Business
Sensitivity Analysis
Sensitivity analysis is a technique used to assess how changes in one variable can impact outcomes in a business model or decision-making process. It involves testing different scenarios to understand the sensitivity of the model to changes in key inputs. By conducting sensitivity analysis, businesses can identify the most critical variables and make more informed decisions based on potential outcomes.
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11 Key excerpts on "Sensitivity Analysis"
- M. Chidambaram(Author)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
S ensitivity analysis is concerned with the study of the effect of small (infinitesimal) changes in model parameters on the changes in the model outputs. In this chapter, methods of calculating the sensitivity are reviewed. Several examples are given. 8.1 INTRODUCTION The sensitivity information can be used to estimate which parameters are most influential in affecting the behaviour of the system (Verma and Marbidelli, 1999). Such information is crucial for experimental design, data assimilation, reduction of complex nonlinear models, and evaluating optimization gradients and Jacobians in the setting of dynamic optimization and parameter estimation. The Sensitivity Analysis also plays a very important role in the dynamical systems. For example, when investigating periodic orbits, Lyapunov exponents, or other chaos indicators, and for general bifurcation analysis, computation of the sensitivities with respect to the initial conditions of the problem is a key component of the analysis. To control a system means that by altering parameters and input variables, we can produce the desirable output. If varying a parameter does not alter system output (i.e., the system is insensitive to the parameter), then that parameter is not useful for control. Therefore, the Sensitivity Analysis can be used to identify which parameters have potential as control inputs. Typically, the Sensitivity Analysis is carried out to the parameters of differential equations model. If some of the parameters are very sensitive on the output of our interest, then these parameters are to be estimated more precisely. When comparing with the experimental work, the effect of these parameters on the experimental results should be compared with that of the models. In the control system design problem, the variables which are very sensitive on the output variables, are to be considered as the manipulated variables. The objective in mathematical modelling of systems is to Sensitivity Analysis 8
eBook - ePubUsing Excel for Business Analysis
A Guide to Financial Modelling Fundamentals
- Danielle Stein Fairhurst(Author)
- 2012(Publication Date)
- Wiley(Publisher)
CHAPTER 11
Stress-Testing, Scenarios, and Sensitivity Analysis in Financial Modelling
Any good financial model will usually contain scenario and Sensitivity Analysis functionality, at least to some degree. Scenarios are an important part of financial modelling, and the reason we have left this to near the end of the book is because it is usually a task performed at the end of the model-building process. If the model has been properly designed using best practice, it is not difficult to add, edit, and change scenarios in the model.Scenarios and Sensitivity Analysis are great ways to insulate your model from risk. What would be the absolute worst that could happen? If everything that can go wrong does go wrong, will my business/project/venture still be okay? There are usually effects and interactions between multiple variables that may change in the model.Scenarios can assist with decision analysis. They are laid out in advance so that the decision makers can see the expected impact of each course of action. How close to reality these scenarios are really depends on the accuracy of the assumptions implicit in the model—but that’s another story! (See “Document Your Assumptions” in Chapter 3.)Scenario analysis is a very important part of financial modelling—in fact, in some cases, being able to perform a scenario analysis is almost the whole point of building a financial model in the first place! Many of the principles of best practice in financial modelling discussed in earlier sections were to ensure that the model is set up in such a way that scenarios can be easily included in our model.There are several different technical methods of creating scenarios and sensitivities in financial models, which we will discuss, but all scenarios involve changing input variables to see the impact of the change on the model outputs. By following good practice when building the model in the first place—particularly when it comes to linking to the source, and only entering data once—creating scenarios and sensitivities in the model is quite simple. (See Chapter 3, “Best Practice Principles of Modelling.”) With a well-built model that has all inputs linked to outputs, it is relatively easy to change inputs and watch the outputs change.
