Modelling 2 Aspects of Modelling

Treating certainty, uncertainty and risk – What if analysis – Sensitivity analysis – Scenario analysis Normative vs descriptive models Static vs dynamic models 7/14/20152

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. 7/14/20153

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%? 7/14/20154

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. 7/14/20155

Scenario Analysis Examine the best case, worst case, most likely and average case scenarios. 7/14/20156

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? 7/14/20157

Types of Model Normative (Optimisation) the chosen alternative is demonstrably the best of all possible alternatives. e.g. Linear Programming 87/14/2015 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 € investment. Find alternative with highest ratio of goal attainment to cost. Find alternative with the lowest cost that wll achieve acceptable level of goals. 7/14/20159

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? 7/14/201510

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? 7/14/201511

Lecture 812 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.

Lecture 813 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.

Lecture 814 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

Lecture 815 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.

Lecture 816 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 817 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 Variables e.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 Alternatives 2.Predicting the outcome of each alternative 3.Measuring outcomes –value in terms of goal attainment e.g. profit,customer satisfaction – no. complaints, level of loyalty to product, ratings found by surveys. 7/14/201520

Rationality vs Bounded rationality?

Descriptive Model Examples 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. Scenario analysis Environmental impact analysis Simulation Waiting line (queue) management Narratives. 7/14/201522

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 plug Water in the tap

Swine Flu Simulation. n1/ loads/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. 7/14/201525

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. 7/14/201526

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.

7/14/2015Source Turban 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 SimulationUse experimentation HeuristicsFind good enough solution using rules Heuristic programming, expert systems Other ModelsSolve a what-if case using a formula Financial modelling, waiting lines Predictive modelsPredict future for given scenario Forecasting models