The evolution of optimization technologies

Dash Optimization, Alkis VazacopoulosINFORMS New York Metro ClubOctober 11, 2005, The Penn Club, New York

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Agenda

• Optimization Applications– Companies that offer optimization – Companies that use optimization

• Development priorities past and now• Development priorities – Future• Case Studies

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Companies that Offer Optimization

• Modeling and Optimization– Dash Optimization ****– AIMMS– Ilog ****– Maximal– GAMS– AMPL– **** develop State of the Art solvers

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Companies – complete solutions

• SAP (Supply Chain) *** ERP • Oracle (Retail, Supply Chain) *** ERP• Combinenet (procurement)• Carmen Systems (airlines ) • i2 (supply chain )• Smartops (inventory Optimization)• Fair Isaac (Banks, Marketing

Optimization)

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Customers that use Optimization • NFL (Scheduling) (Current Schedule)• Baseball League (Scheduling)• Frito-Lay (Production Planning )• American Airlines (Training Pilots)• Wachovia (Financial)• Siemens (process scheduling)• Toyota (discrete planning and

scheduling)

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Verticals

• Process Industry• Airlines• Energy• Retail• Financial Applications• Pharma

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Process industry problems

• Refinery Scheduling • Vehicle Routing Problems• Refinery Expansion/sizing

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Airlines

• Crew rostering and scheduling• Pricing (revenue Management)• Capacity Planning (size of fleet)• Service maintenance• Parts inventory

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Energy

• Unit commitment problems • Capacity Planning• Pricing based on Uncertain Demand• Project selection

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Retail

• Markdown Optimization • Replenishment of Inventory (inventory

Optimization)• Warehouse Management

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Financial Applications

• Security valuation and selection– Mortgage backed securities

• Bond Trading• Crossing• Index tracking

– Track sector indices at minimum cost• Portfolio tracking

– Track performance at minimum cost

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Pharma

• Sales promotions• Assign sales reps to physicians

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Edelman Award

• UPS• NBC• Procter & Gamble• Aspentech (last year)

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Characteristics

• Size of Problems– 100000 variables

• CPU Time – A few seconds

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Development DirectionsEase of use

Type of Problem

Performance

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Development DirectionsEase of use

Type of Problem

•Speed

•Size of problem

•Reliability

Performance

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Development DirectionsEase of use

Type of Problem

•Speed

•Size of problem

•Reliability

Performance

Out-of-the-box

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Primal SimplexSolution Times of Six Models with Recent

Releases of Xpress-MP Primal

0

5000

10000

15000

20000

25000

20772 5637 4454 4194 3588 451

Rel 10.28 Rel 11.14 Rel 12.13 Rel 13.10 Rel 14.05 Rel 15.00

Watson_1PreleKen-18EnergyChineseArtur

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Dual SimplexSolution Times of Six Models with Recent

Releases of Xpress-MP Dual

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

15850 3741 190 158 151 151

Rel 10.28 Rel 11.14 Rel 12.13 Rel 13.10 Rel 14.05 Rel 15.00

Watson_1PreleKen-18EnergyChineseArtur

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Barrier Method (Interior Point)Solution Times of Six Models with Recent

Releases of Xpress-MP Barrier

0

500

1000

1500

2000

2500

3000

2440 1093 779 539 167 160

Rel 10.28 Rel 11.14 Rel 12.13 Rel 13.10 Rel 14.05 Rel 15.00

Watson_1PreleKen-18EnergyChineseArtur

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Optimizer Speed

• Last Ten Years– 30 times faster– 100 times hardware– 3,000 times overall– Year on year gains of 125%

• Expectation– 60% per annum from hardware– 30% per annum from software

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MIP Good Solutions - Fast

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MIP Performance

XPR 14.10 XPR 15.00neos1 >10000 4neos2 4412 6neos3 >10000 29neos13 >10000 1242neos10 261 126

XPR 14.10 XPR 15.00

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Development DirectionsEase of use

Type of Problem

Performance

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Development Directions•Building Applications

•DeploymentEase of use

Type of Problem

Performance

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Modeling Environment

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Development DirectionsEase of use

Type of Problem

Performance

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Type of problem - Technologies

• LP• MIP• QP• MIQP• Constraint

Programming • Nonlinear• Heuristics

• Network design• Capacity Planning• Pricing• Strategic Sourcing• Scheduling

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Supply ChainCapacity Planning,LP, MIP

Network Design LP, MIP

Scheduling,LP, MIP, CP,

HeuristicsSupply Chain

Pricing,LP,

Nonlinear Strategic Sourcing,

LP,MIP, MIQP

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Development DirectionsEase of use