eBook - ePubUsing Excel for Business Analysis
A Guide to Financial Modelling Fundamentals
- Danielle Stein Fairhurst(Author)
- 2015(Publication Date)
- Wiley(Publisher)
CHAPTER 11 Stress-Testing, Scenarios, and Sensitivity Analysis in Financial ModellingAny good financial model will usually contain scenario and Sensitivity Analysis functionality, at least to some degree. Scenarios are an important part of financial modelling, and the reason we have left this to near the end of the book is that it is usually a task performed at the end of the model-building process. If the model has been properly designed using best practice, it is not difficult to add, edit, and change scenarios in the model.Scenarios and Sensitivity Analysis are great ways to insulate your model from risk. What would be the absolute worst that could happen? If everything that can go wrong does go wrong, will my business/project/venture still be okay? There are usually effects and interactions between multiple variables that may change in the model.Scenarios can assist with decision analysis. They are laid out in advance so that the decision makers can see the expected impact of each course of action. How close to reality these scenarios are really depends on the accuracy of the assumptions implicit in the model—but that’s another story! (See “Document Your Assumptions” in Chapter 3.)Scenario analysis is a very important part of financial modelling—in fact, in some cases, being able to perform a scenario analysis is almost the whole point of building a financial model in the first place! Many of the principles of best practice in financial modelling discussed in earlier sections were to ensure that the model is set up in such a way that scenarios can be easily included in our model.There are several different technical methods of creating scenarios and sensitivities in financial models, which we will discuss, but all scenarios involve changing input variables to see the impact of the change on the model outputs. By following good practice when building the model in the first place—particularly when it comes to linking to the source, and only entering data once—creating scenarios and sensitivities in the model is quite simple. (See Chapter 3, “Best Practice Principles of Modelling.”) With a well-built model that has all inputs linked to outputs, it is relatively easy to change inputs and watch the outputs change.
eBook - ePubUsing Excel for Business and Financial Modelling
A Practical Guide
- Danielle Stein Fairhurst(Author)
- 2019(Publication Date)
- Wiley(Publisher)
CHAPTER 11 Stress Testing, Scenarios, and Sensitivity Analysis in Financial ModellingAny good financial model will usually contain scenario and Sensitivity Analysis functionality, at least to some degree. Scenarios are an important part of financial modelling, and the reason we have left this to near the end of the book is that it is usually a task performed at the end of the model-building process. If the model has been properly designed using best practice, it is not difficult to add, edit, and change scenarios in the model.Scenarios and Sensitivity Analysis are great ways to insulate your model from risk. What would be the absolute worst that could happen? If everything that can go wrong does go wrong, will my business/project/venture still be okay? There are usually effects and interactions between multiple variables that may change in the model.Scenarios can assist with decision analysis. They are laid out in advance so that decision-makers can see the expected impact of each course of action. How close to reality these scenarios are really depends on the accuracy of the assumptions implicit in the model—but that's another story! (See “Document Your Assumptions” in Chapter 3 .)Scenario analysis is a very important part of financial modelling—in fact, in some cases, being able to perform a scenario analysis is almost the whole point of building a financial model in the first place! Many of the principles of best practice in financial modelling discussed in earlier sections were to ensure that the model is set up in such a way that scenarios can easily be included in our model.There are several different technical methods of creating scenarios and sensitivities in financial models, which we will discuss, but all scenarios involve changing input variables to see the impact of the change on the model outputs. By following good practice when building the model in the first place—particularly when it comes to linking to the source, and only entering data once—creating scenarios and sensitivities in the model is quite simple. (See Chapter 3
