Summary of the tutorials about simulation (as part of the course ORL-30306; Decision Science 2). Includes the lecture slides and the required additional materials (the articles of Robinson (2008), the article of Tako and Robinson (2012), and Chapter 13 and Appendix B in the book 'Decision Science',...
Tutorial 1: Introduction to discrete-event simulation (DES)
- Lecture slides tutorial 1
- Robinson (2008) “Conceptual modelling for simulation part I: definition and requirements”
- Kettenis and Van der Vorst, Ch13 in Claassen et al. (341.-355)
- Kettenis and Hendrix, Appendix B in Claassen et al. (443-461)
SIMULATION
Simulation is to mimic a real system using a model for answering specific questions about
the system’s behaviour under specific circumstances.
So a definition of computer simulation is that it is the process of designing a model of a
system and conducting experiments with the model for the purpose either of understanding
the behaviour of the system or of evaluating various strategies for the operation of the system.
In this sense, a system is a collection of components that act and interact together toward the
accomplishment of some purpose. A model can be defined by an external and explicit
representation of part of reality (a system) as seen by the people who wish to use that model
to understand, to change, to manage, and to control that part of reality in some way or another.
So a specific system can be represented by different models, depending on the assumptions
made and components of the system that the researcher believes should be included in the
model.
Stochastic simulation is to model uncertainty causing variability. When there is not enough or
no data available you use sample fictious data (randomly choose values; using a probability
distribution function). You can use simulation software, for example a spreadsheet simulation
in Excel, your own developed software, or existing software like Enterprise Dynamics (ED).
+ Experimenting with the real-world system may be too costly or too time-consuming
(interruption of business), too dangerous or irreversible (e.g. surgery and pilot
training) or even impossible (when the system does not exist yet or there are
uncontrollable circumstances).
+ Simulation is faster than in real time, the real-world will not be disturbed by collecting
data and it is easier to change the way of operation in a simulation model than in
reality. You also have better control over the experimental conditions.
- A model is an abstraction of reality and modelling takes much time and money (you
have to identify all relevant processes, collect data and develop a simulation model).
» Discrete Event Simulation (DES) is event driven (computer) simulation: state of a system
changes by events (e.g. arrivals/departures) in discrete time. The timing of the event is
relevant, but the time between events is skipped. DES is event driven: the time jumps are
driven by the timing of events. For discrete event simulation models (DESM) it is
assumed that state changes are connected to a certain moment in time and result from the
initiation or completion of activities. The set of all states that a system may have is called
a state space. An event signifies the transition from one stat to another at a specific point
in time. Entities are the dynamic objects in simulations; they move around, change status,
affect and are affected by other entities and the stat of the system, and they affect the
output performance measures. You can make use of parameter variables, these will
normally be constant, but may vary in different experiments.
» Fixed discrete time models have fixed time jumps: events over a fixed period are
aggregated. So the precise timing of events is irrelevant.
» Continuous simulation: the states changes continuously in time. It is a model by
differential equations (e.g. growth of bacteria), the variables in the model are (at least
conceptually) continuous.
» Monte Carlo Simulation is static simulation, so the time plays no role. For example
gambling in a casino, algorithms for root finding or integration.
,So there are different ways of categorising simulation models:
Continuous simulation models Discrete-event simulation models
Mathematical equations (like algebraic and Description of events in the system (an event
differential equations). signifies the transition from one state or
Variables in the model are continuous, so the another at a specific point in time).
state changes happen continuously in time.
Deterministic models Stochastic models
No probabilistic components; the output is Random effects are present
determined once the set of input quantities
and relationships have been specified;
In general continuous models In general discrete-event models
Dynamic simulation Static simulation
Models represent systems as they change Time plays no role
over time. Monte-Carlo simulation
SIMULATION PROJECT MANAGEMENT
Steps in a simulation study (according to Claassen et al, chapter 13):
A simulation study is not a simple sequential process. In the problem analysis phase, it should
be clear which questions to be answered by the study. The objectives should be validated
(possible to answer the questions by the simulation study) and the problem formulation
should contain all details (for example costs, dates, people involves, etc.).
The conceptual model consists of a textual description of the components involved in the
model and their interactions, and the input data needed.
Conceptual model
Conceptual modelling is the process of abstracting a model from a real or proposed system.
All simulation models are simplifications of reality. The issue in conceptual modelling is to
abstract an appropriate simplification of reality. A well-designed model significantly enhances
the possibility that a simulation study will be a success. When forming a conceptual model,
once should identify all facilities, equipment, events, operating rules, and description of
behaviour, stat variables, decision variables, measures of performance, and so on, that will be
part of the model. And also the relationships between the elements identified.
