abstract
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Linear Programming (LP) has a wide range of industrial applications, including closed-loop systems such as real-time optimization and the steady-state economic optimization at each execution of Model Predictive Controllers. This thesis presents new metrics for monitoring the performance of linear closed-loop real-time optimization systems, as well as new methods for improving their performance when necessary. A novel diagnostic method for ranking parameter importance with respect to the objective function is also presented.
Many standard methods are available for estimating the effects of parameter uncertainty on the objective function without a basis change, and more powerful existing methods require enumeration or sampling. This work introduces new sensitivity methods in LP problems with uncertain coefficients that can be correlated, appear in equality and inequality constraints, and have uncertainties with large enough magnitudes to lead to basis changes.
The new monitoring approach measures the uncertainty effect as the range between the maximum and minimum profit in the plant under closed-loop optimization, termed the Profit Gap, and both its maximum and expected values can be determined.
If the monitoring indicates a substantial Profit Gap could exist, the improvement step designs experiments to reduce parametric uncertainty. The unique experimental design maximizes the total profit during and after the experiment to the end of a production run.
Both the monitoring and improvement methods involve the solution of bilevel optimization problems, which include complementarity constraints. Results of application to a closed-loop gasoline-blending problem demonstrate the power of the methods. The studies include typical uncertainties and measurement noise and show the economic benefits possible through the application of real-time monitoring and improvement.