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Ch58-I044963.fm Page 289 Tuesday, August 1, 2006 4:39 PM
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constraints on the task order will be described in detail, further below. With respect to such a
hierarchal model for the production preparation process, we developed an optimization technique as
shown below.

Production preparation process

Dependency relation of design tasks
Essential constraint
of task order Physical cause-effect
Company's design
relation
standards
of designed object
Figure 2: Hierarchical relation model of production preparation process

Description in relation diagram

The current technique (Sato et ah, 2003) requires the engineer to input the physical relations between
the designed variables, measured process data, and performance measures in the matrix. However,
adding the relations in the matrix is difficult for most practical cases. We found that the matrix
expression is useful to analyze the process, but the engineer is hesitant to use the matrix expression to
visualize their knowledge.

Incidentally the engineers usually use the seven fundamental tool of the QC as the numerical method
for the quality control activity. Furthermore they have the new seven tool of the QC as the linguistic
method. These tools are used as the basic techniques for business reengineering and problem solving
in the production area. The relation diagram is one of the seven new tools of the QC. This diagram is
the method to describe the cause-effect relations if many causes are interacting with each other.
Many engineers are familiar with describing the relation diagram for problem solving.
The proposed method in this paper uses the relation diagram to visualize the physical relation as seen
in Figure 1, and subsequently transforms the diagram to the matrix formation.

Optimization algorithm
In the actual process, there are many causes that constrain the task order strongly coming from
something except for the dependency relation between the tasks. One example is about the time
required to complete each task. The engineers have to do the tasks in the earlier stage, which take long
time to be performed. Another example is the situation that some tasks have been completed when the
target process starts. The optimization algorithm used in the current technique (Sato et al., 2003)
cannot consider the essential constraint on the task order except for the dependency relation between
tasks to generate the task order.
In this paper, one of the modern heuristic methods in the artificial intelligence research field, Genetic
Algorithm (GA) (Holland, 1975), is used. This method can consider various constraints flexibly by
modifying the fitness function. The expressions of the essential constraints and the chromosome of
the GA are explained in the following sections. The crossover operation method and the fitness
function to evaluate each chromosome are also described subsequently.