(599n) Environmentally Conscious Optimization of Chemical Supply Chains Using Dimensionality Reduction Techniques

The growing consumer demand for “green” products and toughening environmental protection legislation have boosted research on how to decrease the negative environmental impacts caused by supply chains (SC). As a result, a variety of multi-objective optimization (MOO) models aiming to balance economic and environmental benefits have been proposed so far. The complexity of these models grows rapidly with the number of objectives. For this reason, most MOO models have included only one single environmental indicator, typically the amount of emitted greenhouse gases (GHGs) emitted. However, several researchers ^6-8 have argued that this strategy is inadequate, mainly because reductions in GHG emissions might be achieved at the expense of increasing other negative environmental effects.

Aggregated environmental metrics ^8-10 have been proposed to provide a holistic picture of the environmental performance while still keeping the model bi-objective, The computation of aggregated metrics involves two main steps: normalization and weighting, which are both applied to a set of single environmental indicators. The aim of normalization is to refer the original impact values to a common basis before being aggregated into a single metric. Weighting procedures range different indicators according to the views of a pannel of experts that reflect the interests of the society or a group of stakeholders. The weakness of aggregation is that it uses fixed normalization and weighting parameters that may not represent the decision-makers' interests. Moreover, when used in a MOO framework, aggregated metrics may change dominance structure of the problem in a manner such that some solutions may be left out of the analysis ¹¹.

An alternative approach  for the environmentally conscious MOO of SCs consists of constructing an approximated model where the key environmental  objectives are kept and the redundant ones are omitted. So far, the elimination of objectives in environmental MOO problems has largely relied on the decision-makers' preferences, who typically select the most relevant criteria and drop the rest. This approach does not rely on any rigorous analysis, and for this reason may lead to large approximation errors. Objective reduction techniques arose in response to this situation. They allow transforming multi-objective problems with a large number of objectives into a meaningful equivalent with a reduced set of them. Ideally, the reduced representation should preserve the characteristics of the original problem, making it possible to identify the solutions of the original full space model by solving its simplified counterpart.

In this work, we propose an enhanced epsilon-constraint method that integrates an MILP-based strategy for dimensionality reduction, which computes the minimum subset of objectives that preserve the structure of a MOO model to the extent possible. To demonstrate the computational advantages of the proposed integrated strategy, we present two case studies of different complexity. These problems were solved via the proposed approach based on dimensionality reduction and the standalone epsilon-constraint method. By comparing the results of these two approaches, we conclude that our method outperforms the traditional epsilon constraint strategy in terms of Pareto quality (measured by the hypervolume indicator) and computational burden.

References

1.         Hugo, A., Rutter, P., Pistikopoulos, S., Amorelli, A., Zoia, G., 2005. Hydrogen infrastructure strategic planning using multi-objective optimization. International Journal of Hydrogen Energy 30 (15), 1523–1534.

2.         Zamboni, A., Murphy, R., Bezzo, F., Shah, N., 2011. Biofuels carbon footprints: Whole-systems optimisation for GHG emissions reduction. Bioresource Technology 102 (16), 7457–7465.

3.         Giarola, S., Zamboni, A., Bezzo, F., 2011. Spatially explicit multi-objective optimisation for design and planning of hybrid first and second generation biorefineries. Computers & Chemical Engineering 35 (9), 1782–1797.

4.         Giarola, S., Shah, N., Bezzo, F., 2012. A comprehensive approach to the design of ethanol supply chains including carbon trading effects. Bioresource Technology 107, 175–185.

5.         Akgul, O., Shah, N., Papageorgiou, L., 2012. An optimisation framework for a hybrid first/second generation bioethanol supply chain. Computers & Chemical Engineering, In Press.

Scharlemann, J. P. W., Laurance, W. F., 2008. Environmental science — how green are biofuels? Science 319 (5859), 43–44.

6.         Vries, S., Ven, G., Ittersum, M., Giller, K., 2010. Resource use efficiency and environmental performance of nine major biofuel crops, processed by first-generation conversion techniques. Biomass & Bioenergy 34 (5), 588–601.

7.         Cooper, D., Sehlke, G., 2012. Sustainability and energy development: influences of greenhouse gas emission reduction options on water use in energy production. Environmental Science & Technology 46 (6), 3509–3518.

8.         Guillén-Gosálbez, G., Grossmann, I., 2009. Optimal design and planning of sustainable chemical supply chains under uncertainty. AIChE Journal 55 (1), 99–121.

9.         Guillén-Gosálbez, G., Mele, F. D., Grossmann, I. E., 2010. A bi-criterion optimization approach for the design and planning of hydrogen supply chains for vehicle use. AIChE Journal 56 (3), 650–667.

10.       Bojarski, A., Laínez, J., Espuña, A., Puigjaner, L., 2009. Incorporating environmental impacts and regulations in a holistic supply chains modeling: An LCA approach. Computers & Chemical Engineering 33 (10),  1747–1759.

11.       Brockhoff, D., Zitzler, E., 2010. New developments in multiple objective and goal programming. Vol. 638 of Lecture Notes in Economics and Mathematical Systems. Springer: Berlin, Ch. Automated aggregation and omission of objectives for tackling many-objective problems.