SIMULATION OPTIMIZATION NEW ADVANCES FOR REAL WORLD OPTIMIZATIONSOFTWARE

SIMULATION OPTIMIZATION: NEW ADVANCES FOR REAL WORLD OPTIMIZATIONSOFTWARE Fred Glover (Opt. Tek) Gary Kochenberger (Opt. Tek & UCD) (Special thanks to Marco Better) OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Outline n Opt. Tek Systems, Inc. n What is simulation optimization? n Why is it important? n Classical approaches n Metaheuristic approaches n Applications n Conclusions OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Opt. Tek Systems, Inc. Snapshot 4 4 4 Founded in 1992 Leading provider of optimization software to the general simulation market. Opt. Quest®, the company’s flagship software product 4 licensed to over 60, 000 users 4 the optimization standard for simulation modeling 4 Alliance partners number over twenty including: 4 4 4 4 4 Halliburton Oracle CSC Flextronics Dassault CACI Lockheed Martin Rockwell Software HP Opt. Tek Systems, Inc. 1919 Seventh Street Boulder, CO 80302 www. opttek. com Consulting and Technical Services OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Simulation Optimization Software Our Channel Partners: n Alion, Micro Analysis and Design Division n n CACI , SIMPROCESS n n Oracle, Decisioneering (Crystal Ball) n n Delmia, a subsidiary of Dassault Systèmes n n Flex. Sim Software Products n Flextronics/Sim. Flex n Frontline Systems (Premium Solver) n GAMS n Glomark n Incontrol Enterprise Dynamics n n n Jada Management Systems Halliburton, Landmark Graphics Division HP, Mercury Division Mesquite Software Planview PROMODEL Corporation Risk Capital Management Rockwell Software (ARENA) SIMUL 8 XJ Technologies OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Opt. Tek Customized Simulation Optimization Software Applications n Portfolio Management securities and capital assets (projects, programs, initiatives, etc. ) n Workforce Optimization Manpower planning, diversity planning n Data Security n Supply Chain Management n Strategic and Operational Planning n Financial Planning n Manufacturing Process Flow n Resource-Constrained Scheduling n Business Process (re)Design OPTIMIZATIONSOFTWARE www. Opt. Tek. com

What is Simulation Optimization? n. Which of possibly many sets of model specifications (i. e. , input parameters and/or structural assumptions) leads to optimal performance? Simulation model Input parameters Measure of performance OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Simulation Optimization Why is it required? 4 Complex models contain many variables and constraints as well as uncertainty 4 What-if approach unlikely to result in an optimal answer due to large number of possible solutions 4 Inability of pure optimization to model complexities, uncertainties and dynamics of scenarios 4 Simulation-Optimization removes these inabilities by combining both approaches OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Simulation-Optimization Why is it required? 4 A total solution requires both capabilities. 4 Integrated two-Step Solution 4 Simulation 4 Optimization 4 Both are necessary, neither is sufficient. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Simulation Optimization Benefits in Dealing with Uncertainty 4 Simulation enables understanding/modeling and communications of uncertainty. 4 Optimization enables management of uncertainty. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Optimization on a Metamodel OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Classical Approaches n Stochastic approximation – Gradient-based approaches n Sequential response surface methodology n Random search n Sample path optimization – Also known as stochastic counterpart n Drawbacks: • Local in their search • Rely heavily on randomness • Lack of intelligent guidance • No learning ability OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Metaheuristic Approaches n Based on neighborhood search – Tabu search – Simulated annealing n Based on combining solutions in a population – Genetic algorithms – Scatter search n Other: – Swarm methods – Hybrid methods (e. g. tabu search + scatter search) OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Modular Design Metaheuristic Optimizer Input parameters Objective function value Simulation Model OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Tabu Search n 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 n The best move may be nonimproving n Memory functions (short and long term) are updated after every move OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Tabu Search: Implementation Issues Feasible point Infeasible point Current point Optimal point Nontabu move Tabu move OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Scatter Search n Combines solutions in a small reference set to create new trial solutions n Uses generalized combination methods with controlled randomization n The selection process is deterministic n The updating of the reference set (aka the “evolution process”) is also deterministic and attempts to create a balance between solution quality and diversity OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Basic Scatter Search P Diversification Generation Method Repeat until |P| = PSize Improvement Method Reference Set Update Method Solution Combination Method Subset Generation Method Ref. Set Stop if no more new solutions OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Linear Combination Method OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Issues Related to Metaheuristics for Simulation Optimization n Aggressiveness of the search – Balance between diversification and intensification n Solution representation – Combination methods n Use of metamodels to “save” on evaluations n Constraint handling (soft vs. hard) n Length of simulation and selection of best solution OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Objective function value Aggressiveness of the Search Less aggressive but diversified Aggressive and less diversified Calls to the simulator OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Solution Representation n Continuous variables n Discrete variables – Resources (e. g. , number of machines, number of technicians, etc. ) – Design choices (e. g. , brand, category, etc. ) n Binary variables – Special case of discrete variables n Permutation variables – Imply so-called all-different constraints OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Use of Meta-models Neural networks, Regression, Data mining, etc. Metaheuristic Optimizer x Metamodel f(x) Simulation Model No large d? Yes Discard x OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Handling Constraints x Constraint Mapping x* F(x*) Simulator G(x*) Penalty Function 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Length of Simulation n Simulation runs during the optimization process are typically shorter than those of confirmation runs n 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 OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Opt. Quest® A potent search engine that can pinpoint the best decisions to optimize plans. 4 4 4 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) OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Efficiency is Critical! OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Opt. Quest Applications n Optimization of Monte Carlo Models – Project portfolio selection – Inventory order management n Optimization of Discrete Event Models – Six Sigma in an Emergency Room – Job shop configuration n Optimization of Agent-based Models – Workforce diversity planning – Manpower planning and scheduling OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Example 1 – Project Portfolio Selection in Oil and Gas OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Problem n Given a set of opportunities and limited resources determine the best set of projects that maximize performance while controlling risk. n Create a new portfolio n Augment an existing portfolio OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Traditional Approaches n Net Present Value Analysis / Ranking Methods – Compute discounted cash flows and pick largest NPV – Ignores uncertainty n Mean-Variance Optimization – Harry Markowitz (1952) Minimize s Such that m > 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Simulation-Based Portfolio Selection n Use Monte Carlo simulation to model projects. – Unlimited ability to model complex situations – Risk can be defined in multiple ways n Use Opt. Quest to select projects – Objectives based on outputs from simulation – Additional constraints based on cash flows, etc. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Components n Simulation Model n Integer Variables e. g. , Only invest in one project within a group n Constraints e. g. , Cash Flow n Multiple Objectives - “Requirements” e. g. , Maximize Return Mean while keeping 5 th percentile of return above some goal (risk control). OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Application Information n 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) n Ten year models that incorporate multiple types of uncertainty OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Budget-Constrained Project Selection n 5 Projects – Expected Revenue and Distribution – Probability of Success – Cost n $2 M Budget OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Base Case n Determine participation levels in each project [0, 1] (Decision Variables) that n Maximize E(NPV) (Forecast) n While keeping s. NPV < 10 M$ (Forecast) n All projects must start in year 1. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Base Case TGP = 0. 4, OWF = 0. 4, DL = 0. 8, OHW = 1. E(NPV) = 37. 4 M s =9. 5 M OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Deferment Case n Determine participation levels in each project [0, 1] AND starting times for each project that n Maximize E(NPV) n While keeping s. NPV < 10 M$ n All projects may start in year 1, year 2, or year 3. (5 x 3=15 Decision Variables) OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Base Case Deferment Case TGP = 0. 4, OWF = 0. 4, DL = 0. 8, OHW = 1. TGP 1 = 0. 6, DL 1=0. 4, OHW 3=0. 2 E(NPV) = 37. 39 M s =9. 50 M E(NPV) = 47. 5 M s =9. 51 M 10 th Pc. =36. 1 M OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Probability of Success Case n Determine participation levels in each project [0, 1] AND starting times for each project that n Maximize P(NPV > 47, 455 M$) n While keeping 10 th Percentile of NPV > 36, 096 M$ n All projects may start in year 1, year 2, or year 3. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Base Case Deferment Case TGP = 0. 4, OWF = 0. 4, DL = 0. 8, OHW = 1. TGP 1 = 0. 6, DL 1=0. 4, OHW 3=0. 2 E(NPV) = 37. 39 M s =9. 50 M E(NPV) = 47. 5 M s =9. 51 M 10 th Pc. =36. 1 M Probability of Success Case TGP 1 = 1. 0, OWF 1=1. 0, DL 1=1. 0, OHW 3=0. 2 E(NPV) = 83. 9 M s =18. 5 M P(NPV > 47. 