1. Constraint Programming in Operations Management
Filippo Focacci – ILOG S.A.

2. Agenda Constraint-Based Scheduling
Concepts
Constraints
Plant PowerOps: an industrial application of CP
Introduction
Architecture
Hybrid approach for Integrating planning and scheduling
Integrate business rules in optimization
Demo

3. Constraint-Based Scheduling
Introduction
Constraint-Based Scheduling = Scheduling + Constraint Programming
Scheduling problems arise in situations where
A set of activities has to be processed
By a limited number of resources
In a limited amount of time

4. Constraint-Based Scheduling
Activities
Non-Preemptive (Interval) Activities
Activity A t
Start time: s(A)
End time: e(A)
Processing time: p(A) = e(A) - s(A)

5. Constraint-Based Scheduling
Activities
Breakable Activities
Preemption at fixed dates (break calendar)
Activity A t p1 pi
... M T W F S
Processing time: p(A) =  pi = e(A)-s(A) - breaks(A)

6. Constraint-Based Scheduling
Resources
Unary
One person, machine, etc.
Discrete
A group of people with the same capabilities
Energy
A limited number of human-days each week
Reservoir
A stock of raw materials or intermediate products
State
An oven with different possible temperatures

7. Constraint-Based Scheduling
Constraints
Temporal constraints
Fixed or variable durations
Precedence constraints
Minimal and maximal delays
Resource constraints
Fixed capacity
Variable capacity (time versus capacity tradeoffs)
Variable capacity over time

8. Constraint-Based Scheduling
Constraints
Calendar Constraints
Time intervals during which a resource is not fully available
e.g., maintenance periods, vacations, forbidden states (at night)
Transition Times
Minimal time required between two activities when in a certain order
e.g., tool setup between two tasks on the same machine, state change (oven temperature or color used in a painting shop), cleaning, etc.

9. Constraint-Based Scheduling
Objective Functions
Examples:
Makespan (max end time)
Sum/max tardiness or earliness
Weighted # of activities
Peak resource usage
Transition times/costs
Weighted # of resources
All possible combinations of the above

10. Constraint-Based Scheduling
Resource Constraint Propagation
Several types of global constraints
All make sure the capacity of the resource is not exceeded at any point
Differ in the strength of the propagation they induce:
Explicit timetables  Disjunctive constraint
Edge-finding  Energetic reasoning
 Balance constraint

11. Constraint-Based Scheduling
Resource Constraint Propagation
In general, more propagation = more effort
The best propagation algorithm depends
On the application
On the resources within a given application (number of activities, resource criticality, …)

12. Constraint-Based Scheduling
Timetables
Identify activities A for which eet(A) > lst(A)
Between lst(A) and eet(A) we know A will be executed

13. Constraint-Based Scheduling
Timetables q Q t
Aggregated necessary demand
QMAX

14. Constraint-Based Scheduling
Edge-Finding B C A 6 16 7 15 4
p=4
p=5
p=2  B C A 6 16 7 15 4
p=4
p=5

15. Constraint-Based Scheduling
Edge-Finding: Unary Resources
Basic Concept
Prove that an activity A executes before (or after) a set of other activities W.
Jackson's Preemptive Schedule [Pinson 88] [Carlier & Pinson 90/94]
O(n2) O(n*log(n))
Iterative algorithm [Nuijten 94] [Martin 96]
O(n2) with no specific data structure
Task intervals [Caseau & Laburthe 94]
O(n3)
Incremental

16. Plant PowerOps Problem Description
Manufacturing planning and scheduling requirements
Continuous production
Determine how to adjust to demand by varying output
Production with co-products and by-products
Determine how to adapt to demand by adjusting the product mix
Campaign and batch production
Determine how to meet demand by determining the length of campaigns, while avoiding costly setups
Industry specific complex constraints
Complex setups, trimming, business policies
Planning and scheduling horizons
Short term – hours to days – re-scheduling and connection with MES
Medium term – days to weeks – integrated planning and scheduling
Long term – weeks to months – planning, what-if analysis

17. Optimization Algorithms
Plant PowerOps
Architecture
Graphical Planning Board
Maintenance & Configuration
GUI
Plant Floor
Planning
Planning/IT IT
Engine
Parameters
Optimization Algorithms
Optimization Algorithms
Data Model
Metadata
Business Models
Middleware
ODF Reader
CSV Reader
ODF Writer
CSV Writer
Optimization Development Framework (ODF) from ILOG and SAP
Optimization Extension Kit (OEK) from ILOG and Oracle

18. Plant PowerOps GUI: Organization Solution Area Problem View Rule
Scenario
Management
Problem
View
Data and Weights
Rule
Explorer
Console

19. Plant PowerOps Integrate planning and scheduling
Key features
Integrate planning and scheduling
Hybrid CP / MIP
Use business rules to configure and maintain the optimization
Modify the model parameters and data
Add constraints

20. ILOG Plant PowerOps Integrate Planning and Scheduling Planning
solution
Data
model
Planning
engine
Lot-sizing
solution
Lot-sizing
engine
Scheduling
Engine
Scheduling
solution

21. Prepare the Production Schedule
Define a rule-based scenario
Activate or deactivate rules and alerts for the current planning or rescheduling scenario

22. Add/Modify Business Policies
Define policy rules upon events
Modify the safety stock policy during machine breakdown