Constraint Programming in Operations Management

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• Constraint Programming in Operations Management

Filippo Focacci ILOG S.A.
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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

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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

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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)
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Constraint-Based Scheduling
Activities

• Breakable Activities
• Preemption at fixed dates (break calendar)

Processing time p(A) ? pi e(A)-s(A) -
breaks(A)
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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

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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

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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.

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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

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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

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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, )

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Constraint-Based Scheduling
Timetables

• Identify activities A for which eet(A) gt lst(A)
• Between lst(A) and eet(A) we know A will be
  executed

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Constraint-Based Scheduling
Timetables
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Constraint-Based Scheduling
Edge-Finding
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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(nlog(n))
• Iterative algorithm Nuijten 94 Martin 96
• O(n2) with no specific data structure
• Task intervals Caseau Laburthe 94
• O(n3)
• Incremental

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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

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Plant PowerOps
Architecture
Graphical Planning Board
Maintenance Configuration
GUI
Planning
IT
Planning/IT
Plant Floor
Engine
Optimization Algorithms
Parameters
Optimization Algorithms
Data Model
Metadata
Business Models
Middleware
CSV Reader
ODF Reader
CSV Writer
ODF Writer

• Optimization Development Framework (ODF) from
  ILOG and SAP
• Optimization Extension Kit (OEK) from ILOG and
  Oracle

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

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ILOG Plant PowerOps
Integrate Planning and Scheduling
Planning solution
Data model
Planning engine
Lot-sizing solution
Lot-sizing engine
Scheduling Engine
Scheduling solution
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Prepare the Production Schedule
Define a rule-based scenario

• Activate or deactivate rules and alerts for the
  current planning or rescheduling scenario

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Add/Modify Business Policies
Define policy rules upon events

• Modify the safety stock policy during machine
  breakdown