Constraint Technology for Real

Applications Methodology Requirements on CP

Applications

Cisco TunnelBuilder Pro

Cosytec CHIP

ILOG OPL Cplex Solver/Scheduler/Dispatcher/Configurator

Others SAP, I2, Manugistix Air Liquide Nurse Rostering/Call Centre Rostering/Timetabling/etc.

Summary

Hardware design Compilation Financial problems Placement Cutting problems Stand allocation Air traffic control Frequency allocation Network configuration Product design Production step planning Production sequencing

Production scheduling Satellite tasking Maintenance planning Product blending Time tabling Crew rotation Aircraft rotation Transport Personnel assignment Personnel requirement planning

TunnelBuilder-Pro (Cisco)

Fast Rerouter Problem Solver

Linear relaxation Interleaved search

Constraints Maximum flows Shared Risk Groups

Status Cisco Product

SERVAIR – CREW (French Railways)

Crew rostering system assign service staff to TGV train timetable joint implementation with GSI

Problem solver generates tours/cycles assigns skilled personnel

Constraints union, physical, calendar

Status operational since Mar 1995 cost reduction by 5%

Air Planner (Parc Technologies)

Schedule Retimer Plan seasonal flight schedule

Problem Solver Minimum perturbation: linear relaxation constraint propagation

Constraints #Aircraft Maximum retiming Airport slots

Status Used for IATA meetings In-house use at BA

Constraint Technology for Real

Applications Methodology Requirements on CP

Real Problems

Wrong solutions Problem formalisation

Software reports no solution Problem formalisation

No solutions found Algorithm

Wrong Solutions

Implicit Constraints

“Can’t unload where cars are parked”

Data errors

“If we don’t know the weight, we just enter 0.0”

“Balance” not achieved Mon Tue Wed Thur Fri

A Off Off Off Off Off

B Day Day Day Off Off

C Off Off Off Day Day

D Night Night Night Night Night

Software reports no solution

Planners break their own rules “Trains depart every 30 minutes”

Current business practice confused with constraints Always use machine1 before machine2

10:30 16:30

11:00 17:00

11:30 17:30

12:05 18:05

12:30 18:30

13:00 19:00

No solutions found

Attempting complete search Bus+train+tube+walking

Poor heuristics Start from origin Start from time zero

Bugs!! Poor propagation Unnecessary waking Repeated discovery of same partial solutions

Project Breakdown

Specification

Modeling

Algorithms

Delivery

Specification

Modeling

Algorithms

Delivery

Project Plan

Time

Specification

Modeling

Algorithms

Delivery

Problem Specification

Business Objectives

Operational Constraints

Solution EvaluationIdentification of evaluation criteria

Definition of cost function

User and System InterfaceUser interactivity

System requirements

Specification

Modeling

Algorithms

Delivery

Modeling

Constraint ModelingOperational Resource Constraints

Operational Time Constraints Marketing and QOS Constraints

Optimisation Function Alternative evaluation functions

User InterfaceSystem architecture

Specification

Modeling

Algorithms

Delivery

Algorithm DevelopmentProblem Analysis

Operational Constraints Detailed study of problem components

Identification of AlgorithmsPotential solvers for problem components

Heuristics

Construction of Algorithms Coding alternative configurations

Evaluation of Algorithms

Specification

Modeling

Algorithms

Delivery

Product Delivery

Graphical User Interface

Schedule/Despatch Editors

Control

Data Feeds

Semi-constant

Dynamic User input

Acceptance Testing

Documentation

Specification

Modeling

Algorithms

Delivery

Timeboxing

Regular Meetings Every 2-4 weeks

Involving multiple stakeholders Technicians Users

Reporting Progress Achievements Demos Obstacles

Planning ahead Tasks Priorities

Constraint Technology for Real

Applications Methodology Requirements on CP

Requirements on Modelling

Logical Specification “All tasks assigned a resource”

High-Level Constraints “At least two days off in any consecutive ten days”

User-definable constraints “Each overseas task requires a full-skills team”

Requirements on Solving

Each solution must satisfy the model All constraints correctly checkable

Performance must be better than current approach All state-of-the-art algorithms available Search control able to mimic current heuristics

Solutions must be found Full and incomplete search Tailored algorithms

Fast prototyping and development Plug and play with algorithms Orthogonal reasoning and search

CLP – Nature and Scope

RepairRepairLibraryLibrary

Linear Linear ProgrammingProgramming

LibraryLibrary

Interval Interval ReasoningReasoning

LibraryLibrary

Finite Finite DomainDomainLibraryLibrary

Algorithm

ModelModel

CPLEXCPLEXXpress-MPXpress-MP

Three Application Algorithms

Cisco Fast Rerouter

BA Schedule Retimer

Wincanton Transport Cooled goods transportation

Fast Rerouter

Problem statement

Reserve 10 for ce on le Reserve 20 for cf on lf Reserve 20 not 30 for ce and cf on kl

10

30

20

.

max

ce

cf

cecf

cecf

Q

Q

QQ

st

QQ

Problem model

dfdfe

ofof

ffefe

nOe nIefefe

f efe

Qdcd

eQoco

st

QX

ece

otherwise

fdn

fon

XXnf

st

X

)(

)(

)( )(

)(:

)(:

.

*max

)(:

0

)(1

)(1

:,

.

min

Xfe = 0/1 if flow f is diverted through edge e

Our Algorithm

(1) Find an alternative route for each flow (2) Find an edge E supporting several alternative routes,

that can’t, in the worst case, support them all. If there aren’t any, we are done!

(3) Choose a flow that must not use edge E (choice point) and go to (1)

Results and Comparison

network

(N,E) flows

opt

obj

MIP

cpu,vars,cstrs

Our

Algorithm

a(38,172) 54 132 18.77, 33, 26 3.38, 5

d(50,464) 178 410 TO, 274, 200 517.60, 29

e(50,464) 418 890 TO, 626, 453 4033.98, 64

f(208,676) 28 256 TO, 73, 60 252.44, 23

j(212,734) 154 fail TO, 380, 300 95.33, 5

k(365,1526) 178 422 OOM, 900, 694 310.90, 12

BA Schedule Retimer

IC-Parc 31

Activity Overlaps ~ Fixed TimesS1

S2S3

E1E2

E3

No. ofResourcesRequired

Time

321

Activities

321

S1 S2S3

Potentialresourcebottleneckpoints

Probing

1. Send temporal constraints to linear solver

2. Set flight times to linear optimum

3. Generate resource profile

4. Identify bottleneck: if there isn’t one we are done!

5. Add temporal precedence constraint on two bottleneck tasksand go back to (1)

Experimental Results

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 20 50

Number of Activities

LP

No

des

Integer/Linear Programming

Our Algorithm

Integer/Linear vs Our Algorithm: LP Nodes

Logistics with Depots

Subtasks

Logistics with Depots Decomposition

(A) consignment routing (B) load consolidation (C) vehicle routing (D) inter-depot consolidation (E) vehicle assignment (F) driver allocation

Hybridisation Solve subproblems sequentially For each subproblem utilise feedback from the next one

Results

Problem constraints respected Result took a scheduler 3 months to assess He thinks it is good Please don’t ask him to check another result

Consultation

Demand this week?