Discussion on different approaches to decision making support is clearly
beyond the scope of this paper.
A large bibliography can be found
e.g. in [EKO90,KLW91,LeW89a,Mak94a,Ste92,WeW93,Mak96].
We will deal with one of the most successful classes of DSSs
(see e.g. [KoW89] for a justification of this statement),
namely with model based DSS which uses
aspiration-led multi-criteria optimization as a tool
for computing and selecting efficient solutions.
This approach, originally proposed in [Wie80,Wie82],
now has more than a dozen slightly different methodological versions.
The theoretical and methodological backgrounds for aspiration based
decision analysis and support is provided
e.g. in [Wie80,LeW89b].
A unified procedure that covers most of these approaches
has been proposed in [GaS94a,GaS94b].
Aspiration-Reservation Based Decision Support ( ARBDS) is an extension
of the aspiration-led multi-criteria model analysis.
The ARBDS methodology has been implemented in a number of
DSSs presented in [LeW89a].
The relations between ARBDS and other approaches to multi-criteria
optimization are discussed in more detail in [Mak94b].
ARBDS can also be considered, as demonstrated by [OgL92],
as an extension of Goal Programming
(see e.g. [ChC67] for details), most probably the oldest
technique for multi-criteria analysis of linear programs.
Today, ARBDS is one of the most promising techniques for
model based decision support.
Here we summarize the ARBDS method as a three-stage approach:
- First, a core model is specified and generated.
The core model contains only constraints that
correspond to logical and physical relations between the
variables used in the model.
Those variables should also include variables that represent
potential criteria
(goals, objectives, performance indices).
- Second, in the preparatory stage of the MCMA,
a DM selects (from the
core model variables)
a set of criteria that will be used for the analysis
of the model, and specifies a type for each criterion.
The selected type declares that a criterion is either
minimized or maximized or targeted at a given value
( goal type of a criterion,
see Section 4.2.1
for details).1
After the selection of a set of criteria, MCMA automatically performs
a series of optimizations in order to compute the Utopia point
and an approximation of the Nadir point.2
The preparatory stage
is finished with computation of the so-called
compromise solution which corresponds
to a problem for
which the aspiration and reservation
levels are (automatically)
set to the Utopia and an approximation
of the Nadir points, respectively.
- Third, an interactive procedure is used for helping the
user in selecting an efficient solution that best corresponds
to his/her preferences.
During such a procedure a DM specifies goals and preferences,
including values of criteria that he/she wants to achieve and to avoid.
The vectors composed of those values are called
aspiration and
reservation levels, respectively.
Such a specification defines component achievement functions
(see Section 2.1) which are used for selection
of a Pareto-optimal solution.
Such a solution is achieved by generation of additional constraints
and variables, which are added by MCMA to
the core model
thus forming an optimization problem, whose solution results
in a Pareto-optimal solution that is nearest (in the sense of a measure
defined by the aspiration and reservation
levels) to the
specified aspiration levels (or uniformly better than these
levels, if they are attainable).
The ISAAP handles the interaction with the user in the third stage
of the problem analysis, therefore we will provide more details
about this stage, which can be described in the form of the following
steps:
The DM specifies new aspiration and reservation
levels for all criteria which have the default status
(see Section 2.2.1).
For each stabilized criterion
(if any), the DM specifies
a corresponding target (desired) value and
aspiration and reservation
levels for a deviation from the specified
target value.
The details of this option are provided in Section 4.3.1.
Optionally, the DM can specify for those criteria his preferences
by a piece-wise linear CAF.
The methodological background for this
option is presented in Section 2.3 and its implementation
is documented in Section 4.4.1.
The DM can change the status of each criterion.
The default status can be changed to
inactive, disregarded or back to the original
status (which is one of min, max, goal, depending on
the type of the criterion).
This is supported by the Status option (see Section 4.4.3).
The DM can change the shape of component achievement function
corresponding to each criterion by either defining piece-wise
linear function (for the criterion values between aspiration and
reservation) or by stabilizing a criterion.
This is supported by the Shape option
(see Section 4.4.1 and 4.4.2, respectively).
The DM can analyze criteria values
of the solutions computed so far
(together with values of aspiration and reservation
levels used
for each solution). This part of analysis is supported by
the History option (see Section 4.5).
The DM may want to store a currently analyzed solution of
the underlying LP or MIP problem for a more detailed
analysis (which is typically problem specific).
This can be done by a selection of Store submenu from
the Solution menu of MCMA (see Figure 50
on page ![[*]](bpageforward.gif)
).
The DM can freely switch between the actions summarized above
until he/she decides that his/her preferences are properly represented
for the next optimization, which is selected as described
in Section 4.3.2.
Once the optimization is selected, the MCMA takes control
of the program flow,
MCMA generates a single-criterion optimization problem whose
solution is a Pareto-optimal solution
which corresponds to the
current preference structure of the DM (see Section 2.1
for details) and executes an appropriate solver, which computes
such a solution.
The DM regains control of the program when the solution of
the last specified problem is ready and added to the previously
obtained solutions.
The steps described above are repeated in order to explore various
Pareto-optimal solutions,
until a satisfactory solution
is found or until the user decides to break the analysis.
In either case the analysis can be continued from the last obtained
solution at a later time.
|
- ...details).1
- Note, that a variable
can represent also more complicated forms of
criteria (like following
a trajectory, minimization of a distance, etc.).
Examples of different types of criteria (which are formally
represented by a variable, whose value is either minimized or
maximized) and the way to handle so-called soft constraints in
the framework of ARBDS can be found e.g. in [Mak94b].
- ...point.2
- Utopia and Nadir points (in the space of criteria)
are vectors composed of best and worst values of the criteria
in the efficient set.
It can be shown (see e.g. [IsS87]) that a computation of
a Nadir point for problems with more than two criteria
may be very difficult.
In our approach the Nadir point plays a minor
informative role (it only bounds values of corresponding
reservation levels).
Therefore, there is no justification for spending resources in order
to get a better approximation.
Hence, we assume as an approximation of Nadir
the worst value (obtained during the analysis)
of a corresponding criterion.
