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Last update: 06/2011

  CODING

 The string size is mxn, where m is the number of machines (operations) and n is the number of jobs. Each string item is a random integer number between [1, n]. This number is repeated as many times as operations are required the job.

For instance, the string size for a 3 machines x 4 jobs problem is 12 (=3 x4). The job1 is represented by number 1 and it is repeated 3 times because the job 1 has 3 operations ( 3 machines). The process is the same for the other jobs. Thus, one possible result is: [ 1 2 4 4 3 2 3 4 1 1 ].

We decode the symbolic representation from left to right:

• The first string's item is 1. It is the first 1. Thus it is decoded as job 1's first operation.

• The second string's item is 2. It is the first 2. Thus it is decoded as job 2's first operation.

• The third string's item is 4. It is the first 4. Thus it is decoded as job 4's first operation.

• The forth string's item is 4. It is the second 4. Thus it is decoded as job 4's second operation.

• The fifth string's item is 3. It is the first 3. Thus it is decoded as job 3's first operation.

• The sixth string's item is 2. It is the second 2. Thus it is decoded as job 2's second operation.

• The seventh string's item is 3. It is the second 3. Thus it is decoded as job 3's second operation.

• The eighth string's item is 2. It is the third 2. Thus it is decoded as job 2's third operation.

• The ninth string's item is 4. It is the third 4. Thus it is decoded as job 4's third operation.

• The tenth string's item is 1. It is the second 1. Thus it is decoded as job 1's second operation.

• The eleventh string's item is 1. It is the third 1. Thus it is decoded as job 1's third operation.

• The twelfth string's item is 3. It is the third 3. Thus it is decoded as job 3's third operation.

     References