The evolution of optimization technologies

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2 The evolution of optimization technologies Dash Optimization, Alkis Vazacopoulos INFORMS New York Metro Club October 11, 2005, The Penn Club, New York

3 Agenda Optimization Applications Companies that offer optimization Companies that use optimization Development priorities past and now Development priorities Future Case Studies 3

4 Companies that Offer Optimization Modeling and Optimization Dash Optimization **** AIMMS Ilog **** Maximal GAMS AMPL **** develop State of the Art solvers 4

5 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) 5

6 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) 6

7 Verticals Process Industry Airlines Energy Retail Financial Applications Pharma 7

8 Process industry problems Refinery Scheduling Vehicle Routing Problems Refinery Expansion/sizing 8

9 Airlines Crew rostering and scheduling Pricing (revenue Management) Capacity Planning (size of fleet) Service maintenance Parts inventory 9

10 Energy Unit commitment problems Capacity Planning Pricing based on Uncertain Demand Project selection 10

11 Retail Markdown Optimization Replenishment of Inventory (inventory Optimization) Warehouse Management 11

12 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 12

13 Pharma Sales promotions Assign sales reps to physicians 13

14 Edelman Award UPS NBC Procter & Gamble Aspentech (last year) 14

15 Characteristics Size of Problems variables CPU Time A few seconds 15

16 Development Directions Ease of use Type of Problem Performance 16

17 Development Directions Ease of use Type of Problem Speed Size of problem Reliability Performance 17

18 Development Directions Ease of use Type of Problem Speed Size of problem Reliability Performance Out-of-the-box 18

19 Primal Simplex Solution Times of Six Models with Recent Releases of Xpress-MP Primal Watson_1 Prele Ken-18 Energy Chinese Artur Rel Rel Rel Rel Rel Rel

20 Dual Simplex Solution Times of Six Models with Recent Releases of Xpress-MP Dual Watson_1 Prele Ken-18 Energy Chinese Artur Rel Rel Rel Rel Rel Rel

21 Barrier Method (Interior Point) 3000 Solution Times of Six Models with Recent Releases of Xpress-MP Barrier Watson_1 Prele Ken-18 Energy Chinese Artur Rel Rel Rel Rel Rel Rel

22 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 22

23 MIP Good Solutions - Fast 23

24 MIP Performance XPR XPR neos1 > neos neos3 > neos13 > neos XPR XPR

25 Development Directions Ease of use Type of Problem Performance 25

26 Development Directions Ease of use Building Applications Deployment Type of Problem Performance 26

27 Modeling Environment 27

28 Development Directions Ease of use Type of Problem Performance 28

29 Type of problem - Technologies Network design Capacity Planning Pricing Strategic Sourcing Scheduling LP MIP QP MIQP Constraint Programming Nonlinear Heuristics 29

30 Supply Chain Network Design LP, MIP Capacity Planning, LP, MIP Pricing, LP, Nonlinear Supply Chain Strategic Sourcing, LP,MIP, MIQP Scheduling, LP, MIP, CP, Heuristics 30

31 Development Directions Ease of use Type of Problem Performance 31

32 64 bit & Parallel 32

33 Future Grid computing Solve millions of small scale lps and mips or nlps in seconds Examples Pricing for Airlines-Hotels-Cars 33

34 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 ) 34

35 Development Directions Ease of use Type of Problem Performance 35

36 Clever Modeling Languages Solve Models in Parallel Profiling models Wizard model development Development of Clever algorithms Expert systems Artificial intelligence 36

37 Wizard decision variables 37

38 Xpress-Application Developer 38

39 Screenshots of XAD apps 39

40 Development Directions Ease of use Type of Problem Performance 40

41 Xpress-SLP Non-Linear MINLP Option Large scale Applications: Process Industry Pricing Energy 41

42 CP, MIP and their combination Optimization Technologies Mixed Integer Programming: MIP Finite Domain Constraint Programming: CP Planning & Scheduling CP CP+MIP MIP Long and mid-term planning: MIP Short-term planning, scheduling: CP Supply chain optimization Requires MIP, CP, and their combination Time Horizon 42

43 Xpress-CP Architecture (cooperative solver approach) Mosel/IVE ENVIRONMENT Mosel Planning and Scheduling Model Xpress-MP KALIS 43

44 Xpress-CP Adopters BASF Chemicals Peugeot Cars Procter and Gamble Discrete products 44

45 Stochastic Programming Basis Represent uncertainty Build problem efficiently Manage scenarios Applications Planning Supply chain Interaction with forecasting 45

46 Stochastic Programming 46

47 Future Data mining Robust Optimization 47

48 Classification Problems: example 48

49 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) 49

50 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. 50

51 Credit Rating Logical Analysis of Data Credit scoring of Countries Credit scoring of Companies 51

52 Medical Applications Different types of Cancer Obesity 52

53 Robust Optimization 53

54 Other examples Robust Portfolio Optimization Robust Inventory policies 54

55 LP SLP MISLP MIP MIQP VERTICAL APP. GUI / STUDIO STO LP MIP QP EXTENSIONS/NAT SOLVERS IVE MOSEL HEURISTICS MODELING PLATFORM XAD 55

56 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 56

57 Portfolio Management Wrap Portfolio Tracks another index / actively managed portfolio Realigns periodically to match risks and returns Provides similar performance at lower management costs 57

58 WRAP Portfolio T=1 T=2 T=3 INDEX INDEX INDEX WRAP WRAP WRAP Re-Balancing 58

59 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 59

60 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 60

61 Portfolio Management Want to automate the complete process Need to combine Business Rules Optimization in a single application 61

62 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 62

63 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 63

64 Benefits Lower monitoring and management costs Lower execution costs Assured compliance 64

65 Other Applications Marketing State Farm Process Industries AspenTech Transport Schneider 65

66 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 66

67 Conclusion Combine Flexibility of business rules and Robustness of optimization Next Generation Intelligent Applications Automation Testing Determining rules? 67

68 Workshop October nd New York University 68

69 Informs San Francisco Preconference Workshop 1 Tutorial 2 talks Exhibit 69

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