Process modeling using linear programming program models

The example used here does not represent any particular process and is simpler than most real life plant cases. It does, how ever, have the elements needed to talk our way through the development of a process design linear program model. All models should have the following ... 

This problem can be cast in linear programming form in which the coefficients are functions of time. In fact, many linear programming problems occurring in applications may be cast in this parametric form. For example, in the petroleum industry it has been found useful to parameterize the outputs as functions of time. In Leontieff models, this dependence of the coefficients on time is an essential part of the problem. Of special interest is the general case where the inputs, the outputs, and the costs all vary with time. When the variation of the coefficients with time is known, it is then desirable to obtain the solution as a function of time, avoiding repetitions for specific values. Here, we give by means of an example, a method of evaluating the extreme value of the parameterized problem based on the simplex process. We show how to set up a correspondence between intervals of parameter values and solutions. In that case the solution, which is a function of time, would apply to the values of the parameter in an interval. For each value in an interval, the solution vector and the extreme value may be evaluated as functions of the parameter. 

In order to make the problem solvable, a linearized process model has been derived. This enables the use of standard Mixed Integer Linear Programming (MILP) techniques, for which robust solvers are commercially available. In order to ensure the validity of the linearization approach, the process model was verified with a significant amount of real data, collected from production databases and production (shift) reports. 

The use of linear programming to optimize the flow of process streams through a petroleum refinery began in the mid-1950 s (Symonds, 1955 Manne, 1956). Now, almost twenty-five years later, it is safe to say that one half of U.S. refining capacity is represented by linear programming or LP models which are routinely optimized to schedule operations, evaluate feedstocks, and study new process configurations. 

Test the plan Optimize the process Start by testing the top few suspected variables through observational analysis. Develop and update a regression model as each new variable is tested. Check the production model to verify any improvement in the process and quality that may have occurred. Now optimize the process using EWIMA, linear programming, iterative solving, and process simulation techniques. 

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