Download - Simulation UNIT-I
SIMULATION
08/09/2016 1Dr. DEGA NAGARAJU, SMEC
08/09/2016 Dr. DEGA NAGARAJU, SMEC 2
08/09/2016 Dr. DEGA NAGARAJU, SMEC 3
War gaming: test strategies; training
Flight SimulatorTransportation systems: Improved operations; urban planning
Computer communicationnetwork: protocol design
Parallel computer systems: developing scalable software
Games
A few more applications …
12/22/2016 3Dr. DEGA NAGARAJU, SMBS
Areas of
Applications
Ma
nu
fact
uri
ng
A
pp
lica
tio
ns
Business Process
Simulation
08/09/2016 4Dr. DEGA NAGARAJU, SMEC
Applications:
COMPUTER SYSTEMS: hardware components, software
systems, networks, data base management, information
processing, etc..
MANUFACTURING: material handling systems, assembly
lines, automated production facilities, inventory control
systems, plant layout, etc..
BUSINESS: stock and commodity analysis, pricing policies,
marketing strategies, cash flow analysis, forecasting, etc..
GOVERNMENT: military weapons and their use, military
tactics, population forecasting, land use, health care
delivery, fire protection, criminal justice, traffic control, etc..
And the list goes on and on...08/09/2016 5Dr. DEGA NAGARAJU, SMEC
Examples of Applications at Disney World
Cruise Line Operation: Simulate the arrival and
check-in process at the dock.
Private Island Arrival: How to transport passengers
to the beach area? Drop-off point far from the
beach. Used simulation to determine whether
to invest in trams, how many trams to purchase,
average transport and waiting times, etc..
08/09/2016 6Dr. DEGA NAGARAJU, SMEC
Why do we go for
simulation?
Is it possible to represent all real
life problems mathematically?
Method of last resort
Logical extension to
the analytical &
mathematical techniques
John Von Neumann & Stanislaw Ulam
Nuclear Shielding problem
1950-Digital Computers
Managerial decision makingAircraft-wind tunnel-aerodynamic characteristicsScale models of machines-plant layoutPilot training-flight simulatorCar Manufacturing SimulationTV games(chess playing game, snake and ladders)08/09/2016 7Dr. DEGA NAGARAJU, SMEC
Why do we go for simulati-
on?
Draw backs of scientific methods?
Draw backs of Analytical methods?
Draw backs of iterative
methods?
Certain processes : too costly or impossible
Difficult-mathematical equations
No straight forward analytical solution
Ex: Queuing problems, Job shop problems,
Multi-integral problems etc.
Difficulty in performing validating
experiments for mathematical models
Dynamic programming, queuing theory,
network models
Dynamic programming-optimal strategies-
uncertainties-analyze multi-planning
problems
DP-simple cases-less number of static
variables
LPP-data does not change over the entire
planning horizon
One time decision process-average values for
decision variables
Many real life situations-uncertainties
08/09/2016 8Dr. DEGA NAGARAJU, SMEC
Webster’s Dictionary:
“ to assume the mere appearance of ,
without the reality”
08/09/2016 9Dr. DEGA NAGARAJU, SMEC
Definition:
Simulation is the process of designing a
model of a real system and conducting
experiments with this model for the purpose
of either understanding the behavior of the
system and/or evaluating various strategies
for the operation of the system.
08/09/2016 10Dr. DEGA NAGARAJU, SMEC
Allows us to:
Model complex systems in a detailed way
Describe the behavior of systems
Construct theories or hypotheses that account for the observed behavior
Use the model to predict future behavior, that is, the effects that will be produced by changes in the system
Analyze proposed systems
08/09/2016 11Dr. DEGA NAGARAJU, SMEC
Brief HistoryNot a very old technique...
World War II
“Monte Carlo” simulation: originated with
the work on the atomic bomb. Used to
simulate bombing raids. Given the
security code name “Monte-Carlo”.
Still widely used today for certain problems
which are not analytically solvable (for
example: complex multiple integrals…)08/09/2016 12Dr. DEGA NAGARAJU, SMEC
Brief History (cont…..)
