Linear program

Thus, if film transfer coefficients vary significantly, then Eq. (7.6) does not predict the true minimum network area. The true minimum area must be predicted using linear programming. However, Eq. (7.6) is still a useful basis to calculate the network area for the purposes of capital cost estimation for the following reasons ... 

Calculate the weighted network area Anetwork from Eq. (7.22). When the weighted h values i4>h) vary appreciably, say, by more than one order of magnitude, an improved estimate of Anetwork can be evaluated by linear programming. ... 

Grossmann, I. E., Mixed-Integer Non-Linear Programming Techniques for the Synthesis of Engineering Systems, Res. Eng. Design, 1 205, 1990. 

Linear paraffins Linear programming Linear rollback model Linear sensor arrays Linear superelasticity Linear topology Linear units Linen... 

A. M. Morshedi, C. R. Cutier, and T. A. Skrovanek, "Optimal Solution of Dynamic Matrix Control with Linear Programming Techniques,"... 

If the source fingerprints, for each of n sources are known and the number of sources is less than or equal to the number of measured species (n < m), an estimate for the solution to the system of equations (3) can be obtained. If m > n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for L. This is the basis of the chemical mass balance (CMB) method (20,21). If each source emits a particular species unique to it, then a very simple tracer technique can be used (5). Examples of commonly used tracers are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. The condition that each source have a unique tracer species is not often met in practice. 

In real-life problems ia the process iadustry, aeady always there is a nonlinear objective fuactioa. The gradieats deteroiiaed at any particular poiat ia the space of the variables to be optimized can be used to approximate the objective function at that poiat as a linear fuactioa similar techniques can be used to represent nonlinear constraints as linear approximations. The linear programming code can then be used to find an optimum for the linearized problem. At this optimum poiat, the objective can be reevaluated, the gradients can be recomputed, and a new linearized problem can be generated. The new problem can be solved and the optimum found. If the new optimum is the same as the previous one then the computations are terminated. 

Otherwise, the iterations consisting of formulation of linear approximations and the solution of the linear programming problem are continually repeated (48). 

Linear programming. Most current commercial codes for hn-... 

Selection of feedstock for thermal cracking to ethylene by linear programming... 

Miirty, Linear Programming, Wiley, New York, 1983. Reklaitis, Ravin-dran, and Ragsdell, Engineeiing Optimization, Wiley—Interscience, New York,... 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are hnear. While the solution is iterative, it can be obtained qmckly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predic tive control. The dominant method used in the refining industiy utilizes the solution of a QP and is called dynamic matrix con-... 

Production Controls The nature of the produc tion control logic differs greatly between continuous and batch plants. A good example of produc tion control in a continuous process is refineiy optimization. From the assay of the incoming crude oil, the values of the various possible refined products, the contractual commitments to dehver certain products, the performance measures of the various units within a refinery, and the hke, it is possible to determine the mix of produc ts that optimizes the economic return from processing this crude. The solution of this problem involves many relationships and constraints and is solved with techniques such as linear programming. 

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. 

Once the highest steam level is set, then intermediate levels must be established. This involves having certain turbines exhaust at intermediate pressures required of lower pressure steam users. These decisions and balances should be done by in-house or contractor personnel having extensive utility experience. People experienced in this work can perform the balances more expeditiously than people with primarily process experience. Utility specialists are experienced in working with boiler manufacturers on the one hand and turbine manufacturers on the other. They have the contacts as well as knowledge of standard procedures and equipment size plateaus to provide commercially workable and optimum systems. At least one company uses a linear program as an aid in steam system optimization. 

Many process engineers think of linear programming (L.P.) as a sophisticated mathematical tool, which is best applied by a few specialists extremely well grounded in theory. This is certainly true for your company s central linear program. The layman does not write a linear program, he only provides input that will model the process in which he is interested. 

The linear program can be designed to deliver a wealth of base case information, such as ... 

If plant expansion is being studied with the idea of determining the best practical upper limit, the linear program can be a great help. Each incremental expansion step can be evaluated and payouts determined off line. Also, each piece of proposed new equipment can be evaluated as to its effect on the entire plant. 

Having a linear program available allows the designer to generate better designs, but does not necessarily make his job easier. In fact, it may put additional pressure on him to be sure his results are optimal rather than just a satisfactory design. 

Process Design vs. Accounting Linear Program Models... 

---