graduate program in business information systems simulation aslı sencer

Graduate Program in Business Information Systems

Simulation

Aslı Sencer

BIS 517-Aslı Sencer

Simulation

– Very broad term – methods and applications to imitate or mimic real systems, usually via computer

Applies in many fields and industries Very popular and powerful method

Advantages of Simulation

Simulation can tolerate complex systems where analytical solution is not available.

Allows uncertainty, nonstationarity in modeling unlike analytical models

Allows working with hazardous systems Often cheaper to work with the simulated system Can be quicker to get results when simulated

system is experimented.



The Bad News

Don’t get exact answers, only approximations, estimates

Requires statistical design and analysis of simulation experiments

Requires simulation expert and compatibility with a simulation software

Softwares and required hardware might be costly Simulation modeling can sometimes be time

consuming.


Different Kinds of Simulation Static vs. Dynamic

Does time have a role in the model?

Continuous-change vs. Discrete-change Can the “state” change continuously or only at

discrete points in time?

Deterministic vs. Stochastic Is everything for sure or is there uncertainty?


Using Computers to Simulate

General-purpose languages (C, C++, Visual Basic)

Simulation softwares, simulators Subroutines for list processing, bookkeeping, time

advance Widely distributed, widely modified

Spreadsheets Usually static models Financial scenarios, distribution sampling, etc.


Simulation Languages and Simulators Simulation languages

GPSS, SIMSCRIPT, SLAM, SIMAN Provides flexibility in programming Syntax knowledge is required

High-level simulators GPSS/H, Automod, Slamsystem, ARENA, Promodel Limited flexibility — model validity? Very easy, graphical interface, no syntax required Domain-restricted (manufacturing, communications)


When Simulations are Used

The early years (1950s-1960s) Very expensive, specialized tool to use Required big computers, special training Mostly in FORTRAN (or even Assembler)

The formative years (1970s-early 1980s) Computers got faster, cheaper Value of simulation more widely recognized Simulation software improved, but they were still languages to

be learned, typed, batch processed


When Simulations are Used (cont’d.)

The recent past (late 1980s-1990s) Microcomputer power, developments in softwares Wider acceptance across more areas

Traditional manufacturing applications Services Health care “Business processes”

Still mostly in large firms Often a simulation is part of the “specs”


When Simulations are Used (cont’d.)

The present Proliferating into smaller firms Becoming a standard tool Being used earlier in design phase Real-time control

The future Exploiting interoperability of operating systems Specialized “templates” for industries, firms Automated statistical design, analysis


Popularity of Simulation Consistently ranked as the most useful, popular tool in the

broader area of operations research / management science 1979: Survey 137 large firms, which methods used?

1. Statistical analysis (93% used it)2. Simulation (84%)3. Followed by LP, PERT/CPM, inventory theory, NLP,

1980: (A)IIE O.R. division members First in utility and interest — simulation First in familiarity — LP (simulation was second)

1983, 1989, 1993: Heavy use of simulation consistently reported

1. Statistical analysis 2. Simulation


Today: Popular Topics

Real time simulationWeb based simulationOptimization using simulation


Simulation Process

Develop a conceptual model of the system Define the system, goals, objectives, decision

variables, output measures, input variables and parameters.

Input data analysis: Collect data from the real system, obtain probability

distributions of the input parameters by statistical analysis

Build the simulation model: Develop the model in the computer using a HLPL, a

simulation language or a simulation software


Simulation Process (cont’d.)

Output Data Analysis: Run the simulation several times and apply statistical

analysis of the ouput data to estimate the performance measures

Verification and Validation of the Model: Verification: Ensuring that the model is free from

logical errors. It does what it is intended to do. Validation: Ensuring that the model is a valid

representation of the whole system. Model outputs are compared with the real system outputs.


Simulation Process (cont’d.)

Analyze alternative strategies on the validated simulation model. Use features like Animation Optimization Experimental Design

Sensitivity analysis: How sensitive is the performance measure to the

changes in the input parameters? Is the model robust?


Static Simulation:Monte-Carlo Simulation Static Simulation with no time dimension. Experiments are made by a simulation model to estimate

the probability distribution of an outcome variable, that depends on several input variables.

Used the evaluate the expected impact of policy changes and risk involved in decision making.

Ex: What is the probability that 3-year profit will be less than a required amount?