Late ‘50s, early ‘60s Computers improve
First languages introduced: SIMSCRIPT,
GPSS (General purpose simulation system) (IBM)
Simulation viewed at the tool of “last resort”
Late ‘60s, early ‘70s Primary computers were mainframes: accessibility
and interaction was limited
GASP IV introduced by Pritsker. Triggered a wave
of diverse applications. Significant in the evolution
of simulation.
08/09/2016 13Dr. DEGA NAGARAJU, SMEC
Brief History (cont…….)
Late ‘70s, early ‘80s SLAM introduced in 1979 by Pritsker and Pegden.
Models more credible because of sophisticated tools.
SIMAN introduced in 1982 by Pegden. First language
to run on both a mainframe as well as a
microcomputer.
Late ‘80s through present Powerful PCs
Languages are very sophisticated (market almost
saturated)
Major advancement: graphics. Models can now be animated.
08/09/2016 14Dr. DEGA NAGARAJU, SMEC
What can be simulated?
Almost anything can
and
almost everything has...
08/09/2016 15Dr. DEGA NAGARAJU, SMEC
Introduction to Simulation
Simulation a) the imitation of the operation of a real-world process or system over time.
b) to develop a set of assumptions of mathematical, logical, and symbolic relationship between the entities of interest, of the system.
c) to estimate the measures of performance of the system with the simulation-generated data.
Simulation modeling can be useda) as an analysis tool for predicting the effect of changes to existing systems.
b) as a design tool to predict the performance of new systems .
Real-world process concerning the behavior of a system
A set of assumptionsModeling &
Analysis
08/09/2016 16Dr. DEGA NAGARAJU, SMEC
Simula-
tion
Imitation of the operation of a real
world process
Whether done by hand or on a ComputerIt involves
1. The generation of an artificial history
of a system & 2. The observation of
that artificial history
Simulation model
Behavior of a system
Set of Assumptions:Mathematical, Logical,Symbolic relationships b/w entities, Objects of interest
Used as:an analysis tool,
a design tool08/09/2016 17Dr. DEGA NAGARAJU, SMEC
Simulation Models
Solved by:Differential Calculus,Probability Theory,Algebraic Methods
Solution Consists:One or more numerical parameters(Measures of
Performance)
Complex real world systems:
Numerical computer based simulation
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08/09/2016 19Dr. DEGA NAGARAJU, SMEC
Problem formulation -1
Policy maker/Analyst understand and agree with the formulation.
Setting of objectives and overall project plan -2
Model conceptualization -3
The art of modeling is enhanced by an ability to abstract the
essential features of a problem, to select and modify basic
assumptions that characterize the system, and then to enrich and
elaborate the model until a useful approximation results.
Data collection -4
As the complexity of the model changes, the required data
elements may also change.
Model translation -5
GPSS/HTM or special-purpose simulation software
Steps in a Simulation Study
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Verified? -6
Is the computer program performing properly?
Debugging for correct input parameters and logical structure
Validated? -7
The determination that a model is an accurate representation of
the real system.
Validation is achieved through the calibration of the model
Experimental design -8
The decision on the length of the initialization period, the length
of simulation runs, and the number of replications to be made of
each run.
Production runs and analysis -9
To estimate measures of performances
Steps in a Simulation Study (Contd….)
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More runs? -10
Documentation and reporting -11
Program documentation : for the relationships between input
parameters and output measures of performance, and for a
modification
Progress documentation : the history of a simulation, a
chronology of work done and decision made.
Implementation -12
Steps in a Simulation Study (Contd….)
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Four phases according to Figure 1.3
First phase : a period of discovery or orientation
(step 1, step2)
Second phase : a model building and data collection
(step 3, step 4, step 5, step 6, step 7)
Third phase : running the model
(step 8, step 9, step 10)
Fourth phase : an implementation
(step 11, step 12)
Steps in a Simulation Study (Contd….)
08/09/2016 23Dr. DEGA NAGARAJU, SMEC
The basic nature of Simulation
Two problems
Continuous
Discrete
State changes continuously with timeDeterministic in nature
Arrival & Sale of Merchandise occur in discrete stepsStochastic in nature
Common features essential to simulation
Common features:Mathematical model of the system under studyChange of the state in accordance with some equations (rules or laws) for a
long periodCollection of information about the system (solution to the problem)Programming the calculations for a digital computerSimulate or mimic the real system with the help of computerContinue the process until the desired analytic solution is obtained
08/09/2016 24Dr. DEGA NAGARAJU, SMEC
Simulation as an analytic tool is useful only when done on a computer
The basic nature of Simulation (Cont….)
