Risk Analysis and Simulation

1. Risk Analysis and Simulation BIS 314 Decision Making with Computers

2. Risk Most practical operations management situations involve uncertainty. Uncertainty about a situation can often indicate risk, which is the possibility of loss, damage, or any other undesirable event. A decision made under conditions of certainty means that there is only one outcome or consequence for a given action. Most decisions are made under conditions of uncertainty or risk, meaning that a particular action will lead to any one of a number of possible outcomes. BIS 314 Decision Making with Computers

3. Risk Analysis and Risk Management Risk Analysis refers to the development and use of quantitative models to help understand the risks and uncertainties involved in a particular local scenario by considering a range of possible outcomes. Risk Management is a wider activity, considering more general and qualitative aspects of risk, and how to deal with it, so that risk analysis is only one part of risk management. BIS 314 Decision Making with Computers

4. Risk Analysis and Risk Management Consider the following simple example: The manager of a bakery is considering the financial implications of making chocolate muffins for general sale. Certainty and uncertainty in decision making BIS 314 Decision Making with Computers

5. Limitations of using ‘What If’ Analysis to handle uncertainty A common way to deal with uncertainty is to generate many scenarios. • However, the difficulty of such an approach is that some scenarios are more likely to occur than others; and it is difficult to create an accurate composite picture. • Moreover, the practical limit for a systematic exploration of varying different input factor values independently is three factors, corresponding to the rows, columns, and different sheets. Linking the values of these different factors together as spreadsheet scenarios allows more factors to be varied but not independently, thus making it difficult to relate the output values to changes in the input factor values. BIS 314 Decision Making with Computers

6. Limitations of using ‘What If’ Analysis to handle uncertainty To deal with these limitations, the manager needs to be able to specify an ‘input factor’ as taking a range of values from a probability distribution, rather than a single fixed value or set of fixed values. Probability Distribution: is a relationship describing the linkage between the chance of specific values or a range of values of a variable occurring and that value or range of values. BIS 314 Decision Making with Computers

7. Probability Distribution and Sampling This ‘input factor’ must be given some particular value. For each uncertain input factor, a process is needed that generates a value that is in keeping with the pattern of uncertainty appropriate for that particular input factor. This process is known as sampling. The individual value generated from this process is called a sample. A trial is the name given to the results of a spreadsheet model with one set of values for the uncertain variables in the model. Minicase Handout: Top Hat Sampling BIS 314 Decision Making with Computers

8. Carrying out Risk Analysis using a Spreadsheet Risk analysis is the process of letting input factor values vary by sampling from appropriate probability distributions, and seeing the effect this has on the calculated variable values. Muffins Example from Slide 4… BIS 314 Decision Making with Computers

9. Carrying out Risk Analysis using a Spreadsheet Suppose the initial production level (number of muffins made in first week) is to be 99 muffins per week. We shall assume for simplicity that the uncertain sales outcome (number of muffins sold in first week) can take all the values from 0 to 99 with equal probability. This would be equivalent to putting 100 pieces of paper in the top hat, each with one of the numbers form 0 to 99 on it. For a computer to reproduce the process of picking a number from the hat, we need the concept of a random number. A random number is one chosen so that all possible values are equally likely, and there is no connection between one number in the series and the following one. This is done using the RAND() function in MS Excel. BIS 314 Decision Making with Computers

10. Carrying out Risk Analysis using a Spreadsheet BIS 314 Decision Making with Computers

11. Carrying out Risk Analysis using a Spreadsheet BIS 314 Decision Making with Computers

12. Provides one value for each of the input factors Base Logic Model Base Data Model Data and Logic Models in Handling Uncertainty When dealing with uncertainty, we need to extend the logic model/data model structure. It is useful to think in terms of beginning with a model based on conditions of certainty, and then extending it by adding the parts that handle uncertainty. BIS 314 Decision Making with Computers

13. Provides one value for each of the constant input factors Base Logic Model Base Data Model Provides random number inputs Extension to the base logic model Extension to the base data model Data and Logic Models in Handling Uncertainty Provides set of values for the varying input factors New logic model New data model BIS 314 Decision Making with Computers

