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Operational Constraints for GHGs Emissions over Time

 

 

 

EES (Base Case) - Optimization Output

 

 

 

EES (Max Case) - Optimization Output

 

An optimal operational line for a fictitious organization is generated as an example of the usability of Multi-Objective Optimization. The firm’s GHG emissions are plotted over a period considering constraints such as Economic, Environmental, and Social. These three objectives have different priority levels, with Economic being the highest, followed by Environmental, and Social constraints.

The plot of Emissions vs Time has lower and upper boundaries for each of the constraints. If the process or activity violates the lower priority item, then the maximum it can go is to move through the lower boundary of the higher priority item. There will be an additional degree of freedom in the area where all the constraints are met and where we can go right to and along the upper bound to be able to maximize the remaining constraint (Economic). When it reaches at the juncture between Social and Environmental constraint, the optimal values can continue along the upper part of the Environmental constraint, to be able to maximize the Economics but still stay within the Environmental and Social constraints. From the crossing point between the upper boundary of the Environmental constraint and the lower bound of the Economic constraint, the optimized values move along the lower part of the Economic constraint till the end to try to minimize the Environmental constraint.

The program performs the simultaneous optimization. The resulting boundary lines are represented by X (Economic or Operational Constraint), Y (Environmental Constraint or Regulations), and Z (Social Constraint). The highest priority is always going to be satisfied within the boundaries. The optimal values follow along the lower boundary of Economic constraint to minimize, then follow the Environmental constraint, and then the Safety constraint.

To maximize the region within the lower and upper boundaries of the Social constraint within the Environmental and Economic constraints, a cost parameter can be added to the Social constraint to solve for the minimization problem.

The updated optimization values are going to be maximized in the area where all the constraints are met and the optimal line is going to the upper bound of the Social constraint, then continue on the Environmental constraint and then continue along the Economic constraint after that.