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Sophisticated Optimization

Making the right decision can be crucial to gaining a competitive advantage. With sophisticated optimization, you can locate the best solution in your model and also determine the precise values for all the choices that need to be made for that decision. Get ahead of the competition by modeling the best set of options to achieve your goal.
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Maximize Value and Minimize Cost

Good business decisions give your organization a competitive advantage. Optimal decisions make that advantage massive. The complex interplay between inputs, assumptions and constraints within the model structure make achieving optimality an impossible task without the right tool.

What is Optimization?

The Monte Carlo method is a computerized mathematical technique that allows people to quantitatively account for risk in forecasting and decision-making. At its core, the Monte Carlo method is a way to use random samples of parameters to explore the behavior of a complex system. A Monte Carlo simulation is used to handle an extensive range of problems in a variety of different fields to understand the impact of risk and uncertainty.

Decision Models for Any Industry

Optimization refers to a process or analysis that determines the set of decisions that maximize or minimize a key model output. These techniques can be applied to any application and is commonly used in construction & engineering, logistics & transportation, finance & banking, insurance & reinsurance, energy & utilities, manufacturing & consumer goods and other industries.

Prescriptive Recommendations

Sophisticated optimization gives the decision maker the precise values for all choices that need to be made – essentially what each controllable input should be. These optimal decisions will preserve logical real-life constraints and business rules, ensuring only feasible solutions are presented. Progress can be tracked visually, during the analysis, to assist in communicating the process and final, optimal outcome.

Use cases are varied, and include:
Inventory management
Budgeting
Resource and production scheduling
Product and marketing mix
Supply chain planning
Market entry timing and more
Project, loan, and investment portfolio maximization

A Range of Outcomes (one col list)

Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows:
the extreme possibilities
the outcomes of going for broke and for the most conservative decision
along with all possible consequences for middle-of-the-road decisions

History of Monte Carlo Simulation

The technique was first used by scientists working on the atom bomb; it was named for Monte Carlo, the Monaco resort town renowned for its casinos. Since its introduction in World War II, Monte Carlo simulation has been used to model a variety of physical and conceptual systems.

How Does Optimization Work?

Optimization operates on your model by trialing a potential solution, checking for feasibility, “learning” from the result, and then determining the best “direction” to search for superior solutions. This process continues until a global optimal solution is found.

To ensure feasibility, decision variables are constrained to the ranges available to the decision maker. Such constraints could be real-life limitations (such as availability of airlines seats or similar inventory) or business rules (such as avoiding overtime costs). Additional, complex constraints on any aspect of the model, or interplay between the decision variables and model assumptions, are tested with each trial to ensure only viable solutions are permitted.

The current best value of the output during an optimization is tracked in real time and can be displayed graphically, highlighting the rapid initial improvement in solutions, occasional spikes as breakthroughs are made, and finally as convergence to the optimal solution is achieved.
The progress of an optimization in real-time, showing how the specified output changes as different solutions are trialed.

100% Microsoft Excel Integration

With PrecisionTree, you never leave your spreadsheet, allowing you to work in a familiar environment, and get up to speed quickly.

Full Statistics Reports and Graphs

See results in risk profile graphs, 2-way sensitivity, tornado graphs, spider graphs, policy suggestion reports, and strategy-region graphs.

Set up your decision tree in Microsoft Excel exactly as you need it with logic nodes, reference nodes, linked trees, custom utility functions, and influence diagrams.

Linear and Nonlinear Optimization

In general, optimization problems fall into one of two categories: linear and nonlinear.

There are many different optimization, or “solving,” methods, some better suited to different types of problems than others. Linear solving methods include techniques known as tabu search, linear programming, and scatter search. Nonlinear solving methods include genetic algorithms. Genetic algorithms mimic the evolutionary processes of biology by introducing random new solutions (called “mutations”) while simultaneously developing what appears to be a promising solution (an “organism”). By introducing random mutations, genetic algorithms are able to “learn” or “evolve” a better overall, or global, solution than linear methods typically can.

