1. DSS & Warehousing Systems
Chapter 8
Efrem Mallach
Prepared by
Luvai Motiwalla
Irwin/McGraw-Hill
Copyright © 2000 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Models in Decision Support Systems
Introduction
Model types
Model types used in DSS
Discrete – event simulation models
Designing a discrete – event simulation model
Complete simulation studies
Random numbers, Pseudo – Random numbers and statistical distributions
Static simulation models

3. Introduction
All DSS above the simplest data - oriented ones are based on models.
Pages 298 to 299
All DSS above the simplest data - oriented ones are based on models.Their purpose usually is to allow a DSS and hence the decision maker who is using it to predict what would happen in the real world if certain choices were made.
If a model can provide decision makers with the same information that observation of the real world would provide, while at the same time offering advantages over observing the real world, that model will be a useful tool. That is the essence of model usage in DSS

4. Model Types
Basic types of system models include graphical models, physical models, mathematical, and symbolic or information – based models.
The information – based models is more accurate, though it is not used as widely because it is a bit more cumbersome.
Pages 299 to 300
Models incorporate procedures and formulas to manipulate their data elements.

5. Model Types Used in DSS Systems versus process models
Static versus dynamic models
Pages 301 to 304
Systems versus process models: A mathematical model, is a information – based representation of an actual system. In the case of decision support systems we want to use this model to help us make decisions. Two types of models can help us towards this goal. One type of model, called a system model, models the system that we wish to study. The other type, called a process model, models the process that humans follow in making a decision about a system. Mathematical models are an important subset of system models. A mathematical model describes the relationships among elements of the system being modeled in the form equations.
Static versus dynamic models: An important distinction between two types of system models is the distinction between static models and dynamic models. Static models show the values that system attributes take when the system is in balance. A static system is one in which the passage of time does not play a part. In a dynamic system, the passage of time, with cause and effect relationships connecting one time period to the next, is essential to system behavior. In a dynamic model, which can only be of a dynamic system, the flow of time is inherent in the modeling process. Data values change over time. An assembly line model works this way as it tracks products through a manufacturing process.

6. Continuous versus discrete- event models
Deterministic versus stochastic models
Pages 304 to 307
Dynamic system models can be divided into two categories: continuous – system models and discrete – event models. Continuous – system simulation models describe physical or economic processes in which the numbers that describe the system vary continuously. Discrete – event models deal with systems in which individual events occur at identifiable points in time and change the state of the system instantaneously from one value to a different one. Socio economic planners use continuous models, because their work is not in the mainstream of corporate DSS. Since discrete – event models suit most business planning needs, they are the most common type of dynamic system model found in real DSS.
Deterministic versus stochastic models: A model is deterministic if its outputs are fixed for a given set of inputs, stochastic if they reflect an element uncertainty. The stochastic models output varies randomly over a range of possible outcomes. Stochastic models, by contrast, fall into what we called the representational model category of DSS .

7. Discrete – Event Simulation Models
The concept of discrete – event simulation
Pages 309 to 325
We call a model a simulation model when we want to make it clear that we are not discussing some other type of model or some other use of a model. A model is a thing and simulation is a process. Simulation cannot exist without a suitable model,and a model meant for use in simulation may be useless for anything else, but the concepts are different.
The concept of discrete- event simulation; the model represents the state of the system by the values of data elements in the computer. Most discrete – event simulation models are stochastic or probabilistic.

8. Designing a Discrete – Event Simulation Model
The process of designing a discrete – event simulation model.
Simulation languages generally include capabilities that will allow you to develop your model more quickly.
Pages 315 to 320
The process consists of the following steps:
Determine the objective of the model. 2) Define the system itself. 3) Define the state of the system in terms of a set of state variables or uncontrollable variables. 4) Define the events that can affect the state of the system and the impact of each event on each state variable. 5) Choose the time units which the simulation will use. 6) Define, statistically, the rate at which each event occurs. 7) Determine the statistics you would like to obtain from your simulation and what data you need in order to obtain them. 8) Define the initial ( starting) state of the system.
Having established the parameters of your model, you can now program it in a special – purpose language such as GPSS or Simscript, or in a general purpose language such as C.

9. Complete Simulation Studies
A full – scale simulation study runs the simulation several times for each state of controllable variables to give us a distribution of results
Pages 323 to 325
Instead of running the model several times, we might consider one long run covering period of time equal to the sum of the shorter individual runs. In general , one long run is not as good as the same total time divided into several shorter ones. The reason is a phenomenon called autocorrelation. Autocorrelation means that what happens later in a run depends on what happened previously in the same run.

10. Random Numbers, Pseudo - Random Numbers and Statistical Distributions-cont’d
The behavior of a simulation model depends on the numbers that determine when each event occurs.
Pages 325 to 329
There are many ways to generate random numbers. Simulation models that use random numbers are often called monte carlo simulations after the casino in Monaco. It is possible to equip a computer with a physical random number generator. Using truly random numbers has the disadvantage that their sequence is not repeatable.
Fro the above reason , virtually all simulation models use pseudo - random numbers. These are numbers generated by a repeatable formula, which behave statistically as if they were truly random. All simulation packages and most programming languages have built – in function that return uniformly distributed pseudo – random numbers over a more useful range. The built – in random number generators of most systems are not perfect. Computer science journals regularly critique popular ones and suggest improvements.

11. Random Numbers, Pseudo - Random Numbers and Statistical Distributions
When you want a non uniform distribution, you must convert the output of the built – in function to a number from the desired distribution. This is done via cumulative distribution function ( CDF).
Pages 325 to 329
In order to obtain the value for the simulation, pseudo – random numbers are used together with the cumulative distribution functions of the statistical distributions that apply to the system being modeled. In practice, CDF’s are usually approximated by a small number of straight – line segments. Simulation packages include a set of standard CDF’s for common distributions. Simulation models must be exercised for long enough for fluctuations due to specific choices of random variables to die down. Several runs of moderate length are generally better for this purpose than one long run of the same aggregate length.

12. Static Simulation Models-cont’d
Simulation models are dynamic. There are also static situations where we can apply the same idea of using pseudo – random numbers to drive a system model.
Pages 329 to 333

13. Static Simulation Models
Packages are available to help decision makers use static, stochastic, simulation models.
Pages 329 to 333
The advantages are :
It is easy to add statistically defined variability to the deterministic model. A wide variety of statistical distributions is available, many of which would be quite difficult for a decision maker to define directly. The parameters of the distributions, are easy to change. The output facilities exceed what spreadsheet packages offer for this type of problem.
The disadvantage are:
There is a need to use two packages, one to define the model and to run it as a simulation. More complex cases call for custom programming.