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Heuristic Fss Methods Notes

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Lecture 9: Heuristic FSS Methods / Heuristic TSP Methods Topics

Reading

Heuristic Approaches to Flow Shop Scheduling Johnson's "Standard" 3 Machines Algorithm Johnson's 3-Machine "Difference" Algorithm 3 Machines Flow Shops: "Sequencing on the Two Dominant Machines" Heuristic Solutions to Traveling Salesman Problems (TSPs)

Key Points

• Why use heuristic approach to FSS

• Johnson's standard 3 machine algorithm

• Makespan

• Johnson's 3 machine difference algorithm

• Sequencing on the two dominant machines

• Travelling salesman problems

Heuristic Approaches to Flow Shop Scheduling

• If none of the 3 conditions of the Johnson's 3-machines algorithm are satisfied, we need an heuristic approach

• Use any approach that may throw up a good schedule

• One heuristic approach may be to use Johnson's 3MC method even though the optimality test fails

Johnson's "Standard" 3 Machines Algorithm

• One step ahead TSP algorithm Definitions

• Makespan = A lower bound on the final project completion time

• Traveling Salesman Problem = Starting from O, you must travel to each of N places. You can travel to each place only once in any sequence and on leaving the Nth destination you must return to O for the first time.

Example of Johnson's Standard 3 Machines Algorithm Formulae

Makespan

• Makespan = A lower bound on the final project completion time

• In the best possible theoretical case:

• No hold-ups occur

• Consider each machine in turn to be a potential bottleneck

• Leads us to three lower bounds on the makespan

○ ∴ In the example above, the lower bound on the makespan will be:

 This tells us that it is impossible for the project to be completed in less that 75 days
 This does not mean that there is or isn't a better schedule than our 78 day one Our conclusion based on the makespan
 "either our project completion time of 78 days is optimal, or, if it is not, it is at most 3 days non-optimal"
 It is very important to clearly conclude this

Johnson's 3-Machine "Difference" Algorithm A variation on the "standard" algorithm

Course Notes Page 15

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