1. Lecture 8: Dispatch Rules
© J. Christopher Beck 2005

2. Outline What is a Dispatch Rule? 1-machine Problems Parallel Machines
Static & dynamic
1-machine Problems
WSPT, EDD, MS, ATC
Parallel Machines
LPT
Applying dispatch rules to a big JSP
© J. Christopher Beck 2005

3. Dispatch Rules Create a queue of operations for each resource
include all operations that can execute at the current time
Whenever a machine becomes free:
update queues
rank activities (based on a [simple] rule)
schedule highest priority activity
© J. Christopher Beck 2005

4. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

5. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

6. How am I picking operations from queue?
Dispatch Rules for JSP J0 J1 J2
How am I picking operations from queue?
© J. Christopher Beck 2005

7. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

8. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

9. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

10. Dispatch Rules for JSP J0 J1 J2
© J. Christopher Beck 2005

11. How did I pick operations?
Dispatch Rules for JSP J0 J1 J2
How did I pick operations?
© J. Christopher Beck 2005

12. Dispatch Rules Create a queue of operations for each resource
include all operations that can execute at the current time
Whenever a machine becomes free:
update queues
rank activities (based on a [simple] rule)
schedule highest priority activity
© J. Christopher Beck 2005

13. 1-Machine Problem & WSPT
rj = 0, dj = ∞, obj = min wjCj
Weighted Shortest Processing Time (WSPT) results in optimal schedule
Order operations in decreasing order of wj/pj
Bonus question: prove that WSPT finds the optimal schedule for min wjCj
© J. Christopher Beck 2005

14. 1-Machine Problem & WSPT
Use WSPT to find min wjCj schedule
Find min Cmax schedule
Does WSPT find optimal schedule if obj = min Cmax?
© J. Christopher Beck 2005

15. 1-Machine Problem & EDD Different problem
rj = 0, obj = min Lmax
Each job has its own dj
Earliest Due Date (EDD) results in optimal schedule
Order operations in increasing order of dj
© J. Christopher Beck 2005

16. WSPT & EDD are Static
Static = basis for ordering operations does not change based on scheduling decisions
You can sort all operations once
Dynamic = scheduling decisions change the order of remaining operations
You need to re-sort operations in queue (potentially) after every decision
© J. Christopher Beck 2005

17. Minimum Slack is Dynamic
1-machine, rj = 0, obj = min Lmax
Minimum Slack (MS) orders operations at time t in descending order of:
max(dj – pj – t, 0)
MS does not guarantee optimal schedule
Question: can you find a 1-machine problem instance where MS doesn’t find the optimal?
© J. Christopher Beck 2005

18. Composite Dispatch Rules
Weighted tardiness
1-machine, rj = 0, obj = min wjTj
Apparent Tardiness Cost rule orders operations in descending order of: MS
WSPT
Scaling parameter
Mean pj
© J. Christopher Beck 2005

19. Good Questions
Given description of a 1-machine problem which dispatch rule would you use and why?
Given a 1-machine problem, produce a schedule using dispatch rule X (show each decision)?
X = WSPT, EDD, MS, ATC, or a dispatching rule (with a given definition)
© J. Christopher Beck 2005

20. Parallel Machines
Like 1-machine but you have a set of machines and operations can go on any machine
Can apply dispatch rules without any optimality guarantee
LPT: Longest Processing Time first
pick operations in descending order of processing time
© J. Christopher Beck 2005

21. Q5.3, p 110 6 identical, unary capacity machines in parallel
Compute makespan using LPT
jobs 1 2 3 4 5 6 7 8 9 10 11 12 13 pj
© J. Christopher Beck 2005

22. JSP
Apply the following dispatch rules to the problem from the last lecture:
SPT MS
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, 4
M2, 9
M4, 2
© J. Christopher Beck 2005

23. Final Words Table C.1 p. 416 is a good summary of many dispatch rules
© J. Christopher Beck 2005