© j. christopher beck 20051 lecture 8: dispatch rules
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© J. Christopher Beck 2005 2
Outline What is a Dispatch Rule?
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 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
p1 = 10w1 = 1
p2 = 2w2 = 2
p3= 5w3 = 0
p4= 7w3 = 3
Use WSPT to find min wjCj schedule Find min Cmax schedule
Does WSPT find optimal schedule ifobj = 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
1-machine, rj = 0, obj = min wjTj
Apparent Tardiness Cost rule orders operations in descending order of:
Weighted tardiness
))0,max(
exp()(pK
tpd
p
wtI
jj
j
jj
WSPT
MS
Mean pj
Scaling parameter
© 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 6 6 6 7 7 8 8 9 9 10
10
11
11
© 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
1 M1, 9 M2, 8 M3, 4
M4, 4
2 M1, 5 M2, 6 M4, 3
M3, 6
3 M3, 10
M1, 4 M2, 9
M4, 2
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