Mixed-Integer Nonlinear Programming Applications

In this chapter was apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems; a production planning problem in BASF’s petrochemical division; a site analysis of one of BASF’s bigger sites; and a process design problem. The first problem is related to a useful nonlinear extension of production planning problems based on time-indexed formulations. The second problem1 leads to a mixedinteger nonlinear model for describing a petrochemical network including several steam crackers and plants located at two different sites. The third problem, a network design problem, leads to mixed-integer nonlinear programming problem dominated by pooling problems (Kallrath and Wilson, 1997, hereafter KW97, Section 11.1.2), as is true for the second problem. The pooling problem refers to the intrinsic nonlinear problem of forcing the same (unknown) fractional composition of multi-component streams emerging from a pool (e.g. a tank or a splitter in a petrochemical network). The fourth problem is concerned with a process design problem in which some process parameters and the topology of a system of chemical reactors are the degrees of freedom to optimize total production, selectivity, energy, and costs. All numerical experiments and production runs have been carried out on a 166MHz Pentium processor.