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Ch43-I044963.fm Page 211 Tuesday, August 1, 2006 3:58 PM
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STEP 3-1: Selection of crossover points
STEP 3-2: Calculation of lower bound of tardiness
STEP 3-3: Determination of dominance of gene
STEP 3-4: Exchange of genes
STEP4 Evaluation of modified production schedule
If the shortest total tardiness of all the new individuals created in STEP3 is shorter than the total
tardiness of the cun'ent production schedule, the new modified production schedule is substituted for
the current production schedule. If the total tardiness of the new production schedule is shorter than the
constraint, the reactive scheduling process is terminated.
All the steps from STEP1 to STEP4 are repeated, until the created production schedule satisfies the
given constraint on the tardiness or all the manufacturing operations have started in the manufacturing
system.

COMPUTATIONAL EXPERIMENTS

Prototype of reactive scheduling system
A prototype of reactive scheduling system was implemented by using an object-oriented language,
Smalltalk. It was developed on a personal computer operating under the Windows system. The
prototype system was applied to some reactive scheduling problems for the tardiness minimization
problems in order to verify the effectiveness of the proposed method. The following experimental
conditions are based on the test cases proposed by Storer, Wu and Vaccari (Storer 1992).

• Job-shop type production scheduling problem
• Number of resources: 10
• Number of jobs: 50
• Parameters of GA: population size, crossover rate and mutation rate were 30, 0.5 and 0.1,
respectively. The values of these parameters were determined based on some case studies of the
job-shop type production scheduling problems.
• Interruptions: Some operations were randomly selected, and their operation times were enlarged.

Experimental results
A prototype of reactive scheduling system was applied to computational experiments for the tardiness
minimization scheduling problems. Some delays of manufacturing processes occurred, while the
manufacturing processes were in progress. The prototype system activated the reactive scheduling
process, in order to modify and to improve the disturbed initial production schedule.

Figure 3 shows the experiment results for the previous reactive scheduling method and the newly
proposed reactive scheduling method. The horizontal axis and the vertical axis show the time and the
total tardiness, respectively. The lines show that the new reactive scheduling method improves the
delayed initial production schedule faster than the previous reactive scheduling method.
Ten experimental results of the new reactive scheduling method were also compared with the results of
four types of rule based real-time scheduling methods, as shown in Figure 4. Through the comparison,
it was shown that the proposed reactive scheduling method improves the total tardiness shorter than
the real-time scheduling methods.