OPTIMIZING AN ALUMINUM EXTRUSION PROCESS

Minimizing the amount of scrap generated in an alum in extrusion process. An optimizing model is constructed in order to select the best cutting pat terns of aluminum logs and billets of various sizes and shapes. The model applied to real data obtained fro m an existing extrusion factory in Kuwait. Results from using the suggested model provided substantial redu ctions in the amount of scrap generated. Using soun d mathematical approaches contribute significantly in reducing waste and savings when compared to the existing non scientific techniques.


INTRODUCTION
Aluminum is the third most abundant element in the Earth's crust and it constitutes 7.3 percent by mass. The Aluminum industry contributes significantly to the global economy as well as too many individual economies. The industry employs over a million people worldwide. Aluminum smelting is a capital-intensive, technology-driven industry concentrated in a few relatively dominant companies. Aluminum consumption has enjoyed substantial average growth over the last few decades due to general economic growth and to its substitution of other materials. Kuwait is a member of the Gulf Cooperation Council (GCC); the GCC countries will boost their share of global aluminum output to 15-17% by the end of the decade. There are two types of aluminum industries; the first is the extrusion industry where profiles of different sizes, colors and shapes are produced, while the second is the fabrication industry where various products such as windows, fences and doors are designed from aluminum profiles.
In the aluminum extrusion industry, logs and billets are cut using various stock cutting patterns; the amount of scrap generated is dependent on the cutting method used. The Stock Cutting Problem (SCP) is discussed thoroughly in the literature. One of the first articles was presented by Gilmore and Gomory (1961) where integer programming was utilized for the cutting stock problem. The problem compromised a large number of variables which generally makes the computation infeasible. Gilmore and Gomory (1964) examined the cutting stock problems involving two or more dimensions. Haessler (1971) described a heuristic procedure for scheduling production-rolls of paper through a finishing operation to cut them down to finished roll sizes. The objective was to minimize the cost of trim-loss and that of the reprocessing. Covesrdale and Wharton (1976) presented a heuristic procedure for a nonlinear cutting stock problem; the problem was solved using the pattern enumeration technique. Sumichrast (1986) addressed a scheduling problem in the woven fiber glass industry as an example of the cutting stock problem with the objective of controlling the wasted production capacity rather than wasted material. A heuristic was developed for the purpose of scheduling the production process. Stadtler (1990) used the column generation method of Gilmore and Gomory (1964) for minimizing the amount of scrap generated from fabricated aluminum made for window frames. Krichagina et al. (1998) examined the cutting process of sheets in a paper plant. The main objective was to minimize the long-run average cost of paper waste. In this regard, a two step procedure consisting of linear programming and Brownian control was developed. Liang et al. (2002) applied an evolutionary algorithm (EP) for cutting stock problems with and without contiguity. Results showed that the EP algorithm is more effective and superior when compared to the genetic algorithm used. Parada et al. (2003) proposed a meta-heuristic approach for solving a non-guillotine stock cutting problem. The approach was a combination of the principles of the constructive and evolutive methods. The results showed an error reduction of around 2%. Hifi (2004) proposed an algorithm for solving a two dimensional constrained cutting stock problem. In the algorithm and for depth search, hybrid approach combining hill climbing strategies and dynamic programming were employed. Cui (2005) developed an algorithm that utilizes the knapsack algorithm and an implicit enumeration technique. The algorithm was applied to real cutting stock data of the manufacture electric generators. Khalifa et al. (2006) built a one dimensional cutting stock problem using genetic algorithm. The objective was to reduce the amount of waste generated in constructing steel bars. Saad et al. (2007) addressed the problem of scrap generated from cutting cylindrical logs produced by an aluminum extrusion company. In this regard, a multiobjective cutting stock problem was constructed. A solution procedure was developed considering the scrap generated as a fuzzy parameter. Chen (2008) presented a recursive heuristic algorithm for the constrained twodimensional stock cutting problems. The algorithm was tested and the computational results produced good solutions in short computing time for problems of different scales. Alves et al. (2009) used several constrained and non constrained integer programming using column generation. lower bounds for the different minimzation patterns were derived. Using actual data,the outcome of these models showed improvement of the lower bounds. Hajeeh (2010) addressed the problem of waste generated in an aluminum fabrication industry. A heuristic was propped for optimizing the cutting of aluminum profiles. The heuristic produced less scrap when compared to the existing procedure used in the company. Macedo et al. (2010) proposed an integer linear programming model to solve the twodimensional stock cutting problem with guillotine constraint. A computer software was used to examine the behavior of the models with data from a wood industry. The lower bound of the model was found to be superior to those of other methods. Kasimbeyli et al. (2011) proposed a linear integer programing with two contarcting objectives for a onedimensional cutting problem. A special heuristic algorithm was used to find the optimim cutting pattern. Berberler et al. (2011) developed a dynamic programming algorithm to address the one-dimensional stock cutting problem. The results obtained from this algorithm was compared to others and results showed its efficeincy and superiority. Cui and Huang (2012) proposed a heuristic to address constrained T-shaped patterns with the objective of maximizing the pattern value and meeting demand. The computation of 58 benchmark instances showed that the algorithm is superior to the two-stage patterns approaches. De Valle et al. (2012) developed an algorithm based on non-fit polygen to examine the two dimensional cutting/packing problem. The algorithm aslo solved problems with items of irregular shapes. Mobasher and Ekici (2013) developed a mixed integer linear and used the column generation method to the study a cutting stock problem with set up cost. The main objective was to find a cutting pattren at minimum production cost.

