Simulation is one of the most widely used quantitative approaches to decision
It is the method for learning about real system by experimenting with a model that
represents the system.
This model containsa)
These two describes how to compute the value of the outputs given the values of
Types of inputs
Any simulation model has two inputs.
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.
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
Probabilistic inputs such as no. of vehicle arrivals and the fraction that want to make a
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.
Risk analysis is a process of predicting the outcome of a decision in the face of uncertainty.
Calculating Risk Analysis without simulation:
Target product- portable printer
Preliminary marketing and financial analysis provided the following selling price, first
year administrative cost and first year advertising cost.
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
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
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
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
(249 – c1-c2)x - 1000000
Disadvantage: Does not indicate the likelihood of the various profit or loss values.
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
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
Flowchart for the Portacom Simulation:
Selling price/unit = $249
Advertising Cost = $600000
Generating Direct Labour cost, C1
Generate Parts cost, C2
Generate First-year Demand, X
Profit = (249-C1-C2)x - 1000000
Random number intervals for generating
values of Direct labour cost/unit:
Direct labour cost/unit
Intervals of Random
0.0 but less than 0.1
0.1 but less than 0.3
0.3 but less than 0.7
0.7 but less than 0.9
0.9 but less than 1.0
From the above table we calculated randomly 10 values for the direct
Direct Labour cost ($)
Calculating the parts cost:
Parts cost = a+r(b-a)
r = random between 0 and 1
a = smallest value for parts cost
b = largest value for parts cost
Parts cost = 80 + r20
Random Generation of 10 values for the parts
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
Random Generation of 10 values for first year Demand:
Portacom Simulation results for 10 trials:
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
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
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.
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.
Quantitative Methods For Business
- Anderson – Sweeny – Williams