08/09/2016 25Dr. DEGA NAGARAJU, SMEC
Simulation of Inventory control manually Pencil and paper
System which can be simulated on a digital computer
Can also be simulated manually
Each application of Simulation is adhoc to a great extent
Simulation is an art
The basic nature of Simulation (Cont….)
08/09/2016 26Dr. DEGA NAGARAJU, SMEC
No unifying theory of computer simulation
No unified theory No fundamental theorems
No underlying principles
Experimental technique
To simulate is to experiment Fast and inexpensive method
Ex: Inventory control problem
When Simulation is the Appropriate Tool (1)
Simulation enables the study of, and experimentation with, the internal interactions
of a complex system, or of a subsystem within a complex system.
Informational, organizational, and environmental changes can be simulated, and the
effect of these alterations on the model’s behavior can be observed.
The knowledge gained in designing a simulation model may be of great value
toward suggesting improvement in the system under investigation.
By changing simulation inputs and observing the resulting outputs, valuable insight
may be obtained into which variables are most important and how variables interact.
Simulation can be used as a pedagogical device to reinforce analytic solution
methodologies.
08/09/2016 27Dr. DEGA NAGARAJU, SMEC
Simulation can be used to experiment with new designs or policies prior to implementation, so as to prepare for what may happen.
Simulation can be used to verify analytic solutions.
By simulating different capabilities for a machine, requirements can be determined.
Simulation models designed for training allow learning without the cost and disruption of on-the-job learning.
Animation shows a system in simulated operation so that the plan can be visualized.
The modern system (factory, wafer fabrication plant, service organization, etc.) is so complex that the interactions can be treated only through simulation.
When Simulation is the Appropriate Tool (2)
08/09/2016 28Dr. DEGA NAGARAJU, SMEC
When Simulation is the appropriate tool?
Study of the internal interactions of a complex System
Effect of Informational,
organizational and environmental
changes on model behavior
Used as a pedagogical device to reinforce analytic
solution methodologies
Experimentation with new design
To verify analytic solutions
Simulation models:For training without
the cost and disruption of on the
job learning
To study the interactions of a complex modern systems: factory, fabrication plant,
service organization
08/09/2016 29Dr. DEGA NAGARAJU, SMEC
When Simulation is not Appropriate
When the problem can be solved using common sense.
When the problem can be solved analytically.
When it is easier to perform direct experiments.
When the simulation costs exceed the savings.
When the resources or time are not available.
When system behavior is too complex or can’t be defined.
When there isn’t the ability to verify and validate the model.
08/09/2016 30Dr. DEGA NAGARAJU, SMEC
When
Simulation is
not
Appropriate?
Wh
en th
e pro
blem
can
be so
lved u
sing
co
mm
on
sen
se
Wh
en t
he
reso
urc
es
or
ti
me
are
no
t av
aila
ble
When there is n’t the ability to verify and validate the model
When the simulation costs exceed the savings
08/09/2016 31Dr. DEGA NAGARAJU, SMEC
Advantages and Disadvantages of Simulation (1)
Advantages New polices, operating procedures, decision rules, information flows, organizational
procedures, and so on can be explored without disrupting ongoing operations of the real system.
New hardware designs, physical layouts, transportation systems, and so on, can be tested without committing resources for their acquisition.
Hypotheses about how or why certain phenomena occur can be tested for feasibility.
Insight can be obtained about the interaction of variables.
Insight can be obtained about the importance of variables to the performance of the system.
Bottleneck analysis can be performed indicating where work-in-process, information, materials, and so on are being excessively delayed.
A simulation study can help in understanding how the system operates rather than how individuals think the system operates.
“What-if” questions can be answered. This is particularly useful in the design of new system.
08/09/2016 32Dr. DEGA NAGARAJU, SMEC
Advantages and Disadvantages of Simulation (2)
Disadvantages
Model building requires special training. It is an art that is learned over time and through experience. Furthermore, if two models are constructed by two competent individuals, they may have similarities, but it is highly unlikely that they will be the same.