- Ashok Kumar Verma(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
293 Model Validation and Sensitivity Analysis 9.5 Role of Sensitivity Analysis The Sensitivity Analysis reveals important information about the effect of various parameters on the output of the process. This information may be used for a better process design, process monitoring and control. Sensitivity Analysis is carried out experimentally or through simulation using the devel-oped model. The Sensitivity Analysis through experiments is not an aim of the present discussion. A few applications of the Sensitivity Analysis using simulation studies are presented in this section. 9.5.1 Process Design The role of sensitivity in optimal process design was discussed by Chen et al. (1970). The method was based on optimisation using a Lagrange mul-tiplier. Two types of optimisation were studied. In one case, the expected value (mean) of objective function or, in the other case, maximum relative sensitivity was minimised. The disturbance following uniform distribution correctly described the large uncertainty in comparison to that following normal distribution. It was shown that the mean system performance may deviate from the deterministic system performance. For uncorrelated param-eters, the deviation is due to the second-order derivative of output with respect to the parameter, 2 2 y i ∂ ∂φ , and the variance of the parameter. The issue of optimal design of a large system was addressed by Takamatsu et al. (1970). A large system is a set of several types of process equipment. Mathematically, a model for such a large system is composed of several sub-models, each representing process equipment. The model for the large sys-tem consists of all equations from all of the sub-models. The range of model output defines the constraints to the optimisation problem. Using the adjoint parameters (Lagrange multiplier), the constrained problem is converted to an unconstrained optimisation problem. The range of the model output is expressed as a sensitivity coefficient.
eBook - PDFShape Mining
Knowledge Extraction from Engineering Design Data
- (Author)
- 2014(Publication Date)
- Cuvillier Verlag(Publisher)
In this respect, the understanding of which design features influence the performance of a design is an essential component. In its general definition, Sensitivity Analysis targets to reveal the influence of one or multiple independent variables on an dependent variable by apply-ing methods for sensitivity estimation, see [Saltelli et al., 2007] and [Cullen and Frey, 1999]. In this context, the dependent variables are representing the cause or input of a model or system, whereas the dependent variable is 57 Dieses Werk ist copyrightgeschützt und darf in keiner Form vervielfältigt werden noch an Dritte weitergegeben werden. Es g ilt nur für den persönlichen Gebrauch. CHAPTER 4. DESIGN Sensitivity Analysis representing its effect. Adopting the general formulation, and applying it to the analysis of design data, the following definition for the process of design Sensitivity Analysis is derived: Design Sensitivity Analysis Design Sensitivity Analysis is the study and quantification of the impact of design feature variations on the variation of the overall design performance. In the shape mining process, the design Sensitivity Analysis is carried out for two purposes. First, it is applied to extract knowledge about the importance of particular design areas with respect to variations of the de-sign performance, and second to filter design variables in order to improve subsequent modeling and data mining steps. A wide range of methodologies concerning the quantification of sensitivity have been studied. Those attempts can be categorized into local and global methods. Local sensitivity estimates aim at directly quantifying the gradi-ent at a certain fixed point by means of calculating the partial derivative | ∂y/∂x i | x 0 , where y is the dependent variable, x i a design variable and x 0 defines the fixed point. Those methods relate to adjoint modeling [Giles and Pierce, 2000; Othmer, 2006; Othmer et al., 2011] and automatic differentia-tion [Verma, 2000].
