Modelling 2

Aspects of Modelling

Aspects of Modelling

• Treating certainty, uncertainty and risk– What if analysis– Sensitivity analysis– Scenario analysis

• Normative vs descriptive models• Static vs dynamic models

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Certainty, Uncertainty and Risk• Certainty - models constructed under assumed certainty

e.g. many financial models. Easy to develop and solve

• Uncertainty –the decision maker does not know, or can’t assess the probability of occurrence of certain outcomes. More information increases certainty.

• Risk analysis involves estimates of risk. Risk can thus be estimated.

• Uncertainty and risk can be examined using what-if and sensitivity analysis. It is a good idea when identifying variables to assess certainty and risk.

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What if analysis• The end user makes changes to variables or relationships

between variables and observes the resulting change in the values of other variables.

Example• Change a revenue amount (variable) or a tax rate formula

in a simple financial spreadsheet model, and recalculate all the affected variables. A manager would be interested in observing and evaluating any changes in values that occurred e.g. net profit after taxes.

• In may cases this is the “bottom line” i.e. a key factor in making many types of decisions.

• What would happen to sales if we cut advertising by 10%?

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Sensitivity analysis

• the value of one variable is changed repeatedly and the resulting changes on the other variables are observed

e.g. value of revenue is changed incrementally in small increments and the effects on other spreadsheet variables noted and evaluated.

e.g. Cut advertising by 10% repeatedly and note effect on sales.

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Scenario Analysis

• Examine the best case, worst case, most likely and average case scenarios.

•

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Examine the Wilmington example.

• How does this model deal with uncertainty?

• What is the best case here for Wilmington?

• What is the worst case?

• What other factors do we need to consider in scenario analysis?

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Types of ModelNormative

(Optimisation)

• the chosen alternative is demonstrably the best of all possible alternatives.

• e.g. Linear Programming

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Descriptive

•Describe things as they are, or as they are believed to be.•Checks the outcome of a given set of alternatives not of all alternatives.•No guarantee of an optimal solution.e.g. simulation models which are used to explore different solutions and relationships between variables

Optimisation Examples

• Get the highest level of goal attainment from a given set of resources e.g. max profit from €1000000 investment.

• Find alternative with highest ratio of goal attainment to cost.

• Find alternative with the lowest cost that wll achieve acceptable level of goals.

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Excel Techniques 1: Goal Seeking

• Finds a value for a variable and links it to an outcome.

E.g.• How many pages do we have to print to make

it worth buying a printer?

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Example : Optimisation problems

– Staff schedules.– Product Mix.– Route Planning

• Note that you are looking for the best or the optimal solution

• What are the goals?• What are the constraints?• What are the decision variables?

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Lecture 8 12

Staff Scheduling

• You are the manager of an amusement park, all of your general staff are paid the same and are on a rota of 5 days work, followed by 2 days off.

• You know how many staff you need each day.– Sunday 22, Monday 17, Tuesday 13, Wednesday 14,

Thursday 15, Friday 18, Saturday 24

• You want to schedule your staffs break days in such a way as to minimise total labour costs while making sure that you have the staff you need.

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Product Mix

• Your company manufactures TVs, stereos and speakers, using a common parts inventory of power supplies, speaker cones, etc.

• Parts are in limited supply and you must determine the most profitable mix of products to build.

• You want to manufacture the products that will maximise your profits.

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Shipping Routes• You have a number of production plants which can

ship goods to warehouses which are in various cities.• The is a known cost for shipping goods from a plant

to a warehouse.• There is a limit on the amount of goods each plant

can supply,• Each city has a known demand.

• You want to satisfy demand while minimising the cost of shipping

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Constraints

• Staff Allocation:– Must have a certain number of staff available on each day.– Staff rota must be 5 days followed by 2 days.

• Product Mix– Each end product uses several parts which have a limited

supply.• Shipping Routes– Each warehouse has contain demands.– Each factory has limited output.

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Decision Variables

• Each problem has a number of different variables which will affect the goal.

• The values which can be given to these variables are limited by the constraints.

• What are the decision variables for each of the three problems?

Lecture 8 17

Decision Variable Answer

• Staff Allocation:– Number of staff on each rota.

• Product Mix– Amount of each product to make.

• Shipping Routes– Amount of goods to ship from each factory to

each city.

Linear Programming• a way of calculating optimal values.

• Decision Variablese.g. How much of each type of product to make.

• Objective Function (for what we want to optimise)e.g. Profit = (profit from product a) * (number of type a)+ (profit from product b) * (number of type b)

• Constraints– Limits on amount of parts available.

• We can use Solver in Excel to give us an optimal answer to these problems.

However ....

• Real life tends to be messier....

Good Enough or Satisficing solutions• decision-maker sets up an aspiration, goal or

desired level of performance and searches the alternatives until one is found which achieves this level. This involves:-

1.Generating Alternatives2.Predicting the outcome of each alternative3.Measuring outcomes –value in terms of goal

attainment e.g. profit ,customer satisfaction – no. complaints, level of loyalty to product, ratings found by surveys.

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Rationality vs Bounded rationality?

Descriptive Model ExamplesDescribe things as they are, or as they are believed to be.Checks the outcome of a given set of alternatives, not of all

alternatives.

• Scenario analysis• Environmental impact analysis• Simulation• Waiting line (queue) management• Narratives.

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Example Simulation Technique : System Dynamics

• Based on stocks and flows in a system• We model the system as a series of stocks flows

and feedback loops.

How is the water level affected?Example : Limits to growth study (Donella Meadows)

Bathtub

Water level

Water out the plugWater in the tap

Swine Flu Simulation.

http://forio.com/simulate/simulation/netsim/h1n1/

http://www.iseesystems.com/community/downloads/NetsimModels.aspx#5

Static Analysis

Static models take a single snapshot of a situation. During this, everything occurs in a single interval or fixed time frame. During a static analysis stability of the relevant data is assumed. e.g. buy or make.

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Dynamic Analysis -time-dependent models

• scenarios that change over time e.g. 5 year profit and loss projection, in which the input data such as costs, prices and quantities change over time.

e.g. in determining how many checkouts need to be open in a supermarket the time of day must be considered.

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Why is time an important factor?

Dynamic models are important because they use, represent or generate trends and patterns over time. e.g. 5 year profit projection where input data such as costs, prices and quantities change over time.

Can be used to create averages per period or moving averages and to prepare comparative analysis. May facilitate the development of business plans, strategies,tactics.

• Dynamic simulation represents when conditions vary from the steady state over time:- there may be variations in the raw materials, or unforeseen events.

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Model categories

Optimisation of Problems with few alternatives

Find best solution from small number of alternatives

Decision tables, trees

Optimisation via algorithm

Find best solution from large number of alternatives using a step-by-step improvement process

Linear and other mathematical programming models, network models

Optimisation via analytic formula

Find best solution using formula

Some inventory models

Simulation Use experimentationHeuristics Find good enough

solution using rulesHeuristic programming, expert systems

Other Models Solve a what-if case using a formula

Financial modelling, waiting lines

Predictive models Predict future for given scenario

Forecasting models