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Ch41-I044963.fm Page 199 Tuesday, August 1, 2006 3:54 PM
3:54 PM
Page 199
Tuesday, August
Ch41-I044963.fm
1, 2006
199
199
Determination of Combination of Next Machining Processes
The coordination holon selects a suitable combination of the job holons and the resource holons from all the pareto
combinations, based on the objective functions of the whole HMS. The following two performance indices of the
whole HMS are considered in this research.
(1) Total slack
The total slack is given by the following equation.

SLACK= l(d- t - TWKRi) (18)

where, a, 4 and t are the number of the job holon in the HMS, the due date of the job holon i, and the current time,
respectively. TWKRi is the average of the total processing time of the remaining machining processes of the job
holon /which is given by following equation.

TWKRi= E (E T ihJy) (19)

where, T ikm is the machining time in the case where the m-\h (m=\,---,y) candidate resource holon carries out the
M i machining process of the job holon /'. /?and ^are the total number of the machining processes of the job holon
z, and the number of the machining processes finished by the current time t.
(2) Sum of the ratio of the next processing time and the remaining processing time
The sum of the ratio of the next processing time and the remaining processing time is given by the following
equation.

PT/TWKR= J.{T i{i +l)m/TWKRi) (20)

where, S and TWKRi are the number of the candidate job holons in the HMS, and the average of the total
processing time of the remaining machining processes of the job holon i, respectively. 7} ^+\yn means the
machining time of the next machining process of the job holon /.
The coordination holon calculates the total slack SLACK or the sum of the ratio of the next processing time and the
remaining processing time PT/TWKR for all the pareto combinations {A p}. Following this, the coordination holon
selects the combination of the job holons and the resource holons, which minimizes the SLACK or PT/TWKR.
That is, the coordination holon applies one of the rules called 'minimum SLACK' and 'minimum PT/TWKR'.

CASE STUDY

Some case studies have been carried out to verify the effectiveness of the proposed methods. The HMS model
consisting of 10 machining centers (MC) is considered for the case study. The individual machining center holons
have the different objective functions and the different machining capacities, such as the machining time 7*,,, the
machining accuracy MAdhn, and the machining cost MCOihn- As regards the job holons, 24 job holons are
considered in the case study, which have the different objective functions and the machining process. 8 cases are
considered in the case study by changing the machining capacities of the individual resource holons.

Figure 1 shows the verification of the objective functions of the individual holons and the whole HMS. The
vertical axis and the horizontal axis in the figures of the left and middle are the average of the objective function
values of all the holons and the type of the objective functions, respectively. It is found that the proposed method
keeps the objective function values of the individual holons in almost same as the ones obtained by the previous
method. The figures in the right give the average values of the total tardiness and the total make span of all the job
holons. Tt is shown that the proposed method improves the total tardiness and the total make span which are the
objective functions of the whole HMS.