eBook - ePubModelling and Simulation of Integrated Systems in Engineering
Issues of Methodology, Quality, Testing and Application
- D J Murray-Smith(Author)
- 2012(Publication Date)
- Woodhead Publishing(Publisher)
5Methods and applications of parameter Sensitivity Analysis
Abstract:
Parameter Sensitivity Analysis provides an efficient way of assessing parametric dependencies in mathemsatical models and computer simulations. This is important for design optimisation, for estimating the effects of modelling errors and uncertainties in the analysis of system performance, for understanding issues such as test input design in experimental modelling and in the external validation of models. This chapter provides a review of methods of parameter Sensitivity Analysis and considers applications involving linear and nonlinear lumped parameter models.Key words sensitivity function output sensitivity sensitivity model sensitivity bond graph5.1 Fundamental concepts of parameter Sensitivity Analysis
Parameter Sensitivity Analysis techniques are important for establishing how responses of a model change when parameters are varied and which of its parameters most influence the model behaviour (see e.g. [1] and [2] ). Models are never exact and it is important to be able to assess parametric dependencies at the model development stage as part of an investigation of modelling assumptions, simplifications and overall credibility. This can lead to an understanding of the effects of component tolerances and how the system performance may degrade as components change with environmental conditions or through the processes of ageing. Sensitivity information is also very important for system optimisation in design and it should be noted that methods of optimisation based on gradient methods make direct use of parameter sensitivity measures.For the applications being considered in this book, the model may be in lumped parameter or distributed parameter form, continuous or discrete, linear or nonlinear. The sensitivity may also be characterised in a number of ways. Common measures are based on the time domain, but frequency-domain measures can also be very important in some fields, as are measures involving a performance index (see e.g. [2]
- John A. White, Kellie S. Grasman, Kenneth E. Case, Kim LaScola Needy, David B. Pratt(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
226 CHAPTER 11 Break-Even, Sensitivity, and Risk Analysis We perform sensitivity analyses in several chapters, although we do not always refer to them as such. For example: • in Chapters 4 and 5, we examine the impact on economic worth of the minimum attractive rate of return; • in Chapter 7, we examine the sensitivity of the optimum replacement interval to changes in the initial investment, the salvage value, the rate of increase in annual operating and management costs, and the minimum attractive rate of return; • in Chapter 9, we examine the sensitivity of after-tax present worth to changes in the depreciation method and to changes in the amount of money borrowed; • in Chapter 10, we examine the sensitivity of after-tax present worth to changes in the inflation rate; we also examine the impact of inflation on the preferred loan repayment method; and • in Chapter 12, we examine the sensitivity of the optimum investment portfolio to changes in the level of investment capital available and the minimum attractive rate of return. A derisive term occasionally used to describe analytical models is GIGO—“garbage-in, garbage-out.” In other words, what you get out of the model is no better than what you put into it. While one cannot always trust the results obtained from models of reality, perfect information is not often required to produce correct decisions. Sensitivity Analysis can be used to determine if, in fact, less-than-perfect estimates of the parameter values will result in the best decision being made. EXAMPLE 11.3 Sensitivity Analysis for a Single Alternative To illustrate how a Sensitivity Analysis might be performed, we consider once more the SMP investment: a $500,000 initial investment, annual savings of $92,500 for a 10-year period, and a salvage value of $50,000.
eBook - PDFTraffic Simulation and Data
Validation Methods and Applications
- Winnie Daamen, Christine Buisson, Serge P. Hoogendoorn, Winnie Daamen, Christine Buisson, Serge P. Hoogendoorn(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
The problem set-up, that includes the choices of algorithm, MoP, and GoF function in the objective, sensibly affects the quality of the solution. In particular, it has influence on the chance of finding a global optimum or at least a stable solution. Punzo et al. (2012) presented an exploratory study on this subject (see Section 4.6.3). In addition most models pres-ent a pronounced asymmetry in the influence of the parametric inputs on their outputs, with a small subset of input parameters accounting for most of the output uncertainty and the others playing little or no role. The calibration of parameters with scarce influence on the outputs along with flat objective functions, for instance, is a challenge for any optimization algorithm. Sensitivity Analysis 125 The key role played by SA may serve a number of useful purposes, depend-ing on the specific setting adopted. The importance ranking of the inputs with regard to their influence on the output uncertainty (factor prioritiza-tion setting) is the most common function of SA. The analysis can be used to identify which input parameters really need to be calibrated (factor fixing setting) and which are the observations are really sensitive to the inputs and thus useful for the estimation. Reducing the number of parameters to calibrate may make feasible an otherwise unfeasible problem while the defi-nition of the most appropriate observations is crucial for guiding the alloca-tion of resources for the collection of new data. Both tasks are obviously crucial to reducing costs and producing a successful analysis. In addition to the importance of ranking of uncertainty sources, SA may be useful for identifying the elements of a modeling process (inputs, assumptions, etc.) and the regions of the inputs that are most responsible for yielding acceptable model realizations or, conversely, exceeding specific thresholds (i/o mapping settings).
