An optimization model: minimizing flour millers’ costs of production by blending wheat and additives

Abstract

ABSTRACT Grands Moulins d'Abidjan (GMA) is a flour milling company operating in Côte d'Ivoire. It wishes to determine the optimal blend of wheat and additives that minimizes its costs of production while meeting its quality specifications. Currently, the chief miller selects the mix of ingredients. The management of the company would like to dispose of a scientific tool that challenges the decisions of the chief miller. The thesis is about building and testing this tool, an optimization model. GMA blends up to six ingredients into flour: soft wheat, hard wheat, gluten, ascorbic acid and two types of enzyme mixes. Quality specifications are summarized into four flour characteristics: protein content, falling number, Alveograph W and specific volume of a baguette after four hours of fermentation. GMA blending problem is transformed into a set of equations. The relationships between ingredients and quality parameters are determined with reference to grains science and with the help of linear regression. The optimization model is implemented in Microsoft Office Excel 2010, in two versions. In the first one (LP for Linear Programming model), it is assumed that weights of additives can take any value. In the second one (ILP for Integer Linear Programming model), some technical constraints restrain the set of values that weights of additives can take. The two models are tested with Premium Solver V11.5 from Frontline Systems Inc., against four situations that actually occurred at GMA in 2011 and 2012,. The solutions provided by the model are sensible. They challenge the ones that were actually implemented. They may have helped GMA save money. The optimization model can nevertheless be improved. The choice of relevant quality parameters can be questioned. Equations that link ingredients and quality parameters, and particularly those determined with the help of linear regression, should be further researched. The optimization model should also take into account some hidden constraints such as logistics that actually influence the decision of GMA chief miller. Finally, sensitivity analyses may also be used to provide alternative solutions.