Constraint Based Scheduling and
Optimization:
From Research to Application
Brian Drabble
Computational Intelligence Research Laboratory
www.cirl.uoregon.edu
[email protected]
&
On Time Systems, Inc
www.otsys.com
27th Nov 2001
Univ. Nebraska
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Overview
• Constraint based scheduling
• Algorithms
– LDS and Schedule Pack
– Squeaky Wheel Optimization
• Applications
– Aircraft assembly
– Ship construction
• Future Directions
• Summary
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Constraint Based Scheduling
• Problem characteristics
• Search based techniques
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Problem Characteristics
– Task details:
• resource requirements
• deadlines/release times
• value
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4
Problem Characteristics
– Task details
– Resource characteristics:
•
•
•
•
type
capacity
availability
speed, etc.
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5
Problem Characteristics
¨
¨
¨
Task details
Resource characteristics
Precedences:
– necessary orderings
between tasks
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6
Problem Characteristics
– Constraints:
¨
Task details
Resource characteristics
¨
Precedences
¨
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•
•
•
•
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setup costs
exclusions
reserve capacity
union rules/business rules
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Problem Characteristics
– Constraints
¨
Task details
¨
Resource characteristics
¨
Precedences
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– Optimization criteria:
• makespan, lateness, cost,
throughput
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Optimization Techniques
• Operations Research (OR)
– LP/IP solvers
• seem to be near the limits of their potential
• Artificial Intelligence (AI)
– search-based solvers
• performance increasing dramatically
• surpassing OR techniques for many problems
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Search-based Techniques
• Systematic
– explore all possibilities
• Depth-First Search
• Limited Discrepancy Search
• Nonsystematic
– explore only “promising” possibilities
• WalkSAT
• Schedule Packing
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Heuristic Search
– A heuristic prefers some choices over others
– Search explores heuristically preferred options
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Limited Discrepancy Search
– Better model of how heuristic search fails
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Limited Discrepancy Search
– LDS-n deviates from heuristic exactly n times
on path from root to leaf
LDS-0
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LDS-1
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Schedule Packing
– Post-processing to exploit opportunities
1
1
2
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Schedule Packing
– schedule longest chains first
• starting from right
1
1
2
2
1
1
2
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2
15
Schedule Packing
– repeat, starting from the left
1
1
2
2
1
1
2
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Squeaky Wheel Optimization
• Key insight: scheduling involves two major
decisions:
– which task to assign next
– where to assign it in the schedule
• Create a dual search space
– priority space
– schedule space
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Priority Space
• Coupled search space
P
S
P’
S’
Priority Space
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Solution Space
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Architecture
• Construct Analyze Prioritize loop
P
Construct
S
Analyze
P’
Prioritize
Construct
Priority Space
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S’
Solution Space
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Construction
• Construct a solution taking each task in
sequence
P
Construct
S
Analyze
Prioritize
P’
Construct
Priority Space
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S’
Solution Space
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Analysis
• Assign blame problem elements, relatively
simple
P
Construct
S
Analyze
P’
Prioritize
Construct
Priority Space
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S’
Solution Space
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Prioritization
• Adjust priority sequence according to blame
P
Construct
S
Analyze
P’
Prioritize
Construct
Priority Space
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S’
Solution Space
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Large Coherent Moves
• High priority tasks handled well lower tasks fill
in.
P
Construct
S
Analyze
P’
Prioritize
Construct
Priority Space
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S’
Solution Space
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Squeaky Wheel Optimization
Mission 1234
AAR 234
SEAD 34
Construct
Mission 4567
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Squeaky Wheel Optimization
A
n
a
l
y
z
e
“High attrition rate”
“Outside target time window”
“Low success rate”
“Not attacked”
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Squeaky Wheel Optimization
P
r
i
o
r
i
t
i
z
e
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Squeaky Wheel Optimization
P
r
i
o
r
i
t
i
z
e
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Squeaky Wheel Optimization
Construct
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Scalability
25
% Over Best
Solution
20
15
TABU
LP/IP
SWO
10
5
0
0
50
100
150
Number of Tasks
200
250
300
Applications
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Aircraft Assembly
McDonnell Douglas / Boeing
– ~570 tasks, 17 resources, various capacities
– MD’s scheduler took 2 days to schedule
– needed:
• better schedules (1 day worth $200K–$1M)
• rescheduler that can get inside production cycles
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Problem Specification
– Task/precedence specification
• mostly already existed for regulatory reasons
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Problem Specification
– Task/precedence specification
• mostly already existed for regulatory reasons
– Resource capacity profiles
• labor profile available from staffing information
• others determined from SOPs, etc.
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Problem Specification
– Task/precedence specification
• mostly already existed for regulatory reasons
– Resource capacity profiles
• labor profile available from staffing information
• others determined from SOPs, etc.
– Optimization criterion
• simple makespan minimization
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34
Problem Specification
– Task/precedence specification
• mostly already existed for regulatory reasons
– Resource capacity profiles
• labor profile available from staffing information
• others determined from SOPs, etc.
– Optimization criterion
• simple makespan minimization
– Solution checker
• available from in-house scheduling efforts
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The Optimizer
• LDS to generate seed schedules
• Schedule packing to optimize
– intensification improves convergence speed
• etc.