JMSS
In the current research work, the extrusion process in a specific industry in Kuwait is thoroughly studied with objective of finding ways for reducing the large amount of scrap generated. The article organized as follows: it start by describing the aluminum profile production process, the amount of scrap generated in the chosen industry from using the existing cutting techniques. Next, the structure of the developed optimization models is provided. For illustration, an example is presented to compare the amount of scarp generated using the existing conventional cutting patterns and the size of scrap generate from the proposed optimization model. Results and discussion section comes next, the article ends with concluding remarks.

Aluminum Profile Production
Aluminum profile production (extrusion) process passes through several stages starting with castings where logs are produced; the logs are next cut into standard billets and are put into extrusion machine to manufacture profiles of different shapes and sizes. The extruded aluminum profiles are placed in the aging furnace in order to increase their durability and strength. Next, the profiles are polished thoroughly and depending on request are either sent for paining, or anodizing before shipping to the customer. In Fig. 1, the detailed process is presented for a specific extrusion company in Kuwait. The type of billets and logs used in the extrusion process in the company along with their lengths and weight is shown in Table 1. The monthly weight and percentage of scrap generated during a specific year in the aluminum extrusion by the same company is as given in Table 2.

JMSS
Where: Z = Total weight of the scarp in kg W 1 = Weight of scrap (kg) generated per 1.5 inch log (0.0381 m) of each billet used to extrude the desired the desired profile W 2 = Weight of scrap (kg) generated from log cutting W 3 = Weight of scrap (kg) generated from producing longer profiles than demanded ν j = Weight (kg) of producing type j billet, j = 1,…,6 ω j = Weight (kg) of log used to produced the j th billet, j = 1,…,6 ξ j = Number of type j billet used y = Number of logs used W L = Weight (kg) of each log W F = Total weight (kg) of profiles demanded

Model II
Although the above problem provides a good solution to the problem, however it has one disadvantage in that, where more than on log is needed, the model considers all logs to be one long log. A superior and more efficient model is based on cutting patterns as given in (2). Equation (3) represents the nenegtivity constraint.
Where: ρ j = Number of cutting pattern j, j = 1, …,6 S j = Amount of scrap generated from cutting pattern j, j = 1, …,6 Q j = Weight of cutting pattern j (kg), j = 1, …,6 Q ML = Total weight of profiles demanded The different cutting billet patterns of 1.5 m log used in the mathematical model are given in Table 3 along with the total length of the different billet combinations (patterns) and the amount of scrap generated in meters.

JMSS
with an amount of 208.08 kg while the least is produce by 2211 with around 41 kg.

DISCUSSION
When comparing the total amount of scrap generated for the different Dies as shown in Table 4, it is found that it is around 56% on average. The total scrap generated produced using the conventional procedure is around 2035 cm whereas it is around 1145 using the suggested optimization model.

CONCLUSION
The aluminum extrusion process produces a sizable amount of scarp; this mainly attributed to the techniques used and the lack of modern scientific experience of the staff. In order to reduce the large amount of scrap, a thorough evaluation of the exiting cutting method should be carrying out. In addition to reduce scrap, an effective an optimal cutting method will contribute to efficient uses of time and other resources. For example the use of the mathematical developed, the reduction of the amount of scrap generated ranged from 21-82% and this constitutes large saving.
Efficient scientific approaches and tools should be used in the different processes within industries; optimization techniques are one of the strong tools that produce good results. It is recommended that the extrusion company should substitute the existing methods with more cost effective approaches which are based on sound scientific ones.