Simulation results may be difficult to interpret. Since most simulation outputs are essentially random variables (they are usually based on random inputs), it may be hard to determine whether an observation is a result of system interrelationships or randomness.
Simulation modeling and analysis can be time consuming and expensive. Skimping on resources for modeling and analysis may result in a simulation model or analysis that is not sufficient for the task.
Simulation is used in some cases when an analytical solution is possible, or even preferable, as discussed in Section 1.2. This might be particularly true in the simulation of some waiting lines where closed-form queueing models are available.
08/09/2016 33Dr. DEGA NAGARAJU, SMEC
1
• New polices, operating procedures, decision rules, information flows, organizational procedures, and so on can be explored without disrupting ongoing operations of the real system
2
• New hardware designs, physical layouts, transportation systems, and so on, can be tested without committing resources for their acquisition.
3• Hypotheses about how or why certain phenomena occur can be tested for feasibility.
4• Insight can be obtained about the interaction of variables.
5• Insight can be obtained about the importance of variables to the performance of the system.
6
• Bottleneck analysis can be performed indicating where work-in-process, information, materials, and so on are being excessively delayed
7
• A simulation study can help in understanding how the system operates rather than how individuals think the system operates.
8• “What-if” questions can be answered. This is particularly useful in the design of new system.
Advantages of Simulation
08/09/2016 34Dr. DEGA NAGARAJU, SMEC
1
• Model building requires special training. It is an art that is learned over time and through experience. Furthermore, if two models are constructed by two competent individuals, they may have similarities, but it is highly unlikely that they will be the same.
2
• Simulation results may be difficult to interpret. Since most simulation outputs are essentially random variables (they are usually based on random inputs), it may be hard to determine whether an observation is a result of system interrelationships or randomness.
3
• Simulation modeling and analysis can be time consuming and expensive. Skimping on resources for modeling and analysis may result in a simulation model or analysis that is not sufficient for the task.
4
• Simulation is used in some cases when an analytical solution is possible, or even preferable. This might be particularly true in the simulation of some waiting lines where closed-form queueingmodels are available.
Disadvantages of Simulation
08/09/2016 35Dr. DEGA NAGARAJU, SMEC
Areas of
Applications
Ma
nu
fact
uri
ng
A
pp
lica
tio
ns
Business Process
Simulation
08/09/2016 36Dr. DEGA NAGARAJU, SMEC
Why do we
study the
System?
To understand the relationships b/w its
components or to predict how the system will
operate under a new policy
Is it possible to
conduct experiment
with the system?
Yes, but not always
New system may not yet exist. It may
be in hypothetical form or at the
design stage.
Example: Developing & testing of
prototype models can be very
expensive and time consuming
Even System exists: No
experimentation.
Example:
Is it possible to double the
unemployment rate to determine the
effect of employment on inflation?
Is it possible to reduce the number of
tellers at the bank to study the effect
on the length of waiting lines?
Is it feasible to change the supply and
demand of goods arbitrarily to study
the economic systems?
How do we
define the
system
model?
Body of information gathered about
the system to study the system.
No unique model of the system
For same system-different models-by
different analysts
Establish the model
Structure: System boundary,
entities, attributes and
activities of the system.
Provide the data: Values of
the attributes, relationships
among the activities.
MODEL OF A SYSTEM
How the model
is derived for
the system?
08/09/2016 37Dr. DEGA NAGARAJU, SMEC
Example for the Model of a SystemENTITY ATTRIBUTE ACTIVITY
SHOPPER NO OF ITEMSARRIVE
GET
BASKET AVAILABILITYSHOP
QUEUECHECK-OUT
COUNTER NUMBER OF OCCUPANCY
RETURNLEAVE
Elements of a Super Market
08/09/2016 38Dr. DEGA NAGARAJU, SMEC
Types of models
Physical
Static Dynamic
Mathematical
Static
Numerical Analytical
Dynamic
Analytical Numerical
System Simulation
TYPES OF MODELS08/09/2016 39Dr. DEGA NAGARAJU, SMEC
Physical Models: Based on some analogy b/w such systems as mechanical & electrical, electrical & hydraulicSystem attributes represented by such measurements as a voltage or the position of a shaftSystem activities are reflected in the physical laws that drive the model:Example: amount of voltage applied – speed of the shaft of the motorVoltage applied – Velocity of the vehicleNumber of revolutions of the shaft – distance traveled by the vehicle
Mathematical
Models:
Used symbolic notations, mathematical equations
etc.
