Simulation modeling is a quantitative analysis tool used to model real-world systems and test various scenarios. The key steps in simulation include defining the problem, identifying variables, constructing a model, testing alternative courses of action by running simulations, analyzing results, and deciding on actions. Monte Carlo simulation specifically handles probabilistic elements by using random sampling and probability distributions. Simulation allows testing of systems without interfering with reality and studying the interactions of components over time. Examples demonstrate how simulation can be used to evaluate inventory policies under uncertain demand and lead times.

1. Simulation
Modeling
Quantitative Business Analysis

2. LEARNING OBJECTIVES:
• Tackle a wide variety of problems using
simulation
• Understand the seven steps of conducting a
simulation
• Explain the advantages and disadvantages of
simulation
• Develop random number intervals and use
them to generate outcomes
• Understand alternative computer simulation
packages available

3. • Simulation is one of the most widely used quantitative
analysis tools
• To simulate is to try to duplicate the features,
appearance, and characteristics of a real system
⚬ build a mathematical model that comes as close as
possible to representing the reality of the system
⚬ physical models can also be built to test systems
⚬ problems can range from simple to extremely
complex
Introduction

4. • Using simulation, a manager should:
• Define a problem
• Introduce the variables associated with the problem
• Construct a simulation model
• Set up possible courses of action for testing
• Run the simulation experiment
• Consider the results (possibly deciding to modify
the model or change data inputs)
• Decide what courses of action to take
Introduction

5. Process of
Simulation

6. • Advantages
• Relatively straightforward and flexible
• Recent advances in computer software make simulation models
very easy to develop
• Can be used to analyze large and complex real-world situations
• Allows "what-if?" type questions
• Does not interfere with the real-world system
• Enables study of interactions between components
• Enables time compression
• Enables the inclusion of real-world complications
Advantages and
Disadvantages of Simulation

7. • Disadvantages
• Often expensive, may require a long complicated process to
develop the model
• Does not generate optimal solutions: it is a trial-and-error
approach
• Requires managers to generate all conditions and constraints of
real-world problem
• Each model is unique and the solutions and inferences are not
usually transferable to other problems
Advantages and
Disadvantages of Simulation

8. Monte Carlo
Simulation

9. • When systems contain elements that exhibit chance in their
behavior, the Monte Carlo method of simulation can be applied
• The basis of the Monte Carlo Simulation is experimentation on the
probabilistic elements through random sampling
• Some examples are:
• inventory demand
• lead time for inventory
• times between machine breakdowns
• times between arrivals
• service times
• times to complete project activities
• number of employees absent
Monte Carlo Simulation

10. • Based on these five steps
• Establishing a probability distribution for important input
variables
• Building a cumulative probability distribution for each variable in
Step 1
• Establishing an interval of random numbers for each variable
• Generating random numbers
• Simulating a series of trials
Monte Carlo Simulation

11. A popular radial tire accounts for a
large portion of the sales
• determine a policy for managing
this inventory
• simulate the daily demand for a
number of days
Harry's Auto Tire
example

12. Step 1: Establishing probability distributions
• one way to establish a probability distribution for a given variable is
to examine historical outcomes
• managerial estimates based on judgement and experience can also
be used
Harry's Auto Tire

14. Step 2: Building a cumulative probability distribution for each variable
• converting from a regular probability to a cumulative distribution is
an easy job
• a cumulative probability is the probability that a variable will be less
than or equal to a particular value
• a cumulative distribution lists all of the possible values and the
probabilities
Harry's Auto Tire

16. Step 3: Setting random number intervals
• assign a set of numbers to represent each possible value or
outcome
• these are called as random number intervals
• a random number is a series of digits that have been selected by a
totally random process
• the range of the random number intervals corresponds exactly to
the probability of the outcomes
• a cumulative probability graph can help assign random numbers
Harry's Auto Tire

19. Step 4: Generating random numbers
• random numbers can be generated in several ways
• large problems will use computer program to generate the needed
random numbers
• for small problems, random processes like spin of a roulette wheel
that has 100 slots or blindly pulling chips from a hat may be used
• the most common manual method is to use a random number table
• everything is random in a random number table so numbers can be
selected from anywhere in the table; every digit or number in the
table has equal chance of occurring.
Harry's Auto Tire