Ex: If the daily order quantity is 100 in a newsboy problem, what is his expected daily cost? (actually we learned how to answer this question analytically)


Ex1: Simulation for Dave’s Candies

Dave’s Candies is a small family owned business that offers gourmet chocolates and ice cream fountain service. For special occasions such as Valentine’s day, the store must place orders for special packaging several weeks in advance from their supplier. One product, Valentine’s day chocolate massacre, is bought for $7,50 a box and sells for $12.00. Any boxes that are not sold by February 14 are discounted by 50% and can always be sold easily. Historically Dave’s candies has sold between 40-90 boxes each year with no apparent trend. Dave’s dilemma is deciding how many boxes to order for the Valentine’s day customers.


Ex1: Dave's Candies Simulation

If the order quantity, Q is 70, what is the expected profit?Selling price=$12Cost=$7.50Discount price=$6 If D<Q

Profit=selling price*D - cost*Q + discount price*(Q-D) D>Q Profit=selling price*Q-cost*Q

Probability Distribution for Demand

Year Demand

2009 90

2008 80

2007 50

2006 60

2005 40

2004 70

2003 90

. .

. .

Demand Distribution

Demand

(xi, i=1,...,6)

Probability

P(Demand=xi)

40 1/6

50 1/6

60 1/6

70 1/6

80 1/6

90 1/6


Generating Demands Using Random Numbers

During simulation we need to generate demands so that the long run frequencies are identical to the probability distribution found.

Random numbers are used for this purpose. Each random number is used to generate a demand.

Excel generates random numbers between 0-1. These numbers are uniformly distributed between 0-1.

Random numbers

0.12878

0.43483

0.87643

0.65711

0.03742

0.46839

0.04212

0.89900


Generating random demands:Inverse transformation techniqueP(demand=xi)

(xi)

40 50 60 70 80 90

1/6

P(demand<=xi)

(xi)

40 50 60 70 80 90

1

5/6

4/6

3/6

2/6

1/6

U1

D1=80

U2

D2=50

1. Generate U~UNIFORM(0,1)2. Let U=P(Demand<=D) then D=P-1(U)


Generating Demands

Demand

(xi)

Probability

P(Demand=xi)

Cumulative Probability

P(Demand<=xi)Random numbers

40 1/6 1/6 [0-1/6]

50 1/6 2/6 (1/6-2/6]

60 1/6 3/6 (2/6-3/6]

70 1/6 4/6 (3/6-4/6]

80 1/6 5/6 (4/6-5/6]

90 1/6 1 (5/6-1]


Ex1: Simulation in Excel for Dave’s CandiesUse the following excel functions to generate a random demand with a given distribution function.

RAND(): Generates a random number which is uniformly distributed between 0-1.VLOOKUP(value, table range, column #): looks up a value in a table to detremine a random demand.IF(condition, value if true, value if false): Used to calculate the total profit according to the random demand.



Dynamic Simulation:Queueing System

Arrivals Departures

Service

is identified by:

•Arrival rate, interarrival time distribution•Service rate, service time distribution•# servers•# queues•Queue capacities•Queue disciplines, FIFO, LIFO, etc.


M/M/1 Queueing System

Arrivals Departures

Service

M: interarrival time is exponentially distributedM: service time is exponentially distributed1: There is a single server


Ex3: Model Specifics Initially (time 0) empty and idle Base time units: minutes Input data (assume given for now …), in minutes:

Part Number Arrival Time Interarrival Time Service Time1 0.00 1.73 2.902 1.73 1.35 1.763 3.08 0.71 3.394 3.79 0.62 4.525 4.41 14.28 4.466 18.69 0.70 4.367 19.39 15.52 2.078 34.91 3.15 3.369 38.06 1.76 2.37

10 39.82 1.00 5.3811 40.82 . .

. . . .

. . . . Stop when 20 minutes of (simulated) time have passed


Queuing Simulation Random variables:

Time between arrivals Service time represented by probability distributions.

Events: Arrival of a customer to the system Departure from the system.

State variables: # customers in the queue Worker status {busy, idle}

Output measures: Average waiting time in the queue % utilization of the server Average time spent in the system


Output Performance Measures

Total production of parts over the run (P) Average waiting time of parts in queue:

Maximum waiting time of parts in queue:

N = no. of parts completing queue waitWQi = waiting time in queue of ith partKnow: WQ1 = 0 (why?)

N > 1 (why?)N

WQN

ii

1

iNi

WQmax,...,1


Output Performance Measures (cont’d.)

Time-average number of parts in queue:

Maximum number of parts in queue:

Average and maximum total time in system of parts:

Q(t) = number of parts in queue at time t

20

)(200 dttQ

)(max200

tQt

iPi

P

ii

TSP

TS

max,...,1

1 ,

TSi = time in system of part i


Output Performance Measures (cont’d.)