System attributes are represented by variables
System activities are represented by mathematical
functions
08/09/2016 40Dr. DEGA NAGARAJU, SMEC
Dynamic Models:
Static Models: Also called as Monte Carlo SimulationRepresents the system at a particular point in time
Represents systems as they change over timeExample: Simulation of a bank from 9.00 am to 4.00 pm
Numerical Models:
Analytical Models: Only certain forms of equations are solvedExample: Linear differential equations are solved
Computational procedure is used to solve the models
08/09/2016 41Dr. DEGA NAGARAJU, SMEC
Monte Carlo Simulation
Statistical distribution functions are created by using a
series of random numbers.
Data can be developed for many months or years in a
matter of few minutes on a digital computer.
Used to solve the problems which can’t be adequately
represented by mathematical models or where
the solution of the model is not possible by
analytical method.
The solution obtained is very close to the optimal but
not exact.
08/09/2016 42Dr. DEGA NAGARAJU, SMEC
Steps in Monte
Carlo Simulation
Objectives,
factors affecting
the objectives
Variables, parameters, decision rules,
conditions to carry experimentation, type of
distribution used, the manner in which time
is changed, relationship b/w variables and
parameters
Starting conditions
for the simulation,
number of
simulation runs
Define a coding system that will
correlate the factors defined in step
1 with random numbers to be
generated;
Select the random number generator and create
the random numbers to be used;
Associate the generated random numbers with
the factors identified in step 1 and coded in step
4(i)
Select the best
course of action
08/09/2016 43Dr. DEGA NAGARAJU, SMEC
Systems and System Environment
System
defined as a group of objects that are joined together in some regular interaction or interdependence toward the accomplishment of some purpose.
System Environment
changes occurring outside the system.
The decision on the boundary between the system and its environment may depend on the purpose of the study.
08/09/2016 44Dr. DEGA NAGARAJU, SMEC
Components of a System Entity : an object of interest in the system.
Attribute : a property of an entity.
Activity : a time period of specified length.
State : the collection of variables necessary to describe the
system at any time, relative to the objectives of the
study.
Event : an instantaneous occurrence that may change the
state of the system.
Endogenous : to describe activities and events occurring
within a system.
Exogenous : to describe activities and events in an
environment that affect the system.
08/09/2016 45Dr. DEGA NAGARAJU, SMEC
Components of a System
08/09/2016 46Dr. DEGA NAGARAJU, SMEC
Discrete and Continuous Systems
Systems can be categorized as discrete or continuous.
Bank : a discrete system
The head of water behind a dam : a continuous system
08/09/2016 47Dr. DEGA NAGARAJU, SMEC
DISCRETE SYSTEMS
State variables change only at a discrete set of points in
time
Example: Bank
State variable: Number of customers in the
bank
Note: The state variable changes only when a new
customer arrives or when the service provided to the
customer is completed08/09/2016 48Dr. DEGA NAGARAJU, SMEC
CONTINUOUS SYSTEMS
State variables change continuously over time
Example: Head of water behind a dam
State variable: Head of water behind a dam
Note: During and for some time after a rain storm,
water flows into the lake behind the dam. Water is
drawn from the dam for flood control and to make
electricity. Evaporation also decreases the water level.
08/09/2016 49Dr. DEGA NAGARAJU, SMEC
A grocery store has one checkout counter. Customers arrive at this checkout counter at
random from 1 to 8 minutes apart and each interval time has the same probability of
occurrence. The service times vary from 1 to 6 minutes, with probability given below:
Simulate the arrival of 6 customers and calculate (i) Average waiting time for a customer,
(ii) Probability that a customer has to wait, (iii) Probability of a server being idle (iv)
Average service time, (v) Average time between arrival. Use the following sequence of
random numbers:
Assume the first customer arrives at time θ. Depict the simulation in a tabular form.
