Lecture 9: Heuristic FSS Methods / Heuristic TSP Methods
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
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
