Integration of Optimization to the Design of Pulp and Paper Production Processes - Simulation and Modeling Methodologies, Technologies and Application - page 231

3 Model for Optimizing Design Process

Optimizing process design is here modelled in terms of a business process model. The
model describes the stakeholders of the optimizing process design and their activities
together with the data, knowledge and utilized mathematical models. Based on these
the requirements for IT support are identified.
In this research, the workflow, roles, data and tools have been considered without
organizational boundaries. In real life, these boundaries can have significant influence
of the realization of this business process model. For example the enterprises can use
different tools and all the data is not necessarily open for everyone. Also the business
models for every stakeholder differ and therefore the different goals have to be taken
into account in design process model.

3.1 Process Design as an Optimization Problem

The process design task can be considered as an optimization problem. There are a
few general requirements for the process. The process must be operable, reliable and
yield products of sufficient quality with minimum operational cost. On the other hand
the investment and maintenance cost of the process should be minimized as well. On
this basis it is natural to consider and model the design problem as a bi-level multi-
objective optimization problem. The mathematical representation of the general bi-
level multi-objective optimization problem is:

min Fx ( ) = ( F x ( ),... F x ( )),

(, xx 1 M

ui )

{ }

subject to x ∈ arg min f ( ),..., x f g x ( ) ≥ 0, h x ( ) = 0 ,

i () x 1 m x ( )

(1)

i

Gx ( ) ≥ 0, H x ( ) = 0,

() L ( ) U

x ≤≤ x x , i = ,..., . n

i i i

where
F (x) are the upper level objective functions,
f (x) the lower level objective functions,
G (x), g (x), H (x) and h (x) the upper and lower level inequality and equality con-
straints.[25]
There are multiple methods for solving bi-level multi-objective optimization
(BLMOO) problems [15] and [26] and the solution method should be chosen accord-
ing to the problem itself and the possibilities for interaction with the decision maker
[27] In the plant design process, there is a logical division to optimization levels, so
that plant structure is the upper level ( F (x)) and the operation of the plant is the lower
level ( G (x)). The nature of the plant design is also multi-objective; the balancing be-
tween design parameters as for example the total cost of the plant, operational costs,
production quality, production volume and expected oee-value is difficult and the
decision of these values belongs to the plant owner, not the designer. Therefore the
gathered requirements should also cover business oriented user preferences.