Industrial Applications of
Constraint Based Scheduling
Helmut Simonis
Parc Technologies Ltd
IC-Parc, Imperial College London
Based on joint work with
Y. Cloner, A. Aggoun (COSYTEC)
Overview
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Global constraints
Scheduling with global constraints
Brief history
Operational examples
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Constraint Programming - in a nutshell
• Declarative description of problems with
– Variables which range over (finite) sets of values
– Constraints over subsets of variables which restrict possible value
combinations
– A solution is a value assignment which satisfies all constraints
• Constraint propagation/reasoning
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Removing inconsistent values for variables
Detect failure if constraint can not be satisfied
Interaction of constraints via shared variables
Incomplete
• Search
– User controlled assignment of values to variables
– Each step triggers constraint propagation
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Need for global constraints
X
1
Y
2
Z
3
U
4
X in {2,3}
Y in {2,3}

U in {1,2,3,4}
Z in {1,3}
local reasoning, no action
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global reasoning, detect implications
by bi-partite matching
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Global constraints
• Work on sets of variables
– Global conditions, not local constraints
• Semantic methods
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Operations Research
Spatial algorithms
Graph theory
Network flows
• Building blocks (high-level constraint primitives)
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Multi-purpose
As general as possible
Usable with other constraints
Very strong propagation
Acceptable algorithmic complexity
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Temporal Relations
• Some task must start after others have
finished
• Easy to model with inequality constraints
• Much better reasoning possible when
considered together with resource
constraints
precedence constraint
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Cumulative (Disjunctive) Resources
Cumulative constraint
Limit
resource
resource
duration
time
start
End
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Machine Choice (Speed)
Diffn (2D)
machine
M6
M5
M4
duration
1
machine
M3
M2
M1
start
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time
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Machine Calendars
Diffn (2D) with calendar rules
machine
Interruptions
M6
M5
M4
duration
1
machine
M3
non-interruptible task
M2
M1
start
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time
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Consumable Resources
Storage
Max capacity
Min capacity
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Storage Assignment
produce
Diffn (2D)
store
consume
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Storage Assignment with Capacity
produce
Diffn (3D)
store
consume
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Sequence Dependent Setup
cycle with distance matrix
variable time
forbidden sequence
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Brief history of CP-based scheduling
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Alice (Lauriere), 1978
CHIP (Dincbas, Van Hentenryck, Simonis), 1987
First commercial CP scheduling application (HIT, ICL), 1989
Cumulative resources (Aggoun, Beldiceanu), 1993
Disjunctive resources (Nuijten, Caseau, LePape), 1994
Machine choices (Beldiceanu, Contejean), 1994
Sequence dependent setup (Beldiceanu, Contejean), 1994
Alldifferent (Regin), 1994
Pre-emptive scheduling constraint (Baptiste, LePape), 1998
LP/CP hybrids (Wallace, Rodosek, El Sakkout), 1998
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PLANE (Dassault)
• Assembly line scheduling
– developed by Dassault Aviation for Mirage 2000 Jet/
Falcon business jet
• Two user system
– production planning 3-5 years
– commercial what-if sales aid
• Optimization
– requirement to balance schedule
– minimize changes in production rate
– minimize storage costs
• Benefits and status
– replaces 2 week manual planning
– operational since Apr 94
– now used in US for business jets
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FORWARD (TECHNIP, COSYTEC)
• Oil refinery production scheduling
– Incorporates ELF FORWARD LP tool
• Schedules daily production
– Crude arrival -> processing -> delivery
– Design, optimize and simulate
• Crude mix optimization
– Ship unloading, storage
– Pipeline transport
• Product blending
– Explanation facilities
– Handling of over-constrained problems
• Status
– Operational at FINA, ISAB, BP,…
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ORDO-VAP (VCA, COSYTEC)
• Production scheduling for glass factory
– integrated with Ingres Information system
– manual and automatic scheduling
• Constraints
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multi-stage manufacturing
consumer/producer
varying production rates, setup
balance manpower utilization
minimize downtime
• Status
– 2 phases
– operational since March 96
– replaced manual operation
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MOSES (Dalgety, COSYTEC)
• Production scheduling for animal feed production
– Feed in different sizes/ for different species
– Contamination human health risk
– Strict regulations imposed by customers
• Constraints
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Avoid contamination risks
Machine setup times
Machine choice (quality/speed)
Limited storage of finished products
Very short lead times (8-48 hours)
Factory structure given as data
• Status
– operational since Nov 96
– installed in 5 mills
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Bandwidth on demand (Schlumberger, IC-Parc, PTL)
• Provide on-demand, high QoS
bandwidth for limited time period
• Use cases
– Well logging
– Video conference
• Runs on MPLS-TE, diffserv
• Temporal extension of general
routing problem
– Hard QoS limits
– Overall bandwidth limits
– Uses hybrid (CP/MIP/local search)
algorithm
• Delivered on Schlumberger’s
Dexa.net
– Self-provisioned by customer
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Conclusion
• Constraints are a mature technology for
scheduling
• Easy to combine different constraints in one
system, flexible for modeling complex systems
• Most useful for hard problems, medium size
(hundreds of tasks, dozens of resources)
• Large variety of solutions in different application
fields using commercial, off-the-shelf tools
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