Many process synthesis, intensification, and optimization problems involve multiple objectives that are conflicting to each other. Some of these objectives, such as sustainability, safety and circularity are not always quantifiable. Others, such as the demands, emissions, and feedstock utilization may evolve with time, new regulations and market variations. Making optimal decisions considering the decision-dependent tradeoffs between different objectives is a challenge [1,2]. Multiobjective optimization using the weighted sum method or the epsilon-constrained method provides Pareto solutions that are considered to be equally good but still depend on the preferences of a decision-maker, which may ultimately lead to suboptimal decisions. To mitigate this, we propose an opportunity cost-based single-objective formulation that appropriately accounts for all the decision-dependent tradeoffs. Specifically, each weight to an objective is replaced by a variable “shadow price†that captures the economic cost of making a unit change to an objective. The shadow price is particularly useful in putting monetary values on intangible objectives. For example, the shadow price of safety is the cost in dollars to make an incremental increase in the safety rating. Under this setting, it captures the tradeoff and interchangeability between the economic and safety objectives. To model how the shadow price (and hence the opportunity cost) depends on design and operational decisions, we use a distance function approach [3,4]. The distance function directly relates the inputs (decisions) with the outputs (objective values) and is a scaled measure of how close the objectives are to optimality [5,6]. Therefore, it can be used to rank different decisions extracted from a set of Pareto solutions. It is in this context that we study the mathematical formalism of distance function-based generalized multiobjective optimization for linear, discrete and nonlinear problems. For example, we study under which conditions this method have exact solutions, when this method reduces to the weighted sum method, and what forms of the distance function are applicable for a given problem type. We showcase the application of this method through comparing different intensified and non-intensified designs for ethylene glycol production. We also illustrate how this method can be used to calculate the cost of circularity of a chemical process in the context of circular economy.
References:
[1] K. Guillen-Cuevas, A. P. Ortiz-Espinoza, E. Ozinan, A. JimeÌnez-GutieÌrrez, N. K. Kazantzis, and M. M. El-Halwagi, “Incorporation of safety and sustainability in conceptual design via a return on investment metric,†ACS Sustain. Chem. Eng., vol. 6, no. 1, pp. 1411–1416, 2017.
[2] M. M. El-Halwagi, “A return on investment metric for incorporating sustainability in process integration and improvement projects,†Clean Technol. Environ. Policy, vol. 19, no. 2, pp. 611–617, 2017.
[3] R. W. Shephard, Theory of cost and production functions. Princeton University Press, 2015.
[4] R. Färe, Fundamentals of production theory. Springer, 1988.
[5] B. Brümmer, T. Glauben, and W. Lu, “The impact of policy reform on productivity and efficiency in Chinese agriculture: A distance function approach,†FE Working Paper, 2004.
[6] D. Abu-Ghunmi, L. Abu-Ghunmi, B. Kayal, and A. Bino, “Circular economy and the opportunity cost of not ‘closing the loop’of water industry: the case of Jordan,†J. Clean. Prod., vol. 131, pp. 228–236, 2016.