5) = 99% 10 th Pc. =53. 4 M OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Benefits n Easy to use n Quickly evaluate many planning alternatives n Optimized financial performance n Better risk control using familiar metrics n Similar results found in larger problems • (e. g. oil & gas investment funnel with 256 projects). OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Example 2 – IT Project Portfolio Selection in Pharmaceuticals OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Problem Setup n Example 2: Monte Carlo Simulation • Portfolio of 20 potential projects • Pharmaceutical product development n Relatively long and costly R&D n 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: n Maximize return n Control risk n Maximize probability of high NPV OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Base Case n 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 OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Case 2 n Example 2: Summary Results (All cases subject to budget constraint). – Case 2: Max E[NPV] While P(5) $ 1, 086 – Result: E[NPV] = $ 2, 346 P(5) = $ 1, 159 St. Dev. = $ 725 OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Case 3 n Example 2: Summary Results (All cases subject to budget constraint). – Case 3: Max P(NPV > $2, 139) – Result: P(NPV > $2, 139) = 62% E[NPV] = $ 2, 346 P(5) = $ 1, 159 St. Dev. = $ 725 OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Example 3 – Six Sigma in an Emergency Room Optimization Driven SIX SIGMA Using Simulation Optimization to Achieve Quality Goals OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Minimizing Cycle Time at an ER Patient Arrival Emergency Room Obje Admit criti ctive = cal p m atien inimize Treatment ts expe cted cycl e tim e fo Approach= optimize current process, r redesign process and re-optimize. Release OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework Current Process for Level 1 Patient Arrive at ER Transfer to room Receive treatment Fill out registration OK? Y Released N Admitted Into Hospital OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Measure current performance – Costs (per 100 hours of operation): • Cost of personnel: $51. 7 K • Fixed ER room cost: $ 0. 9 K • Total operating cost: $52. 6 K – Level of Service (CT of critical patients): • Average: 1. 98 hours • 95% Confidence Interval: [1. 94 – 2. 02] OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Measure current performance (Cont’d. ) – Process is too costly. Six Sigma team has set a new budget goal of $40. 0 K 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Analyze problem to identify causes – Construct a workflow level simulation model of current process. – Use Opt. Quest® to optimize resource levels in order to minimize Level 1 patients’ CT. Why? – Enumeration of all possible scenarios may require: • 7 x 3 x 4 x 4 x 20 = 6, 720 scenarios tested • 30 runs/scenario = 2 min. each 28 workdays to obtain best solution! OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Analyze problem (Cont’d) – Minimize E[CT] for Level 1 Patients – Subject to: • Operating Cost <= $40. 0 K/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 OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n 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. 6 K per 100 hrs. of operation n (TOO COSTLY! New budget <= $40. 0 K) • E[CT] for Level 1 Patients = 1. 98 hours n New process should achieve this result, or better. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Analyze problem (Cont’d) – Next, set up Opt. Quest to run for 100 iterations and 30 runs per iteration. • Each run simulates 100 hours of ER operation. • Results: n Best solution found in 6 minutes n 3 nurses, 3 physicians, 1 PCT, 2 clerks, 12 rooms n E[OC] = $ 36. 2 K (31% improvement) n E[CT] for P 1 = 2. 08 hours (too high!) – Need to redesign process to assure quality goal is achieved on a 95% confidence level. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Improve the results by redesigning processes Arrive at ER Transfer to room Receive treatment Fill out registration Y OK? Released N Admitted Into Hospital Current Process Arrive at ER Transfer to room Receive treatment OK? Fill out registration Redesigned Process Y Released N Admitted Into Hospital OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n Improve the results by redesigning processes – E[CT] for P 1 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 Opt. Quest. – Results: • Best solution found in 8 minutes • 4 nurses, 2 physicians, 2 PCTs, 2 clerks, 9 rooms • E[OC] = $ 31. 8 K (a 12% further improvement) • E[CT] for P 1 = 1. 94 hours (95% C. I. is 1. 91 – 1. 99) • MISSION ACCOMPLISHED! OPTIMIZATIONSOFTWARE www. Opt. Tek. com

DMAIC Framework n 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. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Conclusions n Able to find high-quality solution quickly. n Able to improve the model and re-optimize to find better configurations. n Highly unlikely to find solution of such high quality relying solely on simulation. OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Conclusions There is still much to learn and discover about how to optimize simulated systems both from theoretical and the practical points of view. The opportunities are exciting! OPTIMIZATIONSOFTWARE www. Opt. Tek. com

Questions & Feedback www. Opt. Tek. com (303) 447 -3255 OPTIMIZATIONSOFTWARE www. Opt. Tek. com