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Ch41-I044963.fm Page 198 Tuesday, August 1, 2006 3:54 PM
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198 Page 198 Tuesday, August 1, 2006 3:54 PM
TABLE2
COMBINATION OF RESOURCE AND JOB HOLONS
wait Resoucel Resource2 ... Resource^
wait aoi ... ao r
Jobl flio an an ... a\ y
Job2 tf20 «21 Oil ... air
... . . . . . . ... . . .
Job£ ago am. ... as r
procedure for generating all pareto optimal combinations is formalized as a multi-objective optimization problem,
and the pareto optimal combinations of the job holons and the resource holons are defined as follows.

A matrix A = {<%• (/ = 0, 1, • • •, S,j' = 0, 1, • • •, /}} gives the combinations of job holons and resource holons, as
shown in Table 2. Where a,j= 1, if the job holon i is machined by the resource holon/ in the next time period.
Otherwise, ay = 0. If the job holon i or the resource holon j waits in the next time period, a® = 1 or ay = 1.
Otherwise, a® = 0 or a Oj = 0. Only one job holon is machined by one resource holon, therefore, the following
equations shall be satisfied.

•
S a,,= \ 2=1,2, ",<? (9)
;=0
y = 1 , 2 , •••, y (10)

If A is determined, the objective function values x, (A) of the job holon i and the ones x R (A) of the resource
holon/ are given by following equations, respectively.
' = 1,2, ••-,<? (11)

(12)

where, JOF,{j) and ROFfi) are the objective function values of the job holon / and the resource holony given by
following equations.

ROFj(i) = MEj, +l(i) or MAj, H(f) (14)
The objectives of the individual holons are to minimize their objective function values, therefore, the objective
functions for coordination among holons are given by following equations as the multi-objective optimization
problem.
[
m i n i m i z e d ) X(A) = x l (A), •••, x (A), x K(A), •••, x R (A)] (15)
A * is a pareto optimal combination, if there is no A such that the following equation is satisfied.
x£A) ^ x£A*) fora\lk,k=J uJ2,---Js,RuR2,--;Ry (16)

x{A) < x/(A*) iorstnyl,l=J\,J2,'"Jg,R\,R2,'"Jiy (17)
The coordination holon firstly generates all the candidates of A, which represent all the combinations of the job
holons and the resource holons. This process does not take long time, since the number of 'idling' holons is limited
at the time t. A set ofpareto optimal combinations {A p} are secondly obtained based on Eqn. 16andEqn. 17.