14. 1. Set up logic model 2. Decide on uncertain inputs 3. Choose probability distributions 4. Set up first sample 5. Repeat sampling many times 6. Produce summary model(s) Steps in Building and Using a Risk Analysis Model BIS 314 Decision Making with Computers

15. Number of muffins sold in first week Sales Revenue Selling Price Profit contribution in first week Fixed Cost Variable cost per muffin Total Variable Cost Steps in Building and Using a Risk Analysis Model Set up the base logic model, ignoring the effects of uncertainty on the values in the corresponding data model for the moment. Model not including uncertainty Number of muffins made in first week BIS 314 Decision Making with Computers

16. Random number function Number of muffins sold in first week Sales Revenue Selling Price Profit contribution in first week Fixed Cost Variable cost per muffin Total Variable Cost Number of muffins made in first week Steps in Building and Using a Risk Analysis Model Decide which logic model factors have associated values to be regarded as uncertain in the analysis. If an input factor has an uncertain value, then the value of any calculated variable which depends on it will also be uncertain. Model including uncertainty (Extension Logic Model) BIS 314 Decision Making with Computers

17. Steps in Building and Using a Risk Analysis Model • Choose the appropriate probability distribution to use in the extension to the logic model to represent the uncertainty associated with each input factor. • Once this has been done, the uncertainty in the calculated variables will be taken care of by the relationships in the base logic model. • In the muffins example, all values from 0 to 99 are regarded as equally probable. BIS 314 Decision Making with Computers

18. Steps in Building and Using a Risk Analysis Model • Set up the spreadsheet model to produce a sample value for each input factor, using the RAND function. • In the muffins example, the formula would be INT(99+1)*RAND • While using the RAND function, the recalculation mode of the spreadsheet should be changed from automatic to manual. • Copy the logic model produced in step 4, to generate many trials of the same model, each giving a different result. • Produce summary models from the complete sets of results. BIS 314 Decision Making with Computers

19. Example: Building a Risk Analysis Model Suppose that a brand manager is concerned about the issue of predicting next year’s sales. The manager’s verbalization of the issue is expressed as: Sales prediction = {predicted market size} * {predicted market share (%)}/100 Assuming a uniform distribution, the probability distribution for: Predicted market share range: 30 percent to 35 percent Predicted market size range: $1650 to $1815 Build the risk analysis model with a summary BIS 314 Decision Making with Computers

20. Example: Building a Risk Analysis Model BIS 314 Decision Making with Computers

21. Simulation What is Simulation? An attempt to duplicate the features, appearance, and characteristics of a real system. By performing simulations and analyzing the results, we can gain an understanding of how a present system operates, and what would happen if we changed it -- or we can estimate how a proposed new system would behave. Often -- but not always -- a simulation deals with uncertainty, in the system itself, or in the world around it. BIS 314 Decision Making with Computers

22. Simulation Idea behind Simulation • To imitate a real-world situation mathematically • To study its properties and operating characteristics • To draw conclusions and make action decisions based on the results of the simulation BIS 314 Decision Making with Computers

23. Simulation & Risk Analysis • Risk: Typically defined as the uncertainty associated with an undesirable outcome (such as financial loss). • Simulation allows us to evaluate the risk of a particular situation. • Simulation covers situations where it is only the dynamic behavior of the local scenario that is really of interest, and it is the uncertainty that gives rise to the issues. • The structure developed for risk analysis, of a base logic model and its extension, no longer applies because of the need to link different time periods. • Without uncertainty, the manger would probably not need to use a spreadsheet model to handle the issue. BIS 314 Decision Making with Computers

24. Simulation Applications Here's just a sample of the applications where simulation is used: • Planning the resources to have available at particular times of the day and week in hotels and restaurants • Deployment of equipment in drilling for oil and natural gas • Setting stock levels to meet fluctuating demand at retail stores • Deciding on reservations and overbooking policies for an airline • Selecting projects with uncertain payoffs in capital budgeting • Deciding how many staff to recruit and when for an agency carrying out contract clerical work • Traffic light timing BIS 314 Decision Making with Computers

