Chapter 10 Introduction to Simulation Modeling

1. Chapter 10Introduction to Simulation Modeling BUS ADM – 478: Supply Chain Analytics Mojtaba Heydar SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

2. Introduction • Simulation modelis a computer model that imitates a real-life situation. • It is like other mathematical models, but it explicitly incorporates uncertainty in one or more input variables. • When you run a simulation, you allow these random input variables to take on various values, and you keep track of any resulting output variables of interest. • In this way, you are able to see how the outputs vary as a function of the varying inputs. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

3. Introduction • The fundamental advantage of a simulation model is that it provides an entire distribution of results, not simply a single bottom-line result. • Each different set of values for the uncertain quantities can be considered a scenario. • Simulation allows the company to generate many scenarios, each leading to a particular output. • In the end, it sees a whole distribution of outputs, not a single best guess. The company can see what the outputwill be on average, and it can also see worst-case and best-case results. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

4. Deterministic vs. Simulation • Simulation models are also useful for determining how sensitive a system is to changes in operating conditions. • A huge benefit of computer simulation is that it enables managers to answer these types of what-if questions without actually changing (or building) a physical system. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

5. Spreadsheet Simulation • Spreadsheet simulation modeling is quite similar to the other modeling applications in this book. • You begin with input variables and then relate these with appropriate Excel formulas to produce output variables of interest. • The main difference is that simulation uses random numbers to drive the whole process. These random numbers are generated with special functions that we will discuss in detail. • Each time the spreadsheet recalculates, all of the random numbers change. • This provides the ability to model the logical process once and then use Excel’s recalculation ability to generate many different scenarios. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

6. Probability Distributions • The primary difference between the spreadsheet models you have developed so far and simulation models is that at least one of the input variable cells in a simulation model contains random numbers from a probability distribution. • Important general characteristics of probability distributions: • Discrete versus continuous • Symmetric versus skewed • Bounded versus unbounded • Nonnegative versus unrestricted SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

7. Discrete vs. Continuous • A probability distribution is discrete if it has a finite number of possible values. • A probability distribution is continuous if its possible values are essentially some continuum. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

8. Symmetric vs. Skewed • A probability distribution can either be symmetric or skewed to the left or right. • You typically choose between a symmetric and skewed distribution on the basis of realism. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

9. Bounded vs. Unbounded • A probability distribution is bounded if there are values A and B such that no possible value can be less than A or greater than B. The value A is then the minimum possible value, and the value B is the maximum possible value. • The distribution is unbounded if there are no such bounds. • Actually, it is possible for a distribution to be bounded in one direction but not the other. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

10. Nonnegative vs. Unrestricted • One important special case of bounded distributions is when the only possible values are nonnegative. For example, if you want to model the random cost of manufacturing a new product, you know for sure that this cost must be nonnegative. • There are many other such examples. In such cases, you should model the randomness with a probability distribution that is bounded below by 0. This rules out negative values that make no practical sense. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

11. Simulation and flaw of averages • In August, Walton Bookstore must decide how many of next year’s nature calendars to order. Each calendar costs the bookstore $7.50 and sells for $10. After January 1, all unsold calendars will be returned to the publisher for a refund of $2.50 per calendar. Walton believes that the number of calendars it can sell by January 1 follows the probability distribution with mean 200. Walton believes that ordering to the average demand, that is, ordering 200 calendars, is a good decision. Is it? SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

12. Simulation and flaw of averages SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

13. Simulation with built-in Excel tools • We show how spreadsheet simulation models can be developed and analyzed with Excel’s built-in tools without using add-ins. • We continue analyzing the calendar problem from Example 10.1. This general problem occurs when a company (such as a news vendor) must make a one-time purchase of a product (such as a newspaper) to meet customer demands for a certain period of time. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

14. Simulation with built-in Excel tools • Recall that Walton Bookstore must decide how many of next year’s nature calendar to order. Each calendar costs the bookstore $7.50 and sells for $10. After January 1, all unsold calendar will be returned to the publisher for a refund of $2.50 per calendar. In this case, the demand for calendar is given by the following probability distribution. Walton wants to develop a simulation model to help it to decide how many calendars to order. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

15. @Risk models with a single random input variable • The development of a simulation model is basically a two-step procedure. • The first step is to build the model itself. This step requires you to enter all of the logic that transforms inputs (including @RISK functions such as RISKDISCRETE) into outputs (such as profit). • However, once this logic has been incorporated, @RISK takes over in the second step. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM

16. @Risk models with a single random input variable • Recall that Walton Bookstore buys calendars for $7.50, sells them at the regular price of $10, and gets a refund of $2.50 for all calendars that cannot be sold. We now assume that Walton estimates a triangular probability distribution for demand, where the minimum, most likely, and maximum values of demand are 100, 175, and 300, respectively. The company wants to use this probability distribution to simulate the profit for any particular order quantity. It eventually wants to find the best order quantity. SUPPLY CHAIN ANALYTICS - FALL 2014 - UWM