1. What do you understand by sequencing problem?

2. Write short notes on the following:

- Sequencing decision problem for n jobs on two machines.
- Sequencing decision problem for n jobs on three machines.

1. Shahi Export House has to process five items through two stages of production, viz, cutting & sewing. Processing times are given in the following table:

Items | Time In Hours | |
---|---|---|

Cutting | Sewing | |

A | 7 | 4 |

B | 3 | 8 |

C | 11 | 9 |

D | 5 | 10 |

E | 12 | 6 |

Determine an order in which these items should be processed so as to minimize the total processing time.

2. Find the sequence that minimizes the total elapsed time required to complete the following jobs.

Processing time | Job | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Ai | 3 | 6 | 5 | 4 | 3 | 2 | |

Bi | 7 | 9 | 2 | 3 | 4 | 6 |

3. A book binder has one printing press, one binding machine, and the manuscripts of a number of different books. The times required to perform the printing and binding operations for each book are known. We wish to determine the order in which books should be processed on the machines, in order to minimize the total time required.

Books | Printing time | Binding time |
---|---|---|

1 | 30 | 80 |

2 | 120 | 100 |

3 | 50 | 90 |

4 | 20 | 60 |

5 | 90 | 30 |

6 | 110 | 10 |

4. Six jobs go first over machine I and then over II. The order of the completion of jobs has no significance. The following table gives the machine time in hours for six jobs and the two machines:

Job no. | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Machine I | 7 | 11 | 6 | 9 | 10 | 8 |

Machine II | 9 | 6 | 10 | 5 | 11 | 7 |

Find the sequence of the jobs that minimizes the total elapsed time to complete the jobs.

5. Find the sequence that minimizes the total elapsed time required to complete the following jobs:

Processing times in hours | ||||||
---|---|---|---|---|---|---|

No. of job | 1 | 2 | 3 | 4 | 5 | 6 |

Machine A | 4 | 8 | 3 | 6 | 7 | 5 |

Machine B | 6 | 3 | 7 | 2 | 8 | 4 |

6. We have five jobs, each of which must go through the two machines in the order AB. Processing times are given below:

No. of job | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Machine A | 9 | 1 | 17 | 5 | 19 |

Machine B | 3 | 11 | 13 | 15 | 7 |

Determine a sequence for the five jobs that will minimize the total elapsed time.

7. Find the sequence that minimizes the total elapsed time (in hours)
required to complete all the following jobs on machines M_{1},
M_{2} and M_{3} in the order M_{1}M_{2}M_{3}.

No. of job | A | B | C | D | E |
---|---|---|---|---|---|

M_{1} |
4 | 9 | 8 | 6 | 5 |

M_{2} |
5 | 6 | 2 | 3 | 4 |

M_{3} |
8 | 10 | 6 | 7 | 11 |

8. Find the sequence that minimizes the total time required for performing the following jobs on three machines in the order ABC.

Processing times | |||
---|---|---|---|

Jobs | Machine A | Machine B | Machine C |

1 | 8 | 3 | 8 |

2 | 3 | 4 | 7 |

3 | 7 | 5 | 6 |

4 | 2 | 2 | 9 |

5 | 5 | 1 | 10 |

6 | 1 | 6 | 9 |

9. We have five jobs, each of which must go through the machines A, B and C in the order ABC:

Processing times in hours | |||||
---|---|---|---|---|---|

Job no. | (1) | (2) | (3) | (4) | (5) |

Machine A | 5 | 7 | 6 | 9 | 5 |

Machine B | 2 | 1 | 4 | 5 | 3 |

Machine C | 3 | 7 | 5 | 6 | 7 |

Determine a sequence for the jobs that will minimize the total elapsed time.

10. Two jobs are to be performed on five machines A, B, C, D, and E. Processing times are given in the following table.

Job 1 |
Machine | ||||||
---|---|---|---|---|---|---|---|

Sequence | : |
A | B | C | D | E | |

Time | : |
4 | 5 | 3 | 7 | 3 | |

Job 2 |
Sequence | : |
B | C | A | D | E |

Time | : |
6 | 5 | 4 | 3 | 7 |

Use graphical method to obtain the total minimum elapsed time.