25. Use of Simulation Models • Simulation models enable the manager to experiment with the model as a surrogate for the real system, trying different structures, policies and procedures. • They can then use the insights gained to decide what to implement in the real world. • In a simulation, we perform experiments on a model of the real system, rather than the real system itself. In such a model we use variables to represent key numerical measures of the inputs and outputs of the system, and we use formulas to express mathematical relationships between the inputs and outputs. Each experiment is called a trial, and a simulation run includes many -- often thousands of -- such trials. BIS 314 Decision Making with Computers

26. Simulation Model Example Inventory or Stock-Control System • Assume that a manager is dealing with one product. Daily demand is uncertain (hence the need for a simulation model) and running out of stock has been a problem. Cash is short and any excess stock is to be eliminated. The manager wishes to devise a reordering policy. • Thus, the issue reduces to two related questions: deciding how much to order (reorder quantity) and when to order (reorder level) Assumptions for the model • Initially, the manager assumes that the lead time is 0; and • Uncertain daily demand follows a uniform distribution between a low value of 150 and a high of 250. BIS 314 Decision Making with Computers

27. Yesterday’s closing stock Today’s stock available Today’s opening stock Today’s closing stock Today’s quantity delivered Today’s quantity ordered Reorder level Lead Time Reorder quantity Lower demand limit Today’s Demand Upper demand limit Random number Simulation Model Example Inventory or Stock-Control System Conceptualization of stock-control BIS 314 Decision Making with Computers

28. Simulation Model Example Inventory or Stock-Control System S.1: Stock-Control Simulation – first model On 2 of the 10 days, there has been a stock-out and these are treated as back orders, i.e. supplied late BIS 314 Decision Making with Computers

29. Simulation Model Example Inventory or Stock-Control System • Opening Stock: = Yesterday’s closing stock • Quantity Ordered: IF (opening stock <= reorder level, reorder quantity, 0) • Quantity Delivered: = Quantity ordered (assuming lead time is 0) • Stock Available: = Opening stock + Quantity delivered • Demand: = L+(U-L)*RAND() • Closing Stock: = Stock available – Demand BIS 314 Decision Making with Computers

30. Simulation Model Example Inventory or Stock-Control System S.2: Stock-Control Simulation – second model, first trial Keeping the same values of demand from S.1, Reorder level has been increased to 200. This trial has succeeded in preventing stock-outs BIS 314 Decision Making with Computers

31. Simulation Model Example Inventory or Stock-Control System S.3: Stock-Control Simulation – second model, second trial This trial uses different set of demand values to prove that there are no guarantees to having no stock-outs even though reorder level has been increased. BIS 314 Decision Making with Computers

32. Simulation Model Example Inventory or Stock-Control System • A more precise comparison of different policies requires a summary model. Among the possible measures that could be included in this simulation model are: • Number of days when stock-outs occurred • Mean closing stock level • Number of orders placed • Number of back orders BIS 314 Decision Making with Computers

33. Simulation Model Example Inventory or Stock-Control System S.4: Summary measures for trial BIS 314 Decision Making with Computers

34. Simulation Model Example Inventory or Stock-Control System S.5: Stock-Control Simulation – third model This model has a RL = 200, RQ = 300 and Lead Time = 2days. Another assumption is that there are no outstanding orders. BIS 314 Decision Making with Computers

35. Simulation Model Example Inventory or Stock-Control System • In model S.5 since LT of 2 days has been included, quantity delivered would be calculated as: IF (Day-Lead Time <=0, 0, INDEX (Quantity ordered range, Day-Lead Time)) Condition: Day-Lead Time <=0: This tests whether the lead time is greater than the day. True: If it is, value of quantity delivered is set to 0 False: If not, INDEX function is used to look in the appropriate row of the quantity ordered column. BIS 314 Decision Making with Computers

36. Simulation Model Example Inventory or Stock-Control System S.6: Stock-Control Simulation – fourth model This model has a RL = 220, RQ = 500 and Lead Time = 2days. BIS 314 Decision Making with Computers

37. Simulation Model Example Inventory or Stock-Control System • Create a summary model for S.5 and S.6 using the following measures: • Number of days when stock-outs occurred • Mean closing stock level • Number of orders placed • Number of back orders BIS 314 Decision Making with Computers