Solution of a multi-criteria shampoo production problem

This article presents a tri-criteria industrial problem which takes place in shampoo production. After an introduction of the industrial context, we develop the problem formulation and resent two mixed integer programs. The first is the most natural since it directly translates into mathematical terms all the constraints introduced in the problem formulation. The second model uses a trick to eliminate some variables and constraints. After this mathematical presentation, we focus on a heuristic which minimizes one of the three criteria. At last, we compare numerical results obtained by the solution of the two mathematical models and the heuristic.