This document discusses simulation as a quantitative approach to decision making. It describes how simulation models use mathematical expressions and logical relationships to represent real systems and compute outputs given inputs. The document outlines various applications of simulation, including new product development, traffic flow, and waiting lines. It also covers risk analysis, what-if analysis, inventory simulation, and waiting line simulation. The advantages of simulation include studying systems without building them and performing what-if analysis, while disadvantages include high costs of model building and conducting simulations.

1. Simulation
Sudarshan Kumar Patel
Vinay Uppinal

2. Flow Of Presentation:

Introduction

Models

Applications

Risk Analysis

What-if Analysis

Simulation Method

Inventory Simulation

Wait Lines

Advantages and Disadvantages

References

3. Introduction:
Simulation:

Simulation is one of the most widely used quantitative approaches to decision
making.

It is the method for learning about real system by experimenting with a model that
represents the system.
This model containsa)
Mathematical expressions
b)
Logical relationships
These two describes how to compute the value of the outputs given the values of
inputs.

4. Types of inputs
Any simulation model has two inputs.
i.
Controllable inputs
ii.
Probabilistic inputs
Probabilistic
inputs
Controllable
inputs
Model
Output

Controllable inputs are those inputs which are controlled by decision maker such as
total quantity of goods produced by a firm, unit selling cost of that product

Probabilistic inputs are those inputs which are not controlled by decision maker such as
direct labour cost, demand..etc.

5. Applications of Simulation:
1. New product development:

Determine the probability that a new product will be profitable.

Probabilistic inputs such as demand, parts cost and labour cost.

Controllable input whether to introduce the product.
2. Traffic flow:

Determine the effect of installing a left turn signal on the flow of traffic through a
busy intersection.

Probabilistic inputs such as no. of vehicle arrivals and the fraction that want to make a
left turn.

Controllable inputs such as length of time the left turn signal is on.
3. Waiting lines:

Determine the waiting times for customer at a bank’s ATM.

Probabilistic inputs such as customer arrivals and service times.

Controllable inputs such as the no. of ATM machines installed.

6. Risk Analysis:
Risk analysis is a process of predicting the outcome of a decision in the face of uncertainty.
Calculating Risk Analysis without simulation:
Portacom Project:

Target product- portable printer

Preliminary marketing and financial analysis provided the following selling price, first
year administrative cost and first year advertising cost.

Parameters:
Selling price = $249/unit
Administrative cost = $400,000
Advertising cost = $600,000
Here the cost of direct labour, the cost of parts and first year demand for portable printer
are not known with certainty and are considered probabilistic inputs.
Suppose labour cost = $45/unit
Cost of parts/unit = $90
First year demand = $15,000units

7. What if Analysis:
One approach to risk analysis is called what-if analysis.
This analysis involves generating values for the probabilistic inputs and computing the resulting
values for the output(profit).
Profit = ($249 - direct labour cost/unit - parts cost/unit)* (Demand)- $1000000
Letting ,
C1=direct labour cost/unit.
C2= parts cost/unit.
X = First year demand.
Profit = (249 – c1-c2)x – 1,000,000.
These values constitute the base-case scenario.
profit = (249 – 45 – 90)* (15000) – 1,000,000 = 710,000
Thus the base-case scenario leads to an anticipated profit of $710
Worst case scenario
In this case direct labour cost = $47(the highest value)
Parts cost = $100(highest value)
Demand = 15000(lowest value)
profit = -847000
So the worst-case scenario leads to projected loss of $847000

8. Best-case scenario
In this case direct labour cost = $43(the lowest value)
Parts cost = $80(lowest value)
Demand = 28500(highest value)
profit = $2591000
So the best-case scenario leads to projected profit of $2591000
Direct
Labour
cost
Introduce product
Parts
cost
First
Year
Demand
(249 – c1-c2)x - 1000000
Profit
Disadvantage: Does not indicate the likelihood of the various profit or loss values.

9. Simulation Method:
Using simulation to perform risk analysis for the portacom problem is like playing out many
what-if scenarios by randomly generating values for the probabilistic inputs.
The advantage of simulation is that it allows us to access the probability of a profit and
the probability of a loss.
Direct Labour Cost:
Suppose direct labour cost will range from $43 to $47/unit with probability
Direct labour cost / probability
unit
$43
0.1
$44
0.2
$45
0.4
$46
0.2
$47
0.1

10. Parts Cost = $80 to $100
First year Demand- the mean or expected value of first year demand is 15000 units the
std deviation of 4500 units describes the variability in the first year demand
SD = 4500
Mean = 15000
This process of generating probabilistic inputs and computing the value of output is
called Simulation.

