## Exercise 3 Solution Case Solution

**Part 1**

The new fictitious work centers with their times would be as follows:

Work Center 1 | Work Center 2 | |

David | 3 | 4 |

John | 5 | 5 |

Cindy | 4 | 7 |

Peter | 5 | 4 |

Isabel | 4 | 2 |

Therefore, based upon the above work center processing times it could be said that in the optimal sequence |

the Johnson's rule is being applied and that it would result in the minimization of the globl completion times. |

**Part 2**

The optimal sequence is : | |

David>Cindy>John>Peter>Isabel |

| ||||||

David | Cindy | John | Peter | Isabel | TOTAL | |

Surgery | 2 | 3 | 7 | 11 | 14 | 37 |

Radiology | 1 | 4 | 5 | 6 | 7 | 23 |

Orthopedy | 3 | 7 | 11 | 14 | 15 | 50 |

It will take total of 15 hours to complete all treatments.

| ||||||

David | Cindy | John | Peter | Isabel | TOTAL | |

Surgery | 0 | 2 | 3 | 7 | 11 | 23 |

Radiology | 0 | 1 | 4 | 5 | 6 | 16 |

Orthopedy | 0 | 3 | 7 | 11 | 14 | 35 |

| |

Surgery | 37.84% |

Radiology | 30.43% |

Orthopedy | 30.00% |

**Part 3**

Based upon Gupta's Rule | |

ej | |

David | 1 |

John | 0 |

Cindy | 1 |

Peter | -1 |

Isabel | -1 |

Therefore, the schedule based upon Gupta's rule would be: | |

Peter>Isabel>John>David>Cindy |

The global completion time would be same as compared to part b, | |

however, the waiting times for each patient would differ. |

**Part 4**

If an alternative global completion time is calculated based upon | ||

alternative scheduling based on Gupta's rule then the total | ||

global completion time (makespan) would be same in this case as | ||

the time for treatment for each patient is constant. | ||

| |||||

Peter | Isabel | John | David | Cindy | |

Surgery | 4 | 7 | 11 | 13 | 14 |

Radiology | 1 | 2 | 3 | 4 | 7 |

Orthopedy | 3 | 4 | 8 | 11 | 15 |

It could be seen that still the global completion time is same on alternative scheduling basis...................

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