The design of the model impacts all aspects of the study, in particular the data requirements,
the speed with which the model can be developed, the validity of the model, the speed of
experimentation and the confidence that is placed in the model results.
> Conceptual modelling is about moving from a problem situation, through model
requirements to a definition of what is going to be modelled and how.
, > Conceptual modelling is iterative and repetitive, with the model being continually
revised throughout a modelling study.
> The conceptual model is a simplified representation of the real system.
> The conceptual model is independent of the model code or software (while model
design includes both the conceptual model and the design of the code).
> The perspective of the client and the modeller are both important in conceptual
modelling.
Missing from this diagram are the verification and validation activities involved in a
simulation study. These are carried out in parallel with each of the four processes.
- Objectives
ɔ Modelling objectives; the purpose of the model and modelling project.
ɔ (General) Project objectives; include the time-scale for the project and the
nature of the model and its use.
- Functionality
ɔ Experimental factors (= adjustable inputs = a control); those elements in the
model that can be altered to effect an improvement in, or better understanding
of, the problem situation. They are determined by the objectives.
ɔ Responses (= outputs = performance measures; PFM); report the results from a
run of the simulation model.
- Model content; components that are represented in the model and their
interconnections. Two dimensions:
ɔ The scope of the model; the model boundary or the breadth of the real system
that is to be included in the model.
ɔ The level of detail; the detail to be included for each component in the model’s
scope.
The model content is determined by the inputs and outputs and the level of accuracy
required. More accuracy generally requires a greater scope and level of detail.
While making decision about the content of the model, various assumptions (when
there are uncertainties or beliefs about the real world being modelled) and
simplifications (to enable more rapid model development and use, and to improve
transparency) are normally introduced.
For the model content, it can be useful to make a flow chart, because flow charts show
the scope and level of detail. A flow chart is a diagram representing the product (and
, information) flow through the system and is used to analyze, design and document a
(sub)system. Process operations are represented in boxes, and arrows indicate the
product routing, and thus the sequencing of operations/processes.
- Data requirements
For the data requirement, it can be useful to make an influence diagram, because it
analyses the data requirements and level of detail. When making an influence the
relationship between performance measures and exogenous variables becomes clear.
So you can easily see what data you need. Exogenous variables are those of which a
value is set outside of model/to be sampled.
A conceptual model is now defined as ‘a non-software specific description of the computer
simulation model (that will be, is or has been developed), describing the objectives, inputs,
outputs, content, assumptions and simplifications of the model’.
Simply stated, conceptual modelling is the process of creating the conceptual model, and this
requires the following activities:
˪ Understanding the problem situation (a precursor to conceptual modelling)
˪ Determining the modelling and general project objectives
˪ Identifying the model outputs (responses)
˪ Identify the model inputs (experimental factors)
˪ Determining the model content (scope and level of detail), identifying any
assumptions and simplifications
Careful model design is important; there are a number of reasons why a conceptual model is
important to the development and use of simulation models: the conceptual model provides a
roadmap from the problem situation and objectives to model design and software
implementation and it forms an important part of the documentation for a model. Therefore, a
well-documented conceptual model minimises the likelihood of incomplete, unclear,
inconsistent and wrong requirements, helps build the credibility of the model, guides the
development of the model, forms the basis for verification and builds validation, and guides
experimentation by expressing the objectives, experimental factors and responses.
There are four main requirement of a conceptual model:
◊ Validity: ‘A perception, on behalf of the modeller, that the conceptual model can be
developed into a computer model that is sufficiently accurate for the purpose at hand.’
The notion of validity is the question of whether the model is ‘right’.
◊ Credibility: similar to validity, but taken from the perspective of the clients rather than
the modeller. Need for clients to be convinced. And requires that the model and its
results are understood by the clients.
◊ Utility: ‘A perception, on behalf of the modeller and the clients, that the conceptual
model can be developed into a computer model that is useful as an aid to decision-
making within the specified context.’ Includes issues like ease-of-use, flexibility, run-
speed and visual display. A less accurate (but still sufficiently accurate), more flexible
model that runs faster may have greater utility by enabling a wider range of
experimentation within a time-frame.
◊ Feasibility: ‘A perception, on behalf of the modeller and the clients, that the
conceptual model can be developed into a computer model with the time, resource and
data available.’
A simulation model should be kept as simple as possible, because simple models are easier to
understand and it is easier to explain results, they are faster to develop and run, they are more
flexible and require less data. ‘Keep a model as simple as possible to meet the objectives’ and
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