FEATURES LIST (not always shown)

FeatureBenefitProfessional EditionIndustrial Edition
Optimization under uncertaintyCombines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more.
Efficient Frontier AnalysisEspecially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk
Ranges for adjustable cells and constraintsStreamlined model setup and editing
Genetic algorithmsFind the best global solution while avoiding getting caught in local, “hill-climbing” solutions
Six solving methods, including GAs and OptQuestAlways have the best method for different types of problems
RISKOptimizer Watcher and Convergence MonitoringMonitor progress toward best solutions in real time
Overlay of Optimized vs Original DistributionCompare original output to optimized result to visually see improvements
Original, Best, Last model updatingInstantly see the effects of three solutions on your entire model

Types of Optimization Models

Beyond simple linear versus nonlinear classification of optimization problems, there are a number of other dimensions to this type of analysis.

FEATURES LIST (not always shown)

FeatureBenefitProfessional EditionIndustrial Edition
Optimization under uncertaintyCombines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more.
Efficient Frontier AnalysisEspecially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk
Ranges for adjustable cells and constraintsStreamlined model setup and editing
Genetic algorithmsFind the best global solution while avoiding getting caught in local, “hill-climbing” solutions
Six solving methods, including GAs and OptQuestAlways have the best method for different types of problems
RISKOptimizer Watcher and Convergence MonitoringMonitor progress toward best solutions in real time
Overlay of Optimized vs Original DistributionCompare original output to optimized result to visually see improvements
Original, Best, Last model updatingInstantly see the effects of three solutions on your entire model

FEATURES LIST (not always shown)

FeatureBenefitProfessional EditionIndustrial Edition
Optimization under uncertaintyCombines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more.
Efficient Frontier AnalysisEspecially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk
Ranges for adjustable cells and constraintsStreamlined model setup and editing
Genetic algorithmsFind the best global solution while avoiding getting caught in local, “hill-climbing” solutions
Six solving methods, including GAs and OptQuestAlways have the best method for different types of problems
RISKOptimizer Watcher and Convergence MonitoringMonitor progress toward best solutions in real time
Overlay of Optimized vs Original DistributionCompare original output to optimized result to visually see improvements
Original, Best, Last model updatingInstantly see the effects of three solutions on your entire model

Random Sampling Versus Best Guess

During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called an iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.

Monte Carlo simulation provides a number of advantages over deterministic, or “single-point estimate” analysis:
Probabilistic Results. Results show not only what could happen, but how likely each outcome is.
Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence. This is important for communicating findings to other stakeholders.
Sensitivity Analysis. Deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results. This allows you to identify and mitigate factors which cause the most risk.
Scenario Analysis: In deterministic models, it’s very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred. This is invaluable for pursuing further analysis.
Correlation of Inputs. In Monte Carlo simulation, it’s possible to model interdependent relationships between input variables. It’s important for accuracy to represent how, in reality, when some factors go up or down, others go up or down accordingly.
An enhancement to Monte Carlo simulation is the use of Latin Hypercube sampling, which samples more accurately from the full range of values within distribution functions and produces results more quickly.

How PrecisionTree Is Used

PrecisionTree has a multitude of applications, including:
Oil, Gas, & Mineral Reserves: Map out sequential, probabilistic exploration plans of prospective sites containing oil, natural gas, or other minerals. Estimate uncertain reserves to make wise drilling decisions.
Litigation & Bidding Strategy: Plan step-by-step strategies in complex legal or business negotiations, or when bidding on contracts. Map what could happen at each stage and your response to, along with probabilistic chance events.
Real Options Valution: Quantify the value of real options, or the right to undertake an investment or not, in the face of uncertainty future outcomes.
Supply Chain Management: Develop multi-stage plans for complex supply chains, incorporating probabilities of failures and other chance events.
Medical Treatment Planning: Establish sequential, multi-stage treatment plans for complex medical conditions given uncertain outcomes at each stage.

Enterprise LicensingBetter Research, Insights, and Outcomes for All

Whether your organization’s focus is qualitative, quantitative, or mixed methods data analysis, we can help your whole team work better together — collaborating to aggregate, organize, analyze, and present your findings. Lumivero’s enterprise licensing options offer volume pricing for teams and organizations needing nine (9) or more licenses.

Enterprise licenses allow the flexibility to install Lumivero software and solutions on multiple computers (up to the maximum number of licenses that your site has purchased) with a centralized management solution.

Lumivero’s team-based solutions allow you to:

Stay up-to-date with free upgrades to the latest releases
Reduce IT costs with one platform deployed across your organization
Reassign licenses to different users as teams evolve
Centralize license and subscription management in one place
Streamline budget allocation, especially for smaller groups and consultancy firms
Enjoy a Dedicated Customer Success Manager and pro-rated rates for new users