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problems; and (4) enhanced interfaces to other systems, such as
MATLAB and Java.
LINDO API was the first full-featured solver with a callable
library to offer general nonlinear and integer nonlinear capabilities.
This feature allows developers to incorporate a single, general-
purpose solver into their custom applications. The software’s linear
and integer capabilities provide the user with a comprehensive set
of routines for formulating, solving, and modifying nonlinear
models (although a separate, nonlinear license must be purchased to
access these nonlinear capabilities). The global solver combines
techniques for range bounding (e.g., interval analysis, convex
analysis) and range reduction (e.g., linear programming, constraint
propagation) within a branch-and-bound framework to find proven
global solutions to nonconvex nonlinear programs or mixed-integer
nonlinear programs.

9.6.4 Frontline Systems
Solvers (optimizers) are software tools that help users find the best
way to allocate scarce resources. Frontline Systems (Solver.com,
2009) offers products that cover several problem types and that
allow model definition via an Excel spreadsheet or via a program
written in any of several common programming languages and
environments (e.g., Visual Basic, C/C++/C#, VB.NET, Java, MATLAB).
Models designed using these solver products include decision
variables for quantities of resources as well as calculated results
(constraints) that are subject to limits (e.g., budget, capacity, and/or
time constraints).

9.6.5 ILOG ODM
The ILOG system is geared toward optimizing decisions and thereby
finding the best solutions to complex planning and scheduling
problems. It provides an application environment that supports the
flexible exploration of all the trade-offs and sensitivities. Thus, the
ILOG optimization decision manager (ODM) makes optimization
easier (ILOG, 2006); see Figure 9.9. A unique aspect of ODM-based
applications is that they provide all the features that business people
need to take full advantage of optimization technology. Applications
built using ILOG ODM allow users to create, visualize, and compare
planning or scheduling scenarios, to adjust any of the model’s inputs
or goals, and to comprehend the relevant binding constraints, trade-
offs, sensitivities, and business options.
With ODM-based applications, overconstrained problems are
automatically relaxed during runtime by ILOG CPLEX, which is
programmed to relax the least important (and fewest possible)
constraints. This ensures that a solution will always be found, and
solutions are presented along with clear information about any