UBC Theses and Dissertations

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UBC Theses and Dissertations

Computer-aided formula optimization Vázquez Benítez, María Cecilia


The purpose of this research project was to establish a formula optimization computer program to be used for quality control in the meat processing industry. In contrast to linear programming, such a program would search for the best quality formulations that meet predetermined product specifications within allowable cost ranges. Since quality as a function of the ingredients has been found to be explained better by nonlinear equations, the program had to be able to handle nonlinear equations as objective functions as well as constraints to make it an effective formula optimization method. The first part of the study established the IBM BASIC formula optimization computer program (FORPLEX). The FORPLEX is based on the modified version of the Complex method of Box. The FORPLEX was found to be effective in the optimization of nonlinear objective function problems that were linearly constrained, making it suitable for formula optimization purposes. The second part of this study involved the development of statistically significant quality prediction equations for a 3-ingredient model frankfurter formulation. The three ingredients were: pork fat, mechanically deboned poultry meat and beef meat. Ingredient-quality equations were generated through mixture experimentation. Specific quality parameters were evaluated at observation points given by an extreme vertices design. Scheffe's canonical special cubic model for three components was fitted to the experimental data using multiple regression analysis. The statistical validity of the equations for prediction purposes was assessed by analysis of variance, adjusted multiple coefficient of determination, standard error of the estimate and analysis of residuals. Fourteen of 17 regression models developed were considered adequate to be used for prediction purposes. In order to have a better understanding of the relationship between ingredient proportions and the quality parameters, three different techniques were used: (a) response surface contour analysis, (b) correlation analysis and (c) scatterplot matrices analysis. The third part of this study consisted of the computational optimization of frankfurter formulations using the FORPLEX program. Several frankfurter formulation optimization trials were performed. In each trial, different combinations of quality parameters were considered measures of the formulations' quality. Target quality values were either selected based on a target formulation or were individually selected. In both cases the FORPLEX was able to find best quality formulations that met the constraints imposed on them. Differences between predicted and target quality values existed in all the computed optimum formulations when the target values were individually selected. Differences existed because it was difficult for the formulations to meet all the target quality values. Target quality values should be selected carefully since failure to obtain formulations that meet the target quality as closely as possible lay not with the performance of the FORPLEX but with the selection of the target quality values. Five optimum formulations found by FORPLEX were compared with seven least-cost formulations which were found by increasing the lower limit of the fat binding constraint. The predicted quality of each FORPLEX optimum formulation was close to its respective target quality. The least-cost formulations showed, in general, considerable departure from the target quality values set in the FORPLEX formulations. The adequacy of the models for predicting the quality of frankfurter formulations could not be evaluated since the meat ingredients had been stored frozen for 6 months. The models did not account for the effect of extended frozen storage on the quality of the formulations. Results of this study indicated that formula optimization based on the Complex method (FORPLEX) is the more suitable technique for food formulation. The FORPLEX may be able to replace linear programming computer programs currently being used in the processed meat industry.

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