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• Crude oil scheduling demo (first example)
• Discussion of scheduling problems
• Constraint-based scheduling
• Avionics scheduling (second example)
• Some (very) open questions and irresponsible remarks
Finite-Capacity Scheduling
Specify activities linked to operations (transfers, tool changes, delivery dates, production runs, etc.).
This specification includes:
–Activity start and end times
–Resource usage, including raw materials, power, equipment needed, labor required
Finite capacity schedules can be used to determine predicted inventory levels, campaign completion/product delivery dates, economic performance, unit operating modes, and resource bottlenecks.
Complex Operational Domains
Air Transportation Satellite Operations Autonomous Vehicles
Continuous MfgDiscrete MfgLogistics
Crude Oil Scheduling Demo
Another view of the problem
Time
ProductVolume
Value of Scheduling for Manufacturing
• Reduce Costs
– Reduce disruption frequency and severity (what-if scenarios, detailed maintenance schedules)
– Improve parts/raw material ordering (better tracking of on-hand inventory)
– Reduce Work-In-Process inventory (reduced lot-rot, more timely vendor ordering, better synchronization of production to delivery dates)
– Reduce changeover costs (cleaning, new catalyst, temperature changes, …).
• Enhance Capital Investment Planning
– prioritize and quantify payoff for capital investment
• Increase Effective Capacity
– Identify and remove bottlenecks
– Increase agility (improve “Available to Promise”)
Determining when and how to accomplish some set of tasks.
The classic job shop:• A set J of jobs to be run, each with• a set of tasks to run in sequence, each on some unique
element of• a set M of machines
Common problem statements:• Find a feasible schedule.• Minimize makespan.• Given a set of deadlines, minimize tardiness.
What is Scheduling?
Ti
Possible Complications (a brief sample)
• Choice of resource• Other resource constraints
– (Global) capacity constraints– Inter-activity constraints– Consumable resources
• Complex temporal constraints (latency, preemption, hierarchical activity relationships).
• System dynamics (flow rates, chemical composition, …)
• Activity generation• Reasoning about state
Manufacturing IT Architecture
Strategic Planning
ProductionPlanning
Finite-capacityPlant scheduling
Manufacturing Execution
Distribution
Capital investment, Finance, Long-term supply and demand forecasts
Rough-cut capacity planning, Orders forecasts,Long-leadtime vendor orders
Transportation andWarehouse ManagementVendor orders
Receiving
More than 6 months
1 month to 1 year
2 weeks to 3 months
1 day to 1 month
1 hour to 1 day
Rough-cut Scheduling(Bill of Materials)
MRP-II
How schedules are used is a factor as well
• Schedules are generated to satisfy existing plans.• Schedules are generated in a historical context.• Schedules are usually not constructed completely
automatically.• Schedules frequently require input from multiple parties.• Schedules are used in operations.
– Updating, as events occur.– Rescheduling, as conflicts are detected.– Post mortem examinations.
• (Schedules are persistent artifacts.)• Schedules are large.• Optimization is important, but hard to formalize properly.
Scheduling as a Constraint Satisfaction Problem
CSPs are specified as:– A set V of variables– A set C of constraints, each constraint a relation
specifying tuples of permissible values for some subset of V.
The objective is to find a feasible (alt., optimal) complete assignment for V, consistent with C.
Advantages to a CSP approach
• Flexible, declarative representation.• Lots of previous and current work on solution
methods.• General solution techniques:
– Static structural analysis– Propagation– Search
• Requirements and scheduling decisions can be represented as constraints.
Scheduling as Search Using a Dynamic CSP
CSP Variables:– Activity start and end times– Activity resource assignments
Constraints:– Temporal constraints (duration, ordering, release times,
deadlines, …)– Resource constraints (permissible assignments, usage
requirements, state information, ...)– System dynamics (rate limitations, allowable state
changes, …)
Search over:– Activity generation– Resource assignments– Activity orderings, start and end times
Hybrid Systems
Hybrid systems have both continuous and discrete components, as opposed to:– Combinatorial problems, such as knapsack,
TSP, or jobshop– Continuous problems, captured as sets of
mathematical equations and inequalities.
Combinatorial, continuous, and hybrid constraint problems can all be framed in terms of either satisfiability (CSP) or optimality (COP).
Scheduling is a hybrid constraint problem.
Constraint Envelope Scheduling
Search variables:– Unary resources: < A before B, B before A >– Capacity resources: < A before B, B before A, A overlaps B >
A1
A2
A3
A1 A2A3
CES Solver Architecture
Discrete Constraint Engine
ContinuousConstraint Engine
1. Continuous constraints added as result of discrete decisions
2. Continuous constraint propagation and consistency check.
2.a. Propagation of additional constraints to discrete engine2.b. Propagation of additional constraints to continuous engine, repeat 2.a, 2.b as needed/desired
3. Discrete constraints added as result of continuous decisions
4. Discrete constraint propagation and consistency check.
4.a. Propagation of additional constraints to continuous engine4.b. Propagation of additional constraints to discrete engine,
repeat 4.a, 4.b as needed/desired
Data structures: Discrete Model
• Discrete variable– Legal values– Current constraints on assignable values– Cross-domain constraints: constraints to be added to continuous
domain, depending on value assigned to this variable.
