MINLP-based Analytic Hierarchy Process to simplify multi-objective problems: Application to the design of biofuels supply chains using on field surveys

- We calculate weighting factors on the basis of the Analytical Hierarchy Process.
- Weights reflect experts' preferences on a given problem with maximum consistency.
- We use a weighting-based approach to solve multi-objective optimization problems.
- The proposed framework is applied to the sugar cane industry in Argentina.

Multi-objective optimization (MOO) is widely used in engineering systems design and planning. The solution of a MOO problem leads to a set of efficient points (Pareto set) from which decision-makers should identify the one that best fits their preferences. Generating this set requires large computational efforts, and the post-optimal analysis of the solutions becomes difficult as the number of objectives increases. This work introduces an approach based on the Analytic Hierarchy Process (AHP) to overcome these limitations. Through the definition of an aggregated objective function calculated using the AHP algorithm, a single-objective model is constructed that provides a unique Pareto solution of the original MOO model. The AHP is combined with a mixed-integer non-linear programming (MINLP) formulation that simplifies its application and is particularly suited to deal with many objectives (like those arising in sustainable engineering problems). The capabilities of the approach are demonstrated through a case study addressing the sustainable sugar/ethanol supply chain design problem.