Typical real world optimization problems arise in the
following areas:
Supply Chain
Management
Transport
and Distribution
Production
Planning and Scheduling
Financial
and Investment Optimization
Telecommunication
Network Design
Portfolio
optimization / strategic planning
investment and divestment planning
depot location
problem
network and/or site design
planning
material
flow problems
blending
problems
scheduling and timetabling
problems
cutting stock and trim loss
problems
process design
and engineering
power generation
A Survey of Real World Problems
Here we describe in general some areas in which applications
of (linear and nonlinear) mixed integer optimization are found. This list
is by far not complete.
The brief survey of real world problems given in this
section is typical for
many businesses and industries but many other applications
also occur in
other areas:
Companies which are in a situation to utilize the advantages
of a complex
production network, often because they operate at several
sites, may greatly benefit from production planning and production
scheduling. Of course, scheduling problems occur also in other branches
of industry. These are operational branches and require detailed answers
to the questions: when is the production of a specific product on a specific
machine to be started? What does the daily production sheet of a worker
look like? Scheduling problems belong to a class of the most difficult
problems in optimization. Typical special structures, which can be tackled
by optimization, are minimal production rates, minimal utilization rates,
minimal production or transport amounts. Items of production must also
be sequenced.
Cutting stock or trimloss problems occurs in the metal or
paper industry. Depending on the cutting machines, onedimensional or
twodimensional patterns are cut. It is important that the mathematical
optimization model and algorithms reflects precisely the cutting logic.
Typical for the chemical process industry, but in modified
form also for the
mineral oil or food industry, are blending problems.
They occur in a wide variety. In Kallrath (1995) a model is described for
finding minimal cost blending which simultaneously includes container handling
conditions and other logistic constraints.
In planning it is often required to make a selection
from a series of projects in an optimal manner. This is clearly another
type of optimization problem.
The question of how a telecommunication network should
be structured and
designed when the annual demand is known, or what the
traffic infrastructure
should look like for a given traffic demand lead to network
design problems.
Specific skills often mean that only certain people can
perform specialized
tasks. Thus optimization methods can solve problems of
allocating
personnel
to tasks. Manpower modelling is discussed in Schindler and Semmel (1993).
People often need to be timetabled,
i.e., allocated to sessions
with conflicts being avoided. These applications lead to complex optimization
problems. They can be classified as resource constrained scheduling problem
with time windows.
Problems of distribution and logistics are fruitful
applications for optimization  choosing vehicles, routes, loads and so
on. While the problems listed above can be solved with linear
mixedinteger methods, problems occurring in process industry very
often lead to nonlinear discrete problems. Problems in the refinery
or petrcochemical industry include blending problems leading to socalled
pooling
problems.
If, in addition, we have to consider that plants operate in discrete modes,
or that connections between tanks and cracker or tanks and vacuum columns
have to be chosen selectively, than mixedinteger nonlinear optimization
problems need to be solved. Process network flow or process synthesis problems
usually fall into this category too. Examples are heat exchanger network,
distillation sequencing or mass exchange networks. It should not be inferred from this list of examples that
optimization is confined to large sophisticated problems occurring in large
organizations. Small problems are equally important, but it may be that
the role of techniques to solve problems is less important. Some small
problems lack the structure required for the use of optimization techniques
and for others the use of techniques would be seen as using a sledge hammer
to crack a nut. A balance is required where gains to be obtained by finding
optimal answers to a problem outweigh the effort required to obtain these
answers.
