A. Neumaier,
Mathematical Model Building, Chapter 3 in: Modeling
Languages in Mathematical Optimization (J. Kallrath,
ed.), Kluwer, Boston 2003. (pdf) Some notes on mathematical modeling, listing
motivations, applications, a numerical toolkit, general modeling
rules, modeling conflicts, useful attitudes, and
structuring the modeling work into 16 related
activities by means of a novel modeling diagram.

A. Neumaier, Fuzzy modeling in terms of surprise, Fuzzy Sets and Systems 135
(2003), 21-38.

H. Schichl,
Models and the History of Modeling, Chapter 2 in: Modeling Languages in Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston
2003.(pdf) After a very fast tour through 30,000 years of modeling history, the basic ingredients to models in
general, and to mathematical models in particular, are described.

H. Schichl,
Theoretical Concepts and Design of Modeling
Languages, Chapter 4 in: Modeling Languages in
Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003.(pdf) The basic design features of modeling languages and particularly algebraic modeling languages are presented. An important class of optimization
problems --- global optimization is introduced, and the difficulties in
constructing models for such problems are illustrated.

H. Schichl
and A. Neumaier, The NOP-2 Modeling
Languages, Chapter 15 in: Modeling Languages in
Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003.(pdf) A short overview over the modeling language NOP-2 for specifying general optimization
problems, including constrained local or global nonlinear programs and
constrained single and multistage stochastic programs, is presented. The
proposed language is specifically designed to represent the internal (separable
and repetitive) structure of the problem.

H. Schichl,
A. Neumaier and S. Dallwig,
The NOP-2 modeling language, Ann. Oper.
Research 104 (2001), 281-312. (pdf) An enhanced version NOP-2 of the NOP language for specifying global optimization problems is
described. Because of its additional features, NOP-2 is comparable to other modeling languages like AMPL and GAMS, and allows the user
to define a wide range of problems arising in real life applications such as
global constrained (and even stochastic) optimization programs. NOP-2 permits
named variables, parameters, indexing, loops, relational operators, extensive
set operations, matrices and tensors, and parameter arithmetic. The main
advantage that makes NOP-2 look and feel considerably different from other modeling languages is the display of the internal analytic
structure of the problem. It is fully flexible for interfacing with solvers
requiring special features such as automatic differentiation or interval arithmetic.

Hermann Schichl;
Modeling Languages and Global Optimization

Jan Bisschop;
AIMMS - An All-Round Development Environment

Collective Communication
Optimization with Dynamic Programming in Heterogeneous Cluster Environments

Papers (EconPapers)

Geoffrion, A.M., "Structured Modeling," in *Encyclopedia**
of Operations Research & Management Science*, S.I. Gass
and C.M. Harris (Eds.), Kluwer Academic Publishers
(1996). Revised version
published in the Centennial Edition, 2001.

Geoffrion, A.M., "An Introduction to Structured Modeling," *Management Science*, **33**:5, 547-588 (May 1987).

Geoffrion, A.M., "An Introduction to Structured Modeling," *Management Science*, **33**:5, 547-588 (May 1987).

Geoffrion, A.M., "The Formal Aspects of Structured Modeling," *Operations Research*, **37**:1, 30-51 (January-February
1989).

Geoffrion, A.M., "Computer-Based Modeling
Environments,"
*European Journal of Operational Research*, **41**:1, 33-43 (July 1989).

Geoffrion, A.M., "FW/SM: A Prototype Structured Modeling Environment," *Management Science*, **37**:12,
1513-1538 (December 1991).

Geoffrion, A.M., "The SML Language for Structured Modeling: Levels 1 and 2," *Operations Research*, **40**:1,
38-57 (January-February 1992).

Geoffrion, A.M., "The SML Language for Structured Modeling: Levels 3 and 4," *Operations Research*, **40**:1,
58-75 (January-February 1992).

Geoffrion, A.M., "Indexing in Modeling
Languages for Mathematical Programming," *Management Science*, **38**:3,
325-344 (March 1992).

Geoffrion, A.M., "Structured Modeling:
Survey and Future Research Directions," *ORSA CSTS Newsletter*, **15**:1, 11 pages (Spring, 1994). Updated
May, 1996 and June, 1999 and published in *ITORMS: Interactive Transactions on Operations Research and Management
Science*, **1**:3.

Geoffrion, A.M., "An Informal Annotated Bibliography
on Structured Modeling," *ITORMS: Interactive Transactions on Operations Research and Management
Science*, **1**:2. Most recently updated June, 1999.