Linear programming modeling systems

The above discussion shows the importance of petrochemical network planning in process system engineering studies. In this chapter we develop a deterministic strategic planning model of a network of petrochemical processes. The problem is formulated as a mixed-integer linear programming model with the objective of maximizing the added value of the overall petrochemical network. 

Fries and Marathe (1981) used mathematical models to determine the optimal variable-sized multiple-block appointment system. Calichman (1990) used a linear programming model to btiltmce the bed demand among various surgical services. 

The general production model can be formulated as a linear programming model, and its optimization represents the optimal determination of quantities to produce in order to maximize the profit (Lucertini 1999). In details let b the set of resources of the production system to be transformed in product quantities x through the technological modalities A. A is the technological matrix and its generic element Ay defines the resource of type needed to produce a unit of product j. 

Mathematical modeling, using digital computers, aids in performing a systems-type analysis for either the entire system or parts of it. By means of integer or linear-programming techniques, optimum systems can be identified. The dynamic performance of these can then be determined by simulation techniques. 

This chapter explains the general representation of a petrochemical planning model which selects the optimal network from the overall petrochemical superstructure. The system is modeled as a mixed-integer linear programming (MILP) problem and illustrated via a numerical example. 

A Varian 3400 gas chromatograph equipped with a flame ionization detector and a nonpolar fused silica capillary column (60 m x 0.25 mm i.d. 0.25 pm thickness, SPB-1, Supelco, Inc.) was used to analyze the volatile compounds from the model systems. The injector temperature was 250°C, and the detector temperature was 260°C. The flow rate of the helium carrier gas was 1 mL/min and the split ratio was 50 1. The temperature program consisted of a 10 min isothermal period at 35°C, temperature increases of 2°C/min from 35°C to 120°C and of 4°C/min from 120°C to 235°C, and a 40 min. isothermal period at 235°C. The chromatograms were plotted and integrated on a Varian 4270 integrator. Linear retention indices for the volatile compounds were calculated using n-paraffin standards (C6-C25 Alltech Associates) as references according to the method of Majlat and co-workers (5). 

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