# Heuristic Fss Methods Notes

This is a sample of our (approximately) 4 page long Heuristic Fss Methods notes, which we sell as part of the Operational Research Techniques Notes collection, a 1st Class package written at LSE in 2011 that contains (approximately) 104 pages of notes across 17 different documents.

### Heuristic Fss Methods Revision

The following is a plain text extract of the PDF sample above, taken from our Operational Research Techniques Notes. This text version has had its formatting removed so pay attention to its contents alone rather than its presentation. The version you download will have its original formatting intact and so will be much prettier to look at.

Lecture 9: Heuristic FSS Methods / Heuristic TSP Methods Topics

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

****************************End Of Sample*****************************

Buy the full version of these notes or essay plans and more in our Operational Research Techniques Notes.