Type of Problem

Performance

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64 bit & Parallel

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Future

• Grid computing– Solve millions of small scale lps and mips or

nlps in seconds– Examples – Pricing for Airlines-Hotels-Cars

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Large Scale Programs

• Solve large scale optimization problems• Decompose them• Use different processors to calculate

upper bounds (find feasible solutions and lower bounds – optimality)– Example – pricing for energy in a large

scale (pricing gas in a specific time)– Example (deploy resources after a

catastrophic event – terrorism etc…)

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Development DirectionsEase of use

Type of Problem

Performance

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Clever Modeling Languages

• Solve Models in Parallel • Profiling models• Wizard – model development• Development of Clever algorithms

– Expert systems – Artificial intelligence

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Wizard – decision variables

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Xpress-Application Developer

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Screenshots of XAD apps

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Development DirectionsEase of use

Type of Problem

Performance

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Xpress-SLP

• Non-Linear• MINLP Option• Large scale• Applications:

– Process Industry– Pricing– Energy

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• Optimization Technologies

– Mixed Integer Programming: MIP– Finite Domain Constraint Programming: CP

• Planning & Scheduling

– Long and mid-term planning: MIP– Short-term planning, scheduling: CP

Supply chain optimizationRequires MIP, CP, and their combination

CP, MIP and their combination

CP MIPCP+MIP

Time Horizon

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Xpress-CP Architecture (cooperative solver approach)

Mosel Planning and Scheduling Model

Mosel/IVE ENVIRONMENT

Xpress-MP KALIS

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Xpress-CP Adopters

• BASF– Chemicals

• Peugeot– Cars

• Procter and Gamble– Discrete products

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Stochastic Programming

• Basis– Represent uncertainty– Build problem efficiently– Manage scenarios

• Applications– Planning– Supply chain– Interaction with forecasting

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Stochastic Programming

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Future

• Data mining • Robust Optimization

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Classification Problems:example

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Classification Problems:Application Examples

• Cancer Diagnosis(Mangasarian et al, 1995 –linear separating surfaces)

• Classification of Credit Card Applications, Bonds Rating

(Bugera et al, 2002, 2003 –quadratic separating surfaces)

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Problems

There are two major biomedical data mining problems associated with microarray data:

• Classification: Determine classes of the test samples.

• Gene detection: For each of the classes, select a subset of genes responsible for creating the condition corresponding to the class.Usual noisiness of microarray data complicates solution of these problems.

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Credit Rating

• Logical Analysis of Data• Credit scoring of Countries• Credit scoring of Companies

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Medical Applications

• Different types of Cancer• Obesity

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Robust Optimization

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Other examples

• Robust Portfolio Optimization• Robust Inventory policies

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MOSEL

LP

MIP

SLP

IVE

XAD

MIQP

QPLP

MIP

STO

MISLP

HEURISTICS

VERTICAL APP.

GUI / STUDIO

EXTENSIONS/NAT

SOLVERS

MODELING PLATFORM

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Some Trends• Profitable-to-Promise• Very large problems• Time of the essence• Custom driven supply chains• Flexibility/lifecycle• Analytics & Forecasting /

Data Mining• Out-of-box performance• Non-expert users

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Portfolio Management

• Wrap Portfolio– Tracks another index / actively managed

portfolio– Realigns periodically to match risks and

returns– Provides similar performance at lower

management costs

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WRAP PortfolioT=1 T=2 T=3

INDEX

WRAP

INDEX

WRAP

INDEX

WRAP

Re-Balancing

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Portfolio Management

Challenges– How to realign with minimum trading costs– How closely to track sector, country..

exposures– When and how frequently to re-align– How to automate the complete process

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Portfolio Management

• Optimization– Determine trades to re-align with minimum

costs• Business rules

– Determine when to re-align– Generate test cases to determine

–How closely to track–How frequently to re-align

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Portfolio Management

Want to automate the complete process• Need to combine

Business Rules Optimization

in a ‘single’ application

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Portfolio Management

• Real Time Management– Rules engine monitors tracked index and

portfolio movement – Calls and runs optimization engine when

index and portfolio deviates beyond acceptable limits

– Rules engine evaluates and executes trades

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Portfolio Management

Customization – one step further• Determines acceptable deviation limits for

risk-return combinations– Rules generate scenarios – Optimization engine determines action– Enables to predict returns for risk levels

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Benefits

• Lower monitoring and management costs

• Lower execution costs• Assured compliance

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Other Applications

• Marketing– State Farm

• Process Industries– AspenTech

• Transport– Schneider

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Simple Concept

• Business rules monitor and determine when to re-optimize

• Optimization determines best action• Business rules evaluate and execute

actions to achieve desired effect

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Conclusion

Combine • Flexibility of business

rules and • Robustness of

optimization

Next Generation Intelligent Applications– Automation– Testing– Determining rules ?

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Workshop

• October 21-22nd

• New York University

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Informs San Francisco

• Preconference Workshop• 1 Tutorial • 2 talks • Exhibit