eBook - PDFSpreadsheet Modeling & Decision Analysis
A Practical Introduction to Business Analytics
- Cliff Ragsdale(Author)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
141 Chapter 4 Sensitivity Analysis and the Simplex Method 4.0 Introduction In chapters 2 and 3, we studied how to formulate and solve LP models for a variety of decision problems. However, formulating and solving an LP model does not necessarily mean that the original decision problem has been solved. After solving an LP model, a number of questions often arise about the optimal solution. In particular, we might be interested in how sensitive the optimal solution is to changes in various coefficients of the LP model. Businesses rarely know with certainty what costs will be incurred or the exact amount of resources that will be consumed or available in a given situation or time period. Thus, optimal solutions obtained using models that assume all relevant factors are known with certainty might be viewed with skepticism by management. Sensitivity Analysis can help overcome this skepticism and provide a better picture of how the solution to a problem will change if different factors in the model change. Sensitivity Analysis also can help answer a number of practical managerial questions that might arise about the solution to an LP problem. 4.1 The Purpose of Sensitivity Analysis As noted in chapter 2, any problem that can be stated in the following form is an LP problem: MAX (or MIN): c 1 X 1 1 c 2 X 2 1 . . . 1 c n X n Subject to: a 11 X 1 1 a 12 X 2 1 . . . 1 a 1 n X n # b 1 … a k 1 X 1 1 a k 2 X 2 1 . . . 1 a kn X n $ b k … a m 1 X 1 1 a m 2 X 2 1 . . . 1 a mn X n 5 b m All the coefficients in this model (the c j , a ij , and b i ) represent numeric constants. So, when we formulate and solve an LP problem, we implicitly assume that we can specify the exact values for these coefficients. However, in the real world, these coefficients might change from day to day or minute to minute. For example, the price a company charges for its products can change on a daily, weekly, or monthly basis.
eBook - PDF- David Isaac, John O'Leary, Mark Daley(Authors)
- 2016(Publication Date)
- Red Globe Press(Publisher)
182 9 Risk and Sensitivity Analysis 9.1 Introduction 9.2 Risk and property development 9.3 Risk analysis techniques 9.4 Practical responses to risk 9.5 A baseline project 9.6 Sensitivity Analysis 9.7 Scenario testing 9.8 Statistical approaches 9.9 Software appraisal packages and spreadsheets 9.10 Summary Self-assessment questions Aims This chapter explores the types of risk that affect property developments, and there is discussion on the strengths and weaknesses of risk assessment techniques which have emerged as a response. It will be explained that where significant risk is detected, there are some mitigation methods which a developer can use to reduce some of the risk. However, it will be explained that development risk cannot be eradicated entirely, and it is important that an appropriate profit target is set to compensate for risk bearing. Key terms >> Sensitivity test – adjustments made to the variables in a development appraisal to establish the effect on the outcome. Where a relatively small step change is made to a variable which generates a large swing in the outcome, the variable is deemed to be sensitive, warranting consideration of risk reduction measures. >> Systematic risk – factors such as market fluctuation, legislative change or base rate rises which affect all developments and about which individual develop- ers can do very little. >> Unsystematic risk – the project specific risks that a developer may be able to do something about. For example, a heavy reliance on borrowing for a project means that it is highly geared and vulnerable to meeting loan repay- ments. A developer could explore ways to reduce the reliance on borrowing with equity funding to reduce the risks. Risk and Sensitivity Analysis 183 9.1 Introduction As discussed in the previous two chapters, development appraisals require the calibration of variables such as building costs, rents and sales values.
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