measurements only if it applies according to the project scope by only changing the inputs. Therefore, this experimental implementation involves using the theory of the algorithm as such and put it into practice with a real piece of furniture, in this case the desk. The data required was the dimensions from the cutting pieces, the number of pieces needed from every type of cutting piece, and also the dimensions of the sheet of wood from where the pieces will be cut.

It is as well important to consider the type of material, since normally, one only piece of furniture may contain different types of wood and other products and every type of material must have a opfraciones model.

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Procedure The algorithm is broken down and described next. First of all, it is essential set the pieces in order according to their area, the biggest ones go first.

This algorithm is somehow manual, since to obtain the most optimal result, it is recommended to make one iteration for every different piece. As a next step, one should locate the pieces in the cutting sheet. This could be achieved if one locates the longer edge of the cutting piece in line with the longer edge of the cutting sheet.

After assigning the first piece, it is important to analyze the remaining area of the cutting sheet. On the opposite side, if this excess area is large enough it must be divided into at least two areas of rectangular shape. The dimensions of this new areas must be considered in the next iteration as other sheets available to cut.

This opedaciones must be repeated till all the pieces are done cutting. This desk has nine pieces. The cutting sheets have a standard dimension of x cm.

The dimensions of the cutting pieces are also in centimeters and can be observed in the following models. Afterwards, in the following iterations, the variables l1 p,k and l2 p,k will be the dimensions of cutting sheets. The following iterations will proceed in the same way just adding data to the parameters kind k, belonging to the specifications of the cutting sheets.


After analyzing all the following iterations, the final result could be compared with the one from the following model that represents the maximum utilization of the cutting sheets. L quantity of cutting pieces type i cut out from sheet t ype k 1 1 3. L occupied area in every sheet 1 L remaining area in every sheet 1 L edge 1 regarding the base of remaining area p in sh eet k 1 1 L edge x of cutting piece i asigned to edge h of cuttin g sheet k 1 1 1.

L edge x of cutting piece i asigned to edge b of cuttin g sheet k ALL 0.

L edge y of cutting piece i asigned to edge b of cuttin g sheet k 1 1 1. Pieces number 1,2, 4, 89 and six from number 6 will be cut out from sheet number one, and pieces number 3, 5, 7 and the remaining two from number 6 will be cut out from sheet number 2. L quantity of cutting pieces type i cut out from sheet t ype k 1 2 1 3. Only piece investigacino 6 is distributed in a different way.

This variables will take the number 1 value in the case where that specific edge from the piece must correspond to that specific edge of the sheet.

This particular analysis cannot be observed in the second model, but the ideal result would be that regardless of the pieces arrangement, the total remaining area should be the same in both models.

And in this experiment, that was the case since the remaining area was in both of Then, the second model could work as a verification of the first one. For bigger scale problems, meaning problems with a larger number of cutting pieces and different types of furniture, it is important to take into account the following considerations. First group up all the pieces from the same material. After that, in order to know the ideal number of total sheets to cut, the second model should be used as a first approach.

Then, the first model comes to action to provide the best arrangement of the cutting pieces. If there are too many pieces to cut of each type of piece it would be better to look for homogeneity in the cut patterns, saying it is better to have many pieces from one type in one sheet than have them all mixed up. This will help the cutting process to be faster and to look for a uniform remaining area as well.

Design of the desk Image 2. Cutting area Image 4. The Cutting Stock Problem. Cutting Stock – A very applied method. An improved tabu search approach with mixed objective function for one-dimensional cutting stock problems Adv. Software, 37 8pp. Remember me on this computer. Enter the email address you signed up with and we’ll email you a reset link. Click here to sign up. Help Center Find new research papers in: