OPTIMIZATION SOFTWARE SIMULATION OPTIMIZATION: NEW ADVANCES FOR REAL WORLD OPTIMIZATION Fred Glover (OptTek) Gary Kochenberger (OptTek &

OPTIMIZATIONSOFTWARE www.OptTek.com

SIMULATION OPTIMIZATION: NEW ADVANCES FOR REAL WORLD OPTIMIZATION

Fred Glover (OptTek)

Gary Kochenberger (OptTek & UCD)

(Special thanks to Marco Better)

OPTIMIZATIONSOFTWARE


Outline

OptTek Systems, Inc. What is simulation optimization? Why is it important? Classical approaches Metaheuristic approaches Applications Conclusions


OptTek Systems, Inc. Snapshot

Founded in 1992 Leading provider of optimization software to the general simulation market. OptQuest®, the company’s flagship software product

licensed to over 60,000 users the optimization standard for simulation modeling

Alliance partners number over twenty including: Halliburton Oracle CSC Flextronics Dassault CACI Lockheed Martin Rockwell Software HP

Consulting and Technical Services

OptTek Systems, Inc. 1919 Seventh StreetBoulder, CO 80302www.OptTek.com


Simulation Optimization Software

Alion, Micro Analysis and Design Division CACI , SIMPROCESS Oracle, Decisioneering (Crystal Ball) Delmia, a subsidiary of Dassault Systèmes FlexSim Software Products Flextronics/SimFlex Frontline Systems (Premium Solver) GAMS Glomark Incontrol Enterprise Dynamics

Jada Management Systems Halliburton, Landmark Graphics Division HP, Mercury Division Mesquite Software Planview PROMODEL Corporation Risk Capital Management Rockwell Software (ARENA) SIMUL8 XJ Technologies

Our Channel Partners:


OptTek Customized Simulation Optimization Software Applications

Portfolio Management securities and capital assets (projects, programs, initiatives, etc.)

Workforce Optimization Manpower planning, diversity planning Data Security Supply Chain Management Strategic and Operational Planning Financial Planning Manufacturing Process Flow Resource-Constrained Scheduling Business Process (re)Design


What is Simulation Optimization?

Which of possibly many sets of model specifications (i.e., input parameters and/or structural assumptions) leads to optimal performance?

Inputparameters

Measure of performance

Simulationmodel


Simulation OptimizationWhy is it required?

Complex models contain many variables and constraints as well as uncertainty

What-if approach unlikely to result in an optimal answer due to large number of possible solutions

Inability of pure optimization to model complexities, uncertainties and dynamics of scenarios

Simulation-Optimization removes these inabilities by combining both approaches


Simulation-OptimizationWhy is it required?

A total solution requires both capabilities.

Integrated two-Step Solution

Simulation

Optimization

Both are necessary, neither is sufficient.


Simulation OptimizationBenefits in Dealing with Uncertainty

Simulation enables understanding/modeling and communications of uncertainty.

Optimization enables management of uncertainty.


Optimization on a Metamodel


Classical Approaches

Stochastic approximation

– Gradient-based approaches

Sequential response surface methodology Random search Sample path optimization

– Also known as stochastic counterpart

Drawbacks:• Local in their search

• Rely heavily on randomness

• Lack of intelligent guidance

• No learning ability


Metaheuristic Approaches

Based on neighborhood search– Tabu search

– Simulated annealing

Based on combining solutions in a population– Genetic algorithms

– Scatter search

Other:– Swarm methods

– Hybrid methods (e.g. tabu search + scatter search)


Modular Design

MetaheuristicOptimizer

SimulationModel

Input parameters Objective function value


Tabu Search

Uses a systematic neighborhood search to choose the best neighbor– Size of the neighborhood is controlled by candidate

list strategies

– The selection of the best neighbor is constrained by tabu functions

The best move may be nonimproving Memory functions (short and long term) are

updated after every move


Tabu Search:Implementation Issues

Feasible point

Infeasible point

Current point

Optimal point

Nontabu moveTabu move


Scatter Search

Combines solutions in a small reference set to create new trial solutions

Uses generalized combination methods with controlled randomization

The selection process is deterministic The updating of the reference set (aka the

“evolution process”) is also deterministic and attempts to create a balance between solution quality and diversity


Basic Scatter Search

P

Diversification GenerationMethod

Repeat until |P| = PSize

Subset GenerationMethod

ImprovementMethod

Solution CombinationMethod

ImprovementMethod

Stop if no morenew solutions

Reference SetUpdate Method

RefSet


Linear Combination Method

x3

1 2 3 4 5 6 7 8 9 10 11 12 13

1

2

3

4

5

6

7

8

9

10

x2 = (8,4)

x1 = (5,7)

x3 = x1 - r(x2 - x1)

x4 = x1 + r(x2 - x1)

x5 = x2 + r(x2 - x1)

y

x

x4

x5


Issues Related to Metaheuristics for Simulation Optimization

Aggressiveness of the search– Balance between diversification and intensification

Solution representation– Combination methods

Use of metamodels to “save” on evaluations Constraint handling (soft vs. hard) Length of simulation and selection of best

solution


Aggressiveness of the SearchO

bje

ctiv

e fu

nctio

n va

lue

Calls to the simulator

Aggressive and less diversified

Less aggressive but diversified


Solution Representation

Continuous variables Discrete variables

– Resources (e.g., number of machines, number of technicians, etc.)

– Design choices (e.g., brand, category, etc.)

Binary variables– Special case of discrete variables

Permutation variables– Imply so-called all-different constraints


Use of Meta-models

MetaheuristicOptimizer

SimulationModel

f(x)

Metamodelx

large d?

Discard x

Yes

No

)(ˆ xf

Neural networks,Regression, Data mining, etc.

)()(ˆbestxfxfd


Handling Constraints

ConstraintMapping

x PenaltyFunction

Simulatorx*

F(x*)

G(x*)P(x*)

x = input parameters (possibly infeasible)

x* = mapped input parameters (constraint feasible)

F(x*) = objective function value

G(x*) = value of other output variables used in constraints

P(x*) = penalized objective function value

May allow desirable infeasible solutions from management perspective.


Length of Simulation

Simulation runs during the optimization process are typically shorter than those of confirmation runs

A run can be terminated early if it can be predicted that the outcome will not improve upon the current best solution– This can be done with statistical analysis tools such

as confidence intervals and hypothesis testing


OptQuest®

Scatter Search Advanced Tabu Search Linear Programming Integer Programming Neural Networks Linear Regression

Ten years of Research & Development funded by National Science Foundation (NSF) and Office of Naval Research (ONR)

A potent search engine that can pinpoint the best decisions to optimize plans.


OptQuest vs. RiskOptimizer, Ex. 5 Prob. 14 Best solution = -8695.012285

-4397.23 Risk Pop 10-4576.85 Risk Pop 20

-4272.22 Risk Pop 50

-4765.34 Risk Pop 100

-8543.49 OptQuest Pop 20

-8695.01 OCL Boundary=.7

-9000

-8000

-7000

-6000

-5000

-4000

-3000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Simulations

Ob

ject

ive

Efficiency is Critical!


OptQuest Applications

Optimization of Monte Carlo Models– Project portfolio selection

– Inventory order management

Optimization of Discrete Event Models– Six Sigma in an Emergency Room

– Job shop configuration

Optimization of Agent-based Models– Workforce diversity planning

– Manpower planning and scheduling


Example 1 – Project PortfolioSelection in Oil and Gas


Problem

Given a set of opportunities and limited resources determine the best set of projects that maximize performance while controlling risk.

Create a new portfolio

Augment an existing portfolio


Traditional Approaches

Net Present Value Analysis / Ranking Methods

– Compute discounted cash flows and pick largest NPV

– Ignores uncertainty

Mean-Variance Optimization – Harry Markowitz (1952)

Minimize

Such that > Goal

• Normality of returns of assets must be assumed

• Quadratic Program

• Addresses correlation but limited to variance as measure of risk.

• Additional constraints such as cash flow and performance metrics may not be addressable.


Simulation-Based Portfolio Selection

Use Monte Carlo simulation to model projects.– Unlimited ability to model complex situations

– Risk can be defined in multiple ways

Use OptQuest to select projects– Objectives based on outputs from simulation

– Additional constraints based on cash flows, etc.


Components

Simulation Model Integer Variables

e.g., Only invest in one project within a group

Constraints e.g., Cash Flow

Multiple Objectives - “Requirements”e.g., Maximize Return Mean while keeping 5th percentile of return

above some goal (risk control).


Application Information

5 Projects– Tight Gas Play Scenario (TGP)

– Oil – Water Flood Prospect (OWF)

– Dependent Layer Gas Play Scenario (DL)

– Oil - Offshore Prospect (OOP)

– Oil - Horizontal Well Prospect (OHW)

Ten year models that incorporate multiple types of uncertainty


Budget-Constrained Project Selection

5 Projects– Expected Revenue and Distribution

– Probability of Success

– Cost

$2M Budget


Base Case

Determine participation levels in each project [0,1] (Decision Variables) that

Maximize E(NPV) (Forecast)

While keeping NPV < 10 M$ (Forecast)

All projects must start in year 1.


TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.

E(NPV) = 37.4M =9.5M

Base Case

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71

1,000 Trials 16 Outliers

Forecast: NPV


Deferment Case

Determine participation levels in each project [0,1] AND starting times for each project that

Maximize E(NPV)

While keeping NPV < 10 M$

All projects may start in year 1, year 2, or year 3. (5x3=15 Decision Variables)


TGP1 = 0.6, DL1=0.4, OHW3=0.2

E(NPV) = 47.5M =9.51M 10th Pc.=36.1M

TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.

E(NPV) = 37.39M =9.50M

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71


Forecast: NPV

Base CaseFrequency Chart

M$

Mean = $47,455.10.000

.007

.014

.020

.027

0

6.75

13.5

20.25

27

$25,668.28 $37,721.53 $49,774.78 $61,828.04 $73,881.29


Forecast: NPV

Deferment Case


Probability of Success Case

Determine participation levels in each project [0,1] AND starting times for each project that

Maximize P(NPV > 47,455 M$) While keeping 10th Percentile of NPV > 36,096 M$

All projects may start in year 1, year 2, or year 3.


TGP1 = 0.6, DL1=0.4, OHW3=0.2

E(NPV) = 47.5M =9.51M 10th Pc.=36.1M

Frequency Chart

M$

Mean = $83,971.65.000

.008

.016

.024

.032

0

8

16

24

32

$43,258.81 $65,476.45 $87,694.09 $109,911.73 $132,129.38


Forecast: NPV

TGP1 = 1.0, OWF1=1.0, DL1=1.0, OHW3=0.2

E(NPV) = 83.9M =18.5M P(NPV > 47. 5) = 99% 10th Pc.=53.4M

Probability of Success Case

TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.

E(NPV) = 37.39M =9.50M

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71


Forecast: NPV

Base CaseFrequency Chart

M$

Mean = $47,455.10.000

.007

.014

.020

.027

0

6.75

13.5

20.25

27

$25,668.28 $37,721.53 $49,774.78 $61,828.04 $73,881.29


Forecast: NPV

Deferment Case


Benefits

Easy to use Quickly evaluate many planning alternatives Optimized financial performance Better risk control using familiar metrics

Similar results found in larger problems • (e.g. oil & gas investment funnel with 256 projects).


Example 2 – IT Project Portfolio Selection in Pharmaceuticals


Problem Setup

Example 2: Monte Carlo Simulation• Portfolio of 20 potential projects

• Pharmaceutical product development Relatively long and costly R&D

Probability of Success factor after R&D is complete

• Mutually exclusive (substitute) products

• Dependent (complementary) products

• Choose the best (0,1) set of projects to: Maximize return

Control risk

Maximize probability of high NPV


Base Case

Example 2: Summary Results(All cases subject to budget constraint).

– Base Case: Max E[NPV]

While St.Dev.(NPV) $ 650

– Result: E[NPV] = $ 2,139

P(5) = $ 1,086

St.Dev. = $ 639


Case 2


– Case 2: Max E[NPV]

While P(5) $ 1,086

– Result: E[NPV] = $ 2,346

P(5) = $ 1,159

St.Dev. = $ 725


Case 3


– Case 3: Max P(NPV > $2,139)

– Result: P(NPV > $2,139) = 62%

E[NPV] = $ 2,346

P(5) = $ 1,159

St.Dev. = $ 725


Optimization DrivenSIX SIGMA

Using Simulation Optimization to Achieve Quality Goals

Example 3 – Six Sigma in an Emergency Room


Minimizing Cycle Time at an ER

Treatment

Patient Arrival

Emergency Room

Approach= optimize current process, redesign process and re-optimize.

Objective = minimize expected cycle time for

critical patients

Release

Admit


DMAIC Framework

Define the problem area

– Current ER process is too costly, in terms of operating cost and variability in level of service.

– Need to redesign ER process to reduce costs and guarantee service levels at a 95% confidence level or higher.


DMAIC Framework

Describe the current process– Arriving patients are assigned a priority level according to

the criticality of their condition:• LEVEL 1: immediately taken to an ER Room.

• LEVELS 2 AND 3: first sign in, then undergo a triage assessment before being taken to an ER Room.

• Level 2 and 3 patients’ arrival rate is higher than Level 1 patients’.

• Higher priority patients can preempt resources being used by lower priority patients.


DMAIC Framework

Describe the current process (Cont’d.)

– Current resources available:• Nurses (7)

• Physicians (3)

• Patient Care Technicians (PCTs) (4)

• Administrative Clerks (4)

• ER Rooms (20)

– Rooms not used by ER can be used by other wards.


DMAIC Framework

Arrive at ER

Transfer toroom

Receivetreatment

Fill outregistration

OK? Released

AdmittedInto

Hospital

Y

N

Current Process for Level 1 Patient


DMAIC Framework

Measure current performance

– Costs (per 100 hours of operation):• Cost of personnel: $51.7K

• Fixed ER room cost: $ 0.9K

• Total operating cost: $52.6K

– Level of Service (CT of critical patients):• Average: 1.98 hours

• 95% Confidence Interval: [1.94 – 2.02]


DMAIC Framework

Measure current performance (Cont’d.)

– Process is too costly. Six Sigma team has set a new budget goal of $40.0K per 100 hours of operation.

– Service level variability is too great. New goal: at least 95% of Level 1 patients spend no longer than 2 hours in the ER.


DMAIC Framework

Analyze problem to identify causes– Construct a workflow level simulation model of current

process.

– Use OptQuest® to optimize resource levels in order to minimize Level 1 patients’ CT. Why?

– Enumeration of all possible scenarios may require:• 7x3x4x4x20 = 6,720 scenarios tested

• 30 runs/scenario = 2 min. each

28 workdays to obtain best solution!


DMAIC Framework

Analyze problem (Cont’d)

– Minimize E[CT] for Level 1 Patients

– Subject to:• Operating Cost <= $40.0K/100 hrs of operation

• Number of Nurses between 1 and 7

• Number of Physicians between 1 and 3

• Number of PCTs between 1 and 4

• Number of Clerks between 1 and 4

• Number of ER Rooms between 1 and 20


DMAIC Framework

Analyze problem (Cont’d)– First, run 30 replications of the current operation:

• 7 nurses

• 3 physicians

• 4 PCTs

• 4 Admin. Clerks

• 20 ER Rooms

– Results:• E[OC] = $ 52.6K per 100 hrs. of operation

(TOO COSTLY! New budget <= $40.0K)

• E[CT] for Level 1 Patients = 1.98 hours New process should achieve this result, or better.


DMAIC Framework

Analyze problem (Cont’d)– Next, set up OptQuest to run for 100 iterations and 30

runs per iteration.• Each run simulates 100 hours of ER operation.

• Results: Best solution found in 6 minutes

3 nurses, 3 physicians, 1 PCT, 2 clerks, 12 rooms

E[OC] = $ 36.2K (31% improvement)

E[CT] for P1 = 2.08 hours (too high!)

– Need to redesign process to assure quality goal is achieved on a 95% confidence level.


DMAIC Framework

Improve the results by redesigning processes

Arrive at ER

Transfer toroom

Receivetreatment


OK? Released

AdmittedInto

Hospital

Y

N

Current Process

Arrive at ER

Transfer toroom

Receivetreatment


OK? Released

AdmittedInto

Hospital

Y

N

Redesigned Process


DMAIC Framework

Improve the results by redesigning processes– E[CT] for P1 improves from 2.08 to 1.98 hours;

however, the upper limit of the 95% confidence interval is still above 2 hours.

– Re-optimize new process using OptQuest.

– Results:• Best solution found in 8 minutes

• 4 nurses, 2 physicians, 2 PCTs, 2 clerks, 9 rooms

• E[OC] = $ 31.8K (a 12% further improvement)

• E[CT] for P1 = 1.94 hours (95% C.I. is 1.91 – 1.99)

• MISSION ACCOMPLISHED!


DMAIC Framework

Control the processes to ensure improvement goals are met– Implement changes and a performance

measurement system to continuously assess real performance.

– Readopt this simulation-optimization methodology whenever necessary to maintain adequate performance.


Conclusions

Able to find high-quality solution quickly. Able to improve the model and re-optimize to

find better configurations. Highly unlikely to find solution of such high

quality relying solely on simulation.


Conclusions

There is still much to learn and discover about how to optimize simulated systems both from the

theoretical and the practical points of view.

The opportunities are exciting!


Questions & Feedback

www.OptTek.com

(303) 447-3255

Documents

OPTIMIZATION SOFTWARE SIMULATION OPTIMIZATION: NEW ADVANCES FOR REAL WORLD OPTIMIZATION Fred Glover (OptTek) Gary Kochenberger (OptTek &