1. Lecture 6: Job Shop Scheduling Introduction
© J. Christopher Beck 2005

2. Outline Job Shop Scheduling Introduction to Solution Techniques LEKIN
Basic Definition
Introduction to Solution Techniques
© J. Christopher Beck 2005

3. Job Shop Scheduling Operation/Task/ Activity Job Precedence Constraint
© J. Christopher Beck 2005

4. Job Shop Scheduling JSP is Hard RCPSP is a generalization of JSP
makespan
© J. Christopher Beck 2005

5. Your Very Own JSP Can you find a schedule with a makespan of 31?
Don’t forget about the precedence constraints on the activities in each job
Activities
Jobs 1 2 3 4
M1, 9
M2, 8
M3, 4
M4, 4
M1, 5
M2, 6
M4, 3
M3, 6
M3, 10
M1, 8
M2, 9
M4, 2
© J. Christopher Beck 2005

6. Solving the JSP Many, many approaches
20,300 hits on Google Scholar
Also used to solve other scheduling problems and other optimization problems
We are going to spend the next 6 lectures talking about them
© J. Christopher Beck 2005

7. Dispatch Rules
Whenever a machine is free, look at all operations that can be scheduled and pick on with a simple rule:
SPT: shortest processing time
LPT: longest processing time
EDD: earliest due date
Try out SPT
Activities
Jobs 1 2 3 4
M1, 9
M2, 8
M3, 4
M4, 4
M1, 5
M2, 6
M4, 3
M3, 6
M3, 10
M1, 8
M2, 9
M4, 2
© J. Christopher Beck 2005

8. Shifting Bottleneck Pick most loaded resource
Find optimal one-machine schedule
Pick next most loaded resource
Find optimal one-machine schedule consistent with previous one-machine schedules
(This is a bit simplified)
© J. Christopher Beck 2005

9. Tabu Search Start with a random schedule
Make a “move” (e.g., swap two operations)
Remember you last few moves and don’t undo them
Keep going until you get bored
© J. Christopher Beck 2005

10. Integer Programming and Branch-&-Bound
Represent problem as an IP
Sequence of every pair of operations is a 0-1 variable
Use Branch-&-Bound (B&B) to find solution
Will find optimal solution (if given enough time)
© J. Christopher Beck 2005

11. Constraint Programming
B&B (but not IP) plus inference
Every time you branch, use specialized algorithms to find other decisions that must be true
May also use sophisticated branching heuristics
Also will find optimal given time
© J. Christopher Beck 2005

12. Summary Dispatch Rules Shifting Bottleneck Tabu Search
Heuristic & incomplete:
No guarantees
Dispatch Rules
Shifting Bottleneck
Tabu Search
Integer Programming
Constraint Programming
But: work well for large
problems
Will find optimal
(if given enough time)
© J. Christopher Beck 2005

13. LEKIN Demo
© J. Christopher Beck 2005