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Ch58-I044963.fm Page 291 Tuesday, August 1, 2006 4:39 PM
1, 2006
Tuesday, August
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Ch58-I044963.fm
4:39 PM
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Each generated chromosome includes the corresponding DSM. The proposed method uses the
following functions to calculate the individual's fitness.
(1)

where m tj shows the element of the line i and the column j in the DSM, N is the number of tasks, C,
and C 2 are two coefficients. The first term of Eqn. 1 has the effect to reduce the number of "10" and
"1" in the upper-right field of the matrix. In the DSM expression, the order of the matrix represents
"
the task order, and the 1" in the upper-right field represents the point for the back loop of the process.
Therefore, the first term has the effect to reduce the possibility of the back loop coming from the
dependency relations between the tasks and satisfy the essential constraints. The second term shortens
"
the distance from the "10" and/or 1 " to the diagonals, which is represented as j-i in the equation as
seen in Figure 5. This effectively makes the size of the back loop smaller with the satisfaction of the
essential constraint.
Distance is equal to 3
/
CM in to CO
Task Task in TasI. \ i CO TasI.
Task 1 0 a 1 fa ^ 0 I 0 0
Task 2 • 0• 0 10 jo 0 0
Task 3 0 0 I I 1 '0 1 0
Task 4 1 0 0• 0 0 0
Task 5 0 1 0 0 i 0 1 0
Task 6 0 0 0 1i 1 . 0 0
Task 7 0 1 0 0 0 ol 1 0
Task 8 0 o 0 0 0 of 0•
Figure 5: Expression of chromosome

CASE STUDY
The new technique to improve the oversea production preparation was evaluated using a hot forging
trial process. This process can be divided into the following three trial phases.
• Trial phase with an experimental set up
• Domestic trial phase by machines used after starting the production
• Overseas trial phase

A total of 95 physical parameters in this process are extracted as shown in Table 1. The process
optimization using the presented method was able to improve the lead time by around 40%, in
comparison with the sequential trial. Furthermore, the proposed method realized the optimized process
while satisfying all the essential constraints. Figure 6 shows the part of the matrix which includes the
essential constraints on the task order. Figure 6(a) shows the result of the method without
consideration for the essential constraints on the task order. The task group in Figure 6 shows the
tasks which should be performed together. Task A and Task E compose one group. Figure 6(b) shows
the result of the method considering the constraints. The task groups in both cases are the same. But
the order of the tasks differs between Figure6(a) and (b). Only the process in Figure 6(b) satisfies the
essential constraints.