11. Flowchart for the Portacom Simulation:
Model Parameters
Selling price/unit = $249
Administrative Cost=$400000
Advertising Cost = $600000
Generating Direct Labour cost, C1
Generate Parts cost, C2
Next
Trial
Generate First-year Demand, X
Computer Profit
Profit = (249-C1-C2)x - 1000000

12. Random number intervals for generating
values of Direct labour cost/unit:
Direct labour cost/unit
Probability
Intervals of Random
no.s
$43
0.1
0.0 but less than 0.1
$44
0.2
0.1 but less than 0.3
$45
0.4
0.3 but less than 0.7
$46
0.2
0.7 but less than 0.9
$47
0.1
0.9 but less than 1.0
From the above table we calculated randomly 10 values for the direct
labour cost/unit

13. Trial
Random Number
Direct Labour cost ($)
1
0.9101
47
2
0.2841
44
3
0.6531
45
4
0.0367
43
5
0.3451
45
6
0.2757
44
7
0.6859
45
8
0.6246
45
9
0.4936
45
10
0.8077
46
Calculating the parts cost:
Parts cost = a+r(b-a)
Where
r = random between 0 and 1
a = smallest value for parts cost
b = largest value for parts cost
Parts cost = 80 + r20

14. Random Generation of 10 values for the parts
cost/ unit
Trial
Random number
Parts cost
1
0.2680
85.36
2
0.5842
91.68
3
0.6675
93.35
4
0.9280
98.56
5
0.4180
88.36
6
0.7342
94.68
7
0.4325
88.65
8
0.1186
82.37
9
0.6944
93.89
10
0.7869
95.74

15. How to Calculate Demand:
Using excel the following formula can be placed into a cell to obtain a value for a
probabilistic input i.e., normally distributed
= NORMINV(RAND(),Mean,SD)
Random Generation of 10 values for first year Demand:
Trial
Random no.
Demand
1
0.7005
17366
2
0.3204
12900
3
0.8968
20686
4
0.1804
10888
5
0.4346
14259
6
0.9605
22904
7
0.5646
15732
8
0.7334
17804
9
0.0216
5902
10
0.3218
12918

16. Portacom Simulation results for 10 trials:
Trial
Direct labour
cost/unit ($)
Parts
cost/unit ($)
Units sold
Profit ($)
1
47
85.36
17366
1025570
2
44
91.68
12900
461828
3
45
93.35
20686
1288906
4
43
98.56
10888
169807
5
45
88.36
14259
648911
6
44
94.68
22904
1526679
7
45
88.65
15732
814686
8
45
82.37
17804
1165501
9
45
93.89
5902
-350131
10
46
95.74
12918
385585
Total
449
912.64
151359
7137432
Average
44.90
91.26
15136
713743

17. Inventory Simulation:
In inventory simulation we describe how simulation can be used to establish an inventory
policy for a product that has uncertain demand.
Sharma Electrical supply company:
Fan cost = $75
Selling price = $125
Gross profit by sharma = $125 - $75 = $50
Demand
Mean = 100unit
Std Dev = 20units
Sharma receives monthly delivery and replenishes its inventory to level of Q at the
beginning of which month (replenishment level)
If monthly demand < replenishment level then inventory holding cost = $15/unit
If monthly demand > replenishment level then inventory shortage cost = $30/unit
Controllable input = Q
Probabilistic input = Demand
Output = net profit and service level

18. Case 1: D<= Q
Gross profit = $50D
Holding cost = $15(Q –D)
Net Profit = Gross profit – Holding cost = $50D - $15(Q – D)
Case 2: D>Q
Gross profit = $50Q
Shortage cost = $30(D – Q)
Net profit = Gross profit – Shortage cost = $50Q - $30 (D – Q)
Month
Demand
Sales
Gross
Holding
Profit ($) cost ($)
Shotage
cost($)
Net
profit ($)
1
79
79
3950
315
0
3635
2
111
100
5000
0
330
4670
3
93
93
4650
105
0
4545
4
100
100
5000
0
0
5000
5
118
100
5000
0
540
4460
Total
501
472
23600
420
870
22310
Average
100
94
4720
84
174
4462

19. Waiting line Simulation:
The Simulation models discussed thus far have been based on independent trials in
which the results in one trial do not affect what happens in subsequent trials.
Customer Arrival Time:
Probabilistic input arrival time of customer who use the ATM
Customer Service Time:
Probabilistic input the time a customer spends using the ATM machines.

20. Advantages and Disadvantages:
Main advantages of simulation include:

Study the behavior of a system without building it.

Results are accurate in general, compared to analytical model.

Help to find un-expected phenomenon, behavior of the system.

Easy to perform ``What-If'' analysis.
Main disadvantages of simulation include:

Expensive to build a simulation model.

Expensive to conduct simulation.

Sometimes it is difficult to interpret the simulation results.

21. References:

Quantitative Methods For Business
- Anderson – Sweeny – Williams

Wikipedia

Youtube.