1. Dynamic Constraint Models for Complex Production Environments*
07/16/96
Dynamic Constraint Models for Complex Production Environments
Roman Barták
Charles University, Prague *

2. Talk Schedule Problem area Mixing Planning & Scheduling
Conceptual Models
discrete & event based time
static vs. dynamic representation
overview & comparison of models
mixing models
Future research

3. Problem area complex production environments
plastic, petrochemical, chemical, pharmaceutical industries
several different resources
producers, movers, stores
batch/serial processing with time windows
transition patterns (set-up times)
by-products, co-products (re-cycling)
non-ordered production (for store)
alternatives
processing routes, production formulas, raw material

4. Problem area (cont’d) complex production environment Task
preparing a schedule for a given time period (not minimising the makespan)
objective
maximising the profit (minimising the cost)
silo
order
processor B1
purchase
silo
processor A
processor B2
sacks
warehouse
order

5. Planning and Scheduling
finding a sequence of activities transferring the initial world into a required state
high-level view of the factory
low resolution
longer time period
what and how to produce?
AI & CP
Scheduling
allocating the activities to available resources over time respecting the constraints
low-level view of the factory
high resolution
shorter time period
how to produce in detail?
OR & CP

6. Mixing Planning and Scheduling
Problems
too tighten plans (impossible to schedule)
too free plans (less profitable schedule)
backtrack from the scheduler to the planner
what if appearance of the activity depends on the allocation of other activities?
transition patterns (set-ups), alternatives, non-ordered production
Solution
a scheduler with planning capabilities
generating activities during scheduling

7. Conceptual models High-level declarative model of the problem
data structures (composition of variables)
composition of constraints
resource constraints (compatibility, capacity)
transitions between activities (set-ups)
supplier/consumer dependencies
Expressiveness
What could be modelled? (problem area)
What is easy/hard to express? (constraints)
Efficiency
constraint propagation

8. Conceptual models (cont’d)
View of time
discrete (time slices with the same duration)
event-based (activities)
Representation

9. Time-line model discretising the time line into time slices
activities change at the edge between successive time slices
duration = the greatest common divisor of activities’ duration
description of situation at each time point/slice
Example: the store - the stored quantity for each item
good for both planning and scheduling
activities for given time point/slice are chosen during scheduling
a matrix representation (description x time)
static / dynamic / semi-dynamic contents of the cells
easy capture of initial & future situations
Production (item1)
Change-over
Production (item 2)
Production (item 3)
Storing (item 1)
empty
Storing (items 1&B)
No production
Production (item4)
Production (item5)
time
resources
Time slice

10. Order-centric model a chain of activities per order
assigning resources to activities
description of the activity
start, end (duration), resource
representation
production chain = a list of (virtual) activities
time
resources
storing
extruding
polymerizing
slots …
candidate activities

11. How to model? (in order-centric model)
alternatives
pre-processing (chosen by the planner)
alternative activities in slots
set-ups
set-up slot is either empty or contains the set-up activity (depending on the allocation of the next activity)
by-products (re-cycling)
sharing activities between the production chains
non-ordered production
pre-processing (non-ordered production is planned in advance - before the scheduling)

12. Resource-centric model
Activity based
a sequence of activities per resource
“what the resource can process” rather than “how to satisfy the order”
description of the activity
start, end (duration), quantities, state, suppliers, consumers
representation
a list of virtual activities
transition constraints between successive activities
Production (item1)
Change-over
Production (item 2)
Production (item 3)
Storing (item 1)
empty
Storing (items 1&B)
No production
Production (item4)
Production (item5)
time
resources
No order
Order1

13. Comparison of models

14. Mixing the models
Minimising drawbacks while preserving advantages of different models
different task = different model
the time-line model for planning
the order-centric model for scheduling
different resource = different model
producer & mover - activities (resource-centric)
store - time-line

15. What’s next? constraint model implementation expressiveness
a complete specification of the constraints
implementation
propagation (early detection of inconsistencies)
labelling (incremental)
heuristics (choice of alternatives)
expressiveness
secondary resources
traceability
agent based scheduling