## Simulation Optimization at Breakthrough Speed

You can solve **simulation optimization** problems at breakthrough speeds -- often hundreds of times faster than competitive products -- with the combination of Risk Solver and Frontline's Premium Solver or Premium Solver Platform. PSI Technology™, which makes simulations in Risk Solver up to 100 times faster than using Excel alone, also speeds up the simulation optimization process.

With Risk Solver, your models include **uncertain variable **cells defined by **probability distributions**. You can use these uncertain variable cells in any formula in your model, to compute **uncertain functions**. Risk Solver will perform a **Monte Carlo simulation** with thousands of trials, where a different value is sampled for each uncertain variable on each trial, and your model is recalculated with these values.** Statistics** across all the trials are accumulated for each of your uncertain functions. You can access these statistics in worksheet cells, with regular Excel formulas calling PSI Statistics functions. And in Premium Solver, you can use these cells in the **objective** and **constraints** of your optimization model.

When you click Solve, Premium Solver performs a **Monte Carlo simulation** through Risk Solver on **each Trial Solution of the optimization**. Doing this is usually an order of magnitude faster than in competitive products for simulation optimization.

#### Defining a Simulation Optimization Model

Creating a simulation optimization model using Risk Solver and Premium Solver is straightforward. You follow these steps:

- Define
**decision variable cells**(such as A1), using either the Solver Parameters dialog or the PsiVar() function. These are factors that are**under your control**-- you (or the Solver) will decide what values they should have. - Define
**uncertain variable cells**(such as A2), that contain formulas calling PSI Distribution functions supplied by Risk Solver -- for example**PsiUniform()**and**PsiNormal()**. These are factors that are**not under your control**. - Build your model, using cell formulas that may depend on the decision variables, uncertain variables, or both.
- Each cell (such as B1) containing a formula that depends on uncertain variables (say =A1+2*A2) represents
**thousands of trial values**, generated during each Monte Carlo simulation by**sampling different values**for A2 and computing =A1+2*A2. - In other cells (such as C1), define the
**summary statistics**you want, using functions such as**PsiMean(B1)**or**PsiStdDev(B1)**. You may use formulas to compute further values based on these summary statistics. - Define your
**objective**and**constraints**for optimization. These may be cell formulas that depend only on the**decision variables**, depend on the**uncertain variables**through**PSI Statistics functions**, or depend on both.

#### Solving a Simulation Optimization Model

Solving a simulation optimization model using Risk Solver and Premium Solver is also straightforward. Follow these steps:

- Activate
by clicking the**Interactive Simulation****light bulb button**on the Risk Solver Ribbon. - Select
**Tools Premium Solver**to display the Solver Parameters dialog, and click the**Solve**button.

There's much more we could say -- and there's **much more to come**. But even now, simulation optimization with Risk Solver and Premium Solver is far faster and more robust than what's available for competitive Monte Carlo simulation tools for Excel.

If you need to **allocate scarce resources** under **conditions of uncertainty**, Risk Solver is your winning bet!