Service (minutes) 1 2 3 4 5 6
Probability 0.10 0.20 0.30 0.25 0.10 0.05
Random digit for
arrival
913 727 015 948 309 922
Random digit for
service time
84 10 74 53 17 79
08/09/2016 50Dr. DEGA NAGARAJU, SMEC
Time between
arrivals
Probability Cumulative
Probability
Random digit
assignment
1 0.125 0.125 001-125
2 0.125 0.250 126-250
3 0.125 0.375 251-375
4 0.125 0.500 376-500
5 0.125 0.625 501-625
6 0.125 0.750 626-750
7 0.125 0.875 751-875
8 0.125 1.000 876-000
ARRIVAL TIME DISTRIBUTION
Arrival time varies from 1 to 8 minutes with equal probability, meaning that
the probability of each arrival = 1/8 = 0.125
08/09/2016 51Dr. DEGA NAGARAJU, SMEC
Service Time ProbabilityCumulative
Probability
Random digit
assignment
1 0.10 0.10 01-10
2 0.20 0.30 11-30
3 0.30 0.60 31-60
4 0.25 0.85 61-85
5 0.10 0.95 86-95
6 0.05 1.00 96-00
SERVICE TIME DISTRIBUTION
08/09/2016 52Dr. DEGA NAGARAJU, SMEC
Custom
er
Random
No. for
Arrival
Time
since
last
arrival
Arrival
time
Random
No. for
Service
Service
time
Time
service
begins
Time
custome
-r waits
in queue
Time
service
ends
Time
custome
r spends
in
system
Idle
time of
server
1 - - 0 84 4 0 0 4 4 0
2 913 8 8 10 1 8 0 9 1 4
3 727 6 14 74 4 14 0 18 4 5
4 015 1 15 53 3 18 3 21 6 0
5 948 8 23 17 2 23 0 25 2 2
6 309 3 26 79 4 26 0 30 4 1
18 3 21 12
SIMULATION TABLE
08/09/2016 53Dr. DEGA NAGARAJU, SMEC
Total time customer waits in queue 3Average waiting0.5
time for customer Total no. of customers 6
No. of customers who wait 1Pr obability that a0.166
customer has to wait Total no. of customers 6
Total idle time of server 12Pr obability of server0.4
being idle Total run time of system 30
Total service time 18Average service3
time Total no. of customer 6
Sum of all times between arrivals(min utes) 26Average time betweenarrivals No. of arrivals 1 6 1
08/09/2016 54Dr. DEGA NAGARAJU, SMEC
Total timecustomers wait in queue(min utes)Average waiting time of thosewho wait(min utes) Totalnumber of customers who wait
33min utes
1
Total timecustomer spends
in the system(min utes)Average time customer spendsin the system Total number of customers
213.5min utes
6
08/09/2016 55Dr. DEGA NAGARAJU, SMEC
Demand
(daily)0 1 2 3 4
Probability 0.05 0.10 0.30 0.45 0.10
A book store wishes to carry ‘Ramayana’ in stock. Demand is probabilistic and
replenishment of stock takes 2 days (i.e., if an order is placed on March 1, it will be
delivered at the end of the day on March 3). The probabilities of demand are given
below:
Each time an order is placed, the store incurs an ordering cost of Rs. 10 per order.
The store also incurs a carrying cost of Rs. 0.50 per book per day. The inventory
carrying cost is calculated on the basis of stock at the time of each day. The manager
of the book store wishes to compare two options for his inventory decision.
A: Order 5 books when the inventory at the beginning of the day plus order
outstanding is less than 8 books.
B: Order 8 books when the inventory at the beginning of the day plus order
outstanding is less than 8.
Currently (beginning of the first day) the store has stock of 8 books plus 6 books
ordered 2 days ago and expected to arrive next day. Using Monte-Carlo Simulation
for 10 cycles, recommend which option the manager should choose. The two digit
random numbers are given below. 89, 34, 78, 63, 61, 81, 39, 16, 13, 73.
08/09/2016 56Dr. DEGA NAGARAJU, SMEC
Demand Prob. Cum. Prob.Random
Nos.
0 0.05 0.05 01-05
1 0.10 0.15 06-15
2 0.30 0.45 16-45
3 0.45 0.90 46-90
4 0.10 1.00 91-00
Stock in hand = 8, and
stock on order = 6 (expected next day).