Utilization of the machine (proportion of time busy)

Many others possible (information overload?)

t

ttB

dttB

timeat idle is machine the if0

timeat busy is machine the if1)(,

20

)(200


Simulation by Hand

Manually track state variables, statistical accumulators

Use “given” interarrival, service times Keep track of event calendar “Lurch” clock from one event to the next Will omit times in system, “max” computations

here (see text for complete details)


System

Clock

B(t)

Q(t)

Arrival times of custs. in queue

Event calendar

Number of completed waiting times in queue

Total of waiting times in queue

Area under Q(t)

Area under B(t)

Q(t) graph B(t) graph

Time (Minutes) Interarrival times 1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...

Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...

Simulation by Hand: Setup

0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20


System

Clock 0.00

B(t) 0

Q(t) 0


<empty>

Event calendar [1, 0.00, Arr] [–, 20.00, End]

Number of completed waiting times in queue 0

Total of waiting times in queue 0.00

Area under Q(t) 0.00

Area under B(t) 0.00



Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...

Simulation by Hand: t = 0.00, Initialize

0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20


System

Clock 0.00

B(t) 1

Q(t) 0


<empty>

Event calendar [2, 1.73, Arr] [1, 2.90, Dep] [–, 20.00, End]







Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...

Simulation by Hand: t = 0.00, Arrival of Part 1

0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

1


System

Clock 1.73

B(t) 1

Q(t) 1


(1.73)

Event calendar [1, 2.90, Dep] [3, 3.08, Arr] [–, 20.00, End]







Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

12


System

Clock 2.90

B(t) 1

Q(t) 0


<empty>








Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...

Simulation by Hand: t = 2.90, Departure of Part 1

0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

2


System

Clock 3.08

B(t) 1

Q(t) 1


(3.08)








Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

23


System

Clock 3.79

B(t) 1

Q(t) 2


(3.79, 3.08)








Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

234


System

Clock 4.41

B(t) 1

Q(t) 3


(4.41, 3.79, 3.08)







Time (Minutes)

Interarrival times 1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...

Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

2345


System

Clock 4.66

B(t) 1

Q(t) 2


(4.41, 3.79)







Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

345


System

Clock 8.05

B(t) 1

Q(t) 1


(4.41)







Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

45


System

Clock 12.57

B(t) 1

Q(t) 0


()







Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

5


System

Clock 17.03

B(t) 0

Q(t) 0

Arrival times of custs. in queue ()

Event calendar [6, 18.69, Arr] [–, 20.00, End]






Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20


System

Clock 18.69

B(t) 1

Q(t) 0

Arrival times of custs. in queue ()

Event calendar [7, 19.39, Arr] [–, 20.00, End] [6, 23.05, Dep]






Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

6


System

Clock 19.39

B(t) 1

Q(t) 1


(19.39)

Event calendar [–, 20.00, End] [6, 23.05, Dep] [8, 34.91, Arr]






Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

67


Simulation by Hand: t = 20.00, The End

0

1

2

3

4

0 5 10 15 20

012

0 5 10 15 20

67

System

Clock 20.00

B(t) 1

Q(t) 1


(19.39)

Event calendar [6, 23.05, Dep] [8, 34.91, Arr]






Time (Minutes)


Service times 2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...


Ex3:Complete Record of the Hand Simulation


Ex3: Simulation by Hand:Finishing Up Average waiting time in queue:

Time-average number in queue:

Utilization of drill press:

part per minutes 53261715

queue in times of No.queue in times of Total

..

part 79.020

78.15

eclock valu Final

curve )(under Area

tQ

less)(dimension 92.020

34.18

eclock valu Final

curve )(under Area

tB

Randomness in Simulation The above was just one “replication” — a sample of size

one (not worth much) Made a total of five replications:

Confidence intervals for expected values: In general, For expected total production,

nstX n //, 211 )/.)(.(. 56417762803 042803 ..

Notesubstantialvariabilityacrossreplications


Comparing Alternatives

Usually, simulation is used for more than just a single model “configuration”

Often want to compare alternatives, select or search for the best (via some criterion)

Simple processing system: What would happen if the arrival rate were to double? Cut interarrival times in half Rerun the model for double-time arrivals Make five replications


Results: Original vs. Double-Time Arrivals

Original – circles Double-time – triangles Replication 1 – filled in Replications 2-5 – hollow Note variability Danger of making

decisions based on one (first) replication

Hard to see if there are really differences

Need: Statistical analysis of simulation output data


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