Programming models

Bostrom, A., UTDefect - a computer program modelling ultrasonic NDT of cracks and other defects, SKI report 95 53, Stockholm, 1995. 

There are special numerical analysis techniques for solving such differential equations. New issues related to the stabiUty and convergence of a set of differential equations must be addressed. The differential equation models of unsteady-state process dynamics and a number of computer programs model such unsteady-state operations. They are of paramount importance in the design and analysis of process control systems (see Process control). 

The best way to approach the retrofit synthesis of the heat-exchanger network is to model all five tasks simultaneously. A mixed-integer nonlinear programming model is usually formulated to accomplish this goal. 

Process Design vs. Accounting Linear Program Models... 

The process design linear program model is best written with flexibility in mind, such as extra matrix rows to provide flexibility in recycling, adding outside streams intermediate in the process, and determining component incremental values at each processing stage. This subject is discussed more fully later in this chapter. 

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 ... 

Zweifel G., Dorer V., Koschenz M., and Weber A. Building energy and systems simulation programs Model development, coupling and integration. IBPSA Fourth Intetnat. Conference, Madison, WI, Aug. 1995. 

Note that with Cao = Cco = Cqo = 0, Cbo = 1, ki = k3 = 0 the program models a simple first-order parallel reaction sequence. 

ALLEN, D. H. (1971) Brit. Chem. Eng. 16, 685. Linear programming models. 

Both the mixing process and the approximation of the product profiles establish nonconvex nonlinearities. The inclusion of these nonlinearities in the model leads to a relatively precise determination of the product profiles but do not affect the feasibility of the production schedules. A linear representation of both equations will decrease the precision of the objective but it will also eliminate the nonlinearities yielding a mixed-integer linear programming model which is expected to be less expensive to solve. 

A continuous-time mixed integer linear programming model for... 

I. E. (1997) A mixed-integer linear programming model for shortterm scheduling of single-stage multiproduct batch plants with parallel lines. Ind. Eng. 

Formulate a linear programming model for determining how much of each product the firm should produce to maximize profit. 

Assume that all other cash flows are fixed so that the profit to be maximized is total sales income minus the total cost of the constituents. Set up a linear programming model for determining the amount and blend of each grade of gasoline. 

Grossmann, I. E. and J. Hooker. Logic Based Approaches for Mixed Integer Programming Models and Their Application in Process Synthesis. FOCAPD Proceedings, AIChE Symp. Ser. 96 (323) 70-83 (2000). 

Chemical-industry related literature addressing value chain management focuses on production and supply chain management as well as selectively procurement. Companies in the oil and chemical industries have been leaders for almost 50 years in the development and use of linear and mixed integer programming models to support decision-making at all levels of planning (Shapiro 2004). 

J.A. Caballero I.E. Grossmann, 2001, Generalized disjunctive programming model for the optimal synthesis of thermally linked distillation columns,, Industrial Engineering Chemistry Research 40 (10) 2260-2274... 

H. Yeomans and I. Grossmann. Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res., 39(ll) 4326-4335, 2000. 

All in all, the petroleum industry has invested considerable effort in developing sophisticated mathematical programming models to help planners provide overall planning schemes for refinery operations, crude oil evaluation, and other related tasks. 

Addams, F.G. and Griffin, J.M. (1972) Economic-linear programming model of the U.S. petroleum refining industry. Journal of American Statistics Association, 67, 542. 

Manne, A. (1958) A linear programming model of the US petroleum refining industry. Econometrica, 26, 67. 

The use of mathematical programming models on an enterprise-wide scale to address strategic decisions considering various process integration alternatives yields substantial benefits. These benefits not only materialize in terms of economic considerations, but also in terms of process flexibility and improvements in the understanding of the process interactions and systems limitations. 

Jimenez, G.A. and Rudd, D.F. (1987) Use of a recursive mixed-integer programming model to detect an optimal integration sequence for the Mexican petrochemical industry. Computers e[ Chemical Engineering, 11, 291. 

Lee, H., Pinto, J.M., Grossmann, I.E., and Park, S. (1996) Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management Industrial el Engineering Chemistry Research, 35, 1630. 

---