08/09/2016 57Dr. DEGA NAGARAJU, SMEC
Demand Distribution
Random
No.
Demand
sales
Opt. stock
in handReceipt
Cl. stock
in hand
Opt. stock
on order
Order
Qty.
Cl. Stock
on order
89 3 8 - 5 6 - 6
34 2 5 6 9 - - -
78 3 9 - 6 - 5 5
63 3 6 - 3 5 - 5
61 3 3 - 0 5 5 10
81 3 0 5 2 5 5 10
39 2 2 - 0 10 - 10
16 2 0 5 3 5 - 5
13 1 3 5 7 0 5 5
73 3 7 - 4 5 - 5
No. of orders =4 Ordering cost = 4 x 10 = Rs. 40.
Closing stock of 10 days = 39, Carrying cost = 39 x 0.50 = 19.50
Cost for 10 days = 59.50
OPTION A
08/09/2016 58Dr. DEGA NAGARAJU, SMEC
OPTION B
Random
No.
Demand
sales
Opt. stock
in handReceipt
Cl. stock
in hand
Opt. stock
on order
Order
Qty.
Cl. Stock
on order
89 3 8 - 5 6 - 6
34 2 5 6 9 - - -
78 3 9 - 6 - 8 8
63 3 6 - 3 8 - 8
61 3 3 - 0 8 - 8
81 3 0 8 5 - 8 8
39 2 5 - 3 8 - 8
16 2 3 - 1 8 - 8
13 1 1 8 8 - - -
73 3 8 - 5 - 8 8
No. of orders =3 Ordering cost = 3 x 10 = Rs. 30.
Closing stock of 10 days = 45, Carrying cost = 45 x 0.50 = 22.50
Cost for 10 days = 52.50
Since, option B has lower cost, manager should choose option B
08/09/2016 59Dr. DEGA NAGARAJU, SMEC
Discrete-event simulation (General Principles)
The basic building blocks of all discrete-event simulation models
: entities and attributes, activities and events.
A system is modeled in terms of
its state at each point in time
the entities that pass through the system and the entities that represent system resources
the activities and events that cause system state to change.
Discrete-event models are appropriate for those systems for which changes in system state occur only at discrete points in time.
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System : A collection of entities (e.g., people and machines) that interact
together over time to accomplish one or more goals.
Model : An abstract representation of a system, usually containing
structural, logical, or mathematical relationships which describe a
system in terms of state, entities and their attributes, sets, processes,
events, activities, and delays.
System state : A collection of variables that contain all the information
necessary to describe the system at any time.
Entity : Any object or component in the system which requires explicit
representation in the model (e.g., a server, a customer, a machine).
Attributes : The properties of a given entity (e.g., the priority of a waiting
customer, the routing of a job through a job shop).
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List : A collection of (permanently or temporarily) associated entities, ordered
in some logical fashion (such as all customers currently in a waiting line,
ordered by first come, first served, or by priority).
Event : An instantaneous occurrence that changes the state of a system
(such as an arrival of a new customer).
Event notice : A record of an event to occur at the current or some future
time, along with any associated data necessary to execute the
event; at a minimum, the record includes the event type and
the event time.
Event list : A list of event notices for future events, ordered by time of
occurrence also known as the future event list (FEL).
Activity : A duration of time of specified length (e.g., a service time or
inter arrival time), which is known when it begins (although it may be
defined in terms of a statistical distribution).
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Delay : A duration of time of unspecified indefinite length, which is not
known until it ends (e.g., a customer's delay in a last-in, first-out
waiting line which, when it begins, depends on future arrivals).
Clock : A variable representing simulated time, called CLOCK in the
examples to follow.
An activity typically represents a service time, an inter arrival time, or any other
processing time whose duration has been characterized and defined by the modeler.
An activity's duration may be specified in a number of ways:
1. Deterministic-for example, always exactly 5 minutes;
2. Statistical-for example, as a random draw from among 2, 5, 7 with equal
probabilities;
3. A function depending on system variables and/or entity attributes-for example,
loading time for an iron ore ship as a function of the ship's allowed cargo
weight and the loading rate in tons per hour.
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