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Performance
– ~570 tasks, 17 resources, various capacities
• about 1 second to first solution
• about 1 minute to within 2% of best known
• about 30 minutes to best schedule known
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Performance
– ~570 tasks, 17 resources, various capacities
• about 1 second to first solution
• about 1 minute to within 2% of best known
• about 30 minutes to best schedule known
– 10-15% shorter makespan than best in-house
• 4 to 6 days shorter schedules
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Performance
– ~570 tasks, 17 resources, various capacities
• about 1 second to first solution
• about 1 minute to within 2% of best known
• about 30 minutes to best schedule known
– 10-15% shorter makespan than best in-house
• 4 to 6 days shorter schedules
– 2 orders of magnitude faster scheduling
• scheduler runs inside production cycle
• less need for rescheduler
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Extensions
Boeing:
–
–
–
–
multi-unit assembly
interruptible tasks
persistent assignments
multiple objectives
• e.g., time to first completion, average makespan, time to
completion
• fast enough to use for “what-iffing”
– discovered improved PM schedule
• Noise is your friend!!!
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Submarine Construction
General Dynamics / Electric Boat
– 7000 activities per hull, approx 125 resource types
– Electric Boat’s scheduler takes 6 weeks
– needed:
• cheaper schedules
• faster schedules to deal with contingencies
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Problem Specification
• reschedule shipyard operations to reduce
wasted labor expenses
• efficient management of labor profiles
– reduce overtime and idle time
– hiring and RIF costs
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Optimizer
• ARGOS is new technology developed
specifically with these goals in mind
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Performance: One Boat
• Labor costs of existing schedule: $155m
• Time to produce existing schedule: ~6 weeks
Iteration Time
1
2 min
7
10 min
20
34 min
Savings
8.4% $13.0M
11.4% $17.7M
11.8% $18.2M
Ultimate ~24hrs
15.5% $24.0M
• 15% reduction in cost, 50x reduction in
schedule development time
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Performance: Whole Yard
• All hulls, about 5 years of production
• Estimated cost of existing schedule: $630M
Iteration
1
7
20
Time
24 min
60 min
4 hours
Ultimate 4 days
Savings
7.8% $49M
10.2% $65M
10.7% $68M
11.5% 73M
• No existing software package can deal with
the yard coherently
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Extensions
• Shared resources
– dry dock
– cranes
• Sub-assemblies
– provided by different yards and suppliers
• Repair
– dealing with new jobs
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Future Applications
• Workflow management
– STRATCOM checklist manager
– IBM
• E-Business
– supply chain management
• Military
– air expeditionary forces
– logistics
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Future Work
• Robustness
• Distributed scheduling
• Common task description
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Penalty Box Scheduling
• Sub-set of the tasks with higher probability of
success.
– 90% probability of destroying 90% of the targets?
– 96% probability of destroying 75% of the targets?
• Inability to resource leads to a task “squeak”
• Blame score related to user priority and
“uniqueness”
• Reduce the target percentage until no
significant improvement is found
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Semi-Flexible Constraints
• The time constraints provided by the users
tended to be ad-hoc and imprecise
– heuristics based on sortie rate, no of targets, etc
– this is what we did last time so it must be right!!
• Not a preference
– this is what I want until you can prove otherwise!!
• Two algorithms were investigated
– pointer based
– ripple based
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Semi-Flexible Constraints:
Pointer Based
“Attack the IAD before power system”
IAD-E
0
IAD-L
Power-E
3000
Power-L
6000
Time (Minutes)
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Semi-Flexible Constraints:
Pointer Based
“Attack the IAD before power system”
IAD-E
0
IAD-L
Power-E
3000
Power-L
6000
Time (Minutes)
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Semi-Flexible Constraints:
Pointer Based
“Attack the IAD before power system”
IAD-E
0
IAD-L
Power-E
3000
Power-L
6000
Time (Minutes)
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Semi-Flexible Constraints:
Ripple Based
“Attack the IAD before power system”
IAD-E
0
IAD-L
Power-E
Power-L
3000
6000
Time (Minutes)
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Semi-Flexible Constraints:
Ripple Based
“Attack the IAD before power system”
IAD-E
0
Power-E
IAD-L
3000
Power-L
6000
Time (Minutes)
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Semi-Flexible Constraints:
Ripple Based
“Attack the IAD before power system”
IAD-E
0
Power-E
IAD-L
3000
Power-L
6000
Time (Minutes)
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Univ. Nebraska
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Semi-Flexible Constraints:
Ripple Based
“Attack the IAD before power system”
IAD-E
0
IAD-L Power-E
3000
Power-L
6000
Time (Minutes)
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Common Task Model
Plan Ready
Fly
30 mins 20 mins
P
Execute
Recover
5 mins
60mins
40 mins
R
F
E
R
Bomb Depot
P
P
R
R
F
F
E
E
R
R
P
AAR
P
R
R
F
F
E
E
R
R
SEAD Flight
B-52 Flight
AWACS
P
P
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“Drop 120, MK-84s
from 3 B-52s at
location X,Y at 22.00
on D+5”
R
F
E
R
R
F
E
CAP Flight
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Weapon Loader
Information & Control
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Example Problem
• The AWACS aborts on take off!
P
R
F
E
R
Bomb Depot
P
P
R
R
F
F
E
E
R
R
P
AAR
R
R
F
F
E
E
R
R
SEAD Flight
B-52 Flight
AWACS
P
P
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P
R
F
E
R
R
F
E
R
Weapon Loader
CAP Flight
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Summary
Advances in search technology:
–
–
–
–
1993:
1996:
1999:
2001:
Tasks
64
~570
1000s
10000s
Resources
6
17
dozens
hundreds
Type
Feasible?
Job Shop X
RCPS
barely
RCPS

RCPS

• Search works!
– search-based technology has matured
– large, real-world, problems are solvable
– tech-transfer path is short
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Questions
?
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