A non-linear model proposal for multi-response surface optimization and application to bread making process

Response surface methodology is a bunch of mathematical and statistical techniques used when multiple factors affect the outcome of a product or process and the aim is to optimize that outcome. The techniques in the response surface methodology are comprised of designing experiments to measure the outcome, development of a model that fits best to the data collected in the experiments and determination of the optimum factor levels that give the optimum outcome. Response surface methodology is used widely around the world especially in production and chemical industry to improve the design of a product, to decide on the formulation of a new product and for process optimization. By using the response surface methodology which makes the systems more robust by decreasing product and process variability, the purposes of quality improvement are satisfied for products and processes. In our country, experimental design and response surface methodology, a special branch of experimental design, are not widely used yet. This is because many industrial organizations don't have sufficient laboratoires to apply these techniques and also they are not known well in the industrial organizations. The aim of this study is to support the users as well as making a contribution to the scientific environment of our country. In response surface methodology models are built by the help of the regression analyze. Regresion coeffıcients are used to find out main and interaction effects of factors on response. In these methods, first step is to determine factors and its levels affect response. To decide most suitable experimental design these two criteria are used. Response surface methodology is generally applied to increase the quality of a product, service or whole system and to increase its performance while decreasing its cots. When all these purposes are considered together, optimizing one performance criterion is not enough; many criteria derived from quality and cost should be simultaneously optimized. Response surface methdology emerged to satify that need and researchers have been working to solve these kinds of problems. Several techniques based on statistics and operations research are used for multi response surface problems; desirability function approach, loss function approach, basic component analysis, distance function approach, multi regression model, linear programming approach, restricted optimization and heuristics. In the study, single response surface methodology is divided into two sections; first degree and second degree models. Several commonly used experimental designs developed for these techniques are investigated. For first degree models, hypothesis testing and lack of fitness tests are mentioned and the situations in which second degree models should be used are expressed. Then, multi-response surfaces are considered and the proposed approaches in the literature for these problems are given as a review. In the study, a non-linear programming model is also proposed by using desirability function approach recommended by Derrringer and Suich for multi-response surface optimization. The developed model enables to simultaneously optimize the response variables that have different units, amounts and objectives (minimization, maximization or a goal value). Additionally, the model has big advantages as the flexibility of being able to modified for different multi-response surface problems easily and allowing to weight different response variables. Lastly, by applying the proposed model into the bread production process, flour characteristics and production parameters are determined for a better-quality bread production. The application is made in EKSUN food organization located in Tekirdag. There are six independent variables in the study; gluten ratio of the flour (24%, 32%), alfa amilaz enzyme addition (0 ppm, 40 ppm), water amount used (60%, 65%), knead duration (7 minute, 11 minute), fermentation temperature (28(_ ^0)C, 38(_ ^0)C) and fermentation duration (45 minute, 75 minute). The four selected criteria for bread quality are; specific volume of bread, peel color and structure, shape uniformity calculated by height and width and inner pore structure. Spesific volume is calculated by dividing the volume of the bread with its weight. Volume measurement is done based on seed displacement method, one of the certified methods of American Grain Chemists Association. The peel color and structures of the breads are evaluated by experts using a 1-10 scale interval. The shape unfiormity is found by dividing the height of bread with the width. The goal value for that variable is decided to be 0.62 to avoid flat or oval shaped breads. Image processing technique is used to rate the pour shape, one of the response variables. For that, the breads are first cut from the middle and scanned with a HP brand scanner in a high resolution (4800 dpi). Later on, by investigating these bread images in image processing software ImageJ 1.48v, the pour distribution of breads are determined. To be able to investigate the squared effects along with linear effects, a second degree model is also used. Box-Behnken experimental design which is highly economical and used widely for second degree models is selected and the data is collected according to this experimental design. To eliminate the effect of randomness and to get better results, the experiments are conducted in a random order and each experiment is replicated 3 times. After getting the data according to the selected experimental design, hierarchical regression analysis is used to find second degree equations representing the relationsship between each response variable and independent variables. By making significance tests for the developed models and estimated coefficients, insignificant parameters are discarded from the model. For these analysis, Minitab v. 17.1.0 is used. After making all the analysis and getting a significant regression equation depended on independent variables for each response variable, desirability functions are defined for response variables. Finally, a non-linear programming model is constructed to optimize the total desirability level. The developed model is solved by GAMS v. 24.1.3 and optimum levels of the factors are obtained. The optimum levels are found as 28.748% for gluten ratio, 34.018 ppm for alfa amilaz enzyme addition, 9.714 minutes for knead duration, 34.988 (_ ^0)C for fermantation temperature and 65.273 minutes for fermantation duration. With determined factor levels, values for response variables are expected as 5.398 milliliter for specific volume, 6.986 for peel color and structure, 0.652 for shape uniformity and 158.663 for inner pore structure.