A simulation algorithm for optimization of mixture design applied to the assignment of weights in a goal programming problem

Abstract

Experimental design approaches are essential for improving products and processes, and their use is often decisive in achieving a successful target result. Thus, mixture design is a method for designing experiments which considers that the result does not depend on the total amount but on the proportions of the components. Mixture design techniques are often applied to problems in food, beverage, pharmaceutical health, and cement-based materials, among others, and one may also use them to help solve multi-objective problems when the weights of the objective function components can interfere with the optimization process. Therefore, given the relevance of studies on mixture planning and the increasing use of methods and techniques to consider uncertainty, the objective of this study is to propose an approach to deal with uncertainties in the coefficients of polynomial objective functions for the optimization of mixture design problem considering optimization via Monte Carlo Simulation. Computational tests were made using R software with instances from a literature study on a waste paper recycling logistics problem where the assignment of model weights is part of the process. Comparing the results to those obtained using the General Algebraic Modeling System language and CPLEX solver, they showed that considering uncertainty in the coefficients of objective function assisted in minimizing the difference between the obtained results, allowing for improvement in the representation of several scenarios. The developed approach also provided solution possibilities to help choose the best weights to optimize goal programming problems.