• Discrete Constraint– n-ary relation on discrete-valued variables (legal combinations of
values)– Constraint type: REQUIREMENT, DECISION, PROPAGATION
EFFECT– Culprit Identification bookkeeping (Decision variable(s)
responsible for this constraint being added).– Propagation method(s)
Data structures: continuous model
• Continuous variable– Current constraints
• Continuous Constraint– Mathematical relation (=, <=, etc.) on several variables– Constraint type: REQUIREMENT, DECISION,
PROPAGATION EFFECT– Culprit Identification bookkeeping (Decision variable(s)
responsible for this constraint being added).– Propagation method(s)
Constraint Envelope Scheduling
Advantages:– No premature commitment– Flexible search strategies– Natural representation for decisions (“do it before lunch”)– Natural interleaving of search and propagation
Disadvantages:– (Somewhat) cumbersome to implement.– Intermediate results are less intuitive to users (more difficult
to present, anyway).– Efficiency concerns (a matter of degree…)
CES vs. Timeline Scheduling
• Activity times and resource usage are precisely specified, if activities appear on the schedule at all, vs.
• Activity extent and resource usage may be incrementally constrained.
The first assumption makes propagation difficult.
The second assumption can get you into trouble in a number of ways:– excessive (and potentially irrelevant) bookkeeping– decisions made in a context that is then invalidated (Andy
Baker’s “Hazards of Fancy Backtracking”).
More Tradeoffs
• Constraints are checked when activities are added to the schedule, vs.
• Constraints are accumulated as scheduling progresses
The first assumption makes incremental rescheduling difficult, throws away information about how the schedule got to its current state.
Under the second assumption, you can accumulate a lot of constraints. Most of them may be subsumed by other constraints, but employing any kind of backtracking search will require that they are maintained in some form.
Implementing a Generic Scheduling Core
• Generic CSP support– variables and constraints– propagation– search
• Continuous model for temporal constraints
• Activities
• Resources
• Resource requirements
Activities
• Interval– temporal constraints, in the
Interval Constraint Engine (ICE)
• Resource requirements
• Hierarchical activities
• Container activities
Interval Constraint Engine (ICE)
A graph of time points, with labeled edges between them.
• Possible temporal relationships:– Release time and deadline (relative to a clock)– Min/max duration– Precedence (minimum separation)– Latency (maximum separation)
• Ordering decisions and start/end time assignments are added as constraints.
• ICE maintains global consistency, reports infeasible (negative-weight) cycles.
Resources
• Unary Resource (manufacturing cell)
• Metric Resource (power)
• Capacity resource (energy)
• State resource (material service)– state-using activities– state-changing activities
Upper and Lower Bounds on Resource Use
Generalized Bounds
Bounds based on temporal constraints are only part of the problem:– Activities on/off the schedule.– Resource choices unconstrained or partially
constrained.– Imprecise usage by individual activities
Resource Requirements
• Match:– by name– by type– by attribute– by procedural attachment
• Effect– metric resource is busy– capacity resource is consumed (or
produced) at a constant rate.– state resource is changed (or not).
Effective Domain Modeling is Hard
Example: large transport pipelines
• Pipeline volume must be modelled explicitly (not like shipping and receiving).
• Currently model is to have slugs of material with associated volume, etc., plus a position in the pipeline.
• Material movement in the pipeline requires both input and output flows.
• Rate is independent of individual movements
Boeing 777 AIMS Scheduling
SAFEbus Scheduler for Boeing 777 AIMS
AIMS requirements represent one of the largest, most comprehensive sets of constraints ever successfully scheduled:
• 29,000 items are scheduled, subject to 97,000 complex metric constraints specified by AIMS applications developers
• More than 230,000 decisions, each with between 4 and 4,000 possible choices were made in scheduling
• This corresponds to finding a solution with a directed search of 107 elements in a state space of 10140000.
Processor Schedule
Data Schedule
How We Solved It
Ginsberg’s “Dynamic Backtracking” algorithm
• Published in 1994
• We fixed a bug
• We extended it
Moral: sometimes the path from research to product takes months, not years.
Scheduling: The Current State of the Art
“Current state of the art” Issues:–60% of manufacturing facilities have no automated scheduling capability.
–30% of airline flights don’t go as planned, on a good day.
–10% reduction in waiting time for trucking industry would allow 6% of all trucks to be taken off the highways altogether.
–Most current scheduling done by unsophisticated means - spreadsheets or manually.
Gaps to be closed by an Integrated Solution:
1) Schedule awareness and editing, then…
2) Autogeneration of feasible schedules, then…
3) Autogeneration of optimal schedules.
Most manufacturing enterprises do not have an effective solution to
address Step 1!
Most manufacturing enterprises do not have an effective solution to
address Step 1!
Scheduling Systems are 95% Boring
PRM
Config
Plan
ExtSched
Plant
ActivityHist
WorkingSchedule
Scheduler
PlanningTool
Marketing
Plant Model
Plant Historian
MES
External Data Interchange
PublishedSchedule
ArchivedSchedule
Scheduling UI
Publish
Archive
DataExternallyAccessible
External Data Interchange
Areas for Further (Interesting!) Work
• Optimal Scheduling (for the right definition of “optimal”)
• Incorporating probabilities
• Robust schedules vs. responsive schedulers
• Moving up into production planning
• Better integration with action selection and states