21. Step 5: Simulating the experiment
• select random numbers from Table 13.4
• the number we select will have a corresponding range in table 13.3
• use the daily demand that corresponds to the probability range
aligned with the random number
Harry's Auto Tire

24. Harry's Auto Tire

25. If this simulation were repeated hundreds or thousands of times it is
much more likely the average simulated demand would be nearly the
same as the expected demand.
The true power of simulation is seen when several random variables are
involved and the situation is more complex.
Harry's Auto Tire

26. Simulation
and
Inventory
Analysis

27. • Previously introduced deterministic inventory models, where
product demand and reorder lead time are constant
• In many real-world inventory situations demand and lead time are
variables
• Accurate analysis is difficult without simulation
• An inventory problem with two decision variables and two
probabilistic components
• The owner of a hardware store wants to establish
⚬ order quantity and reorder point decisions
⚬ product that has probabilistic (uncertain) daily demand and
reorder lead time
Simulation and Inventory Analysis

28. Simkin's Hardware Store
example
• Find a good, low cost inventory policy for the Ace electric drill
• Simkin identifies two types of variables
⚬ controllable inputs (order qty and reorder points)
⚬ uncontrollable inputs ( fluctuation daily demand and variable
lead time)

31. • Step 3 is to develop a simulation model
⚬ a flow diagram, or flowchart, is helpful in this process
• Step 4 in the process is to specify the values of the variables to be
tested
⚬ the first policy is an order qty of 10 with a reorder point of 5;
Simkin will make order of 10 items when his on-hand inventory
at the end of the day is 5 or less. Things will arrive not the next
morning but at the beginning of the following working day.
• Step 5 is to actually conduct the simulation
⚬ the process is simulated for a 10 day period
Simkin's Hardware Store

35. • using the table of random numbers, the simulation is conducted
using a four-step process
• begin each day by checking whether an ordered inventory has
arrived (column 2). If it has, increase the current inventory (in
column 3) by the qty ordered.
• generate a daily demand from the demand probability distribution
by selecting a random number. This random number is recorded in
column 4. The demand simulated is recorded in column 5.
Simkin's Hardware Store

36. • .
• .
• Compute the ending inventory every day and record it in column 6.
Ending inventory equals beginning inventory minus demand. If on-
hand inventory is insufficient to meet the day's demand, satisfy as
much as possible and note the number of lost sales (in column 7).
• Determine whether the day's ending inventory has reached the
reorder point (5 units). If it has and if there are no outstanding
orders, place an order (column 8). Lead time for a new order is
simulated by first choosing a random number from Table 13.4 and
recording it in column 9. Finally, we convert this random number
into a lead time by using the distribution in Table 13.7.
Simkin's Hardware Store

38. • The objective is to find a low-cost solution so Simkin must
determine the costs
• Equations for average daily ending inventory, average lost sales, and
average number of orders placed
Analyzing Simkin's
Inventory Cost

39. • Simkin's store is open 200 days a year
• Estimated ordering cost is $10 per order
• Holding cost is $6 per drill per year
• Lost sales cost $8
Analyzing Simkin's
Inventory Cost

40. • Simkin's store is open 200 days a year
• Estimated ordering cost is $10 per order
• Holding cost is $6 per drill per year
• Lost sales cost $8
Analyzing Simkin's
Inventory Cost

41. • For the year, this policy would cost approximately $944
• Simulation should really be extended for many more days
• Even after a larger simulation, the model must be verified and
validated to make sure it truly represents the situation on which it is
based
• If we are satisfied with the model, additional simulations can be
conducted using other values for the variables (Q=10, ROP=4; or
Q=12, ROP=6; or Q=14, ROP=5)
• After simulating all reasonable combinations, Simkin would select
the policy that results in the lowest total cost.
Analyzing Simkin's
Inventory Cost

42. Other Simulation
Points

43. • Simulation models are widely used in business -- not restricted by
assumptions of other models
• Monte Carlo uses concepts of probability distribution and random
numbers to evaluate the system
• Two other types of simulation models
⚬ Operational Gaming
⚬ Systems Simulation
• Theoretically different but computerized simulation has tended to
blur the differences
Other Simulation Points

44. • Operational gaming refers to simulation involving two or more
competing players
⚬ best examples are military games and business games
⚬ allow the testing of management and decision-making skills in
hypothetical situations of conflict
Operational Gaming

45. • Systems Simulation is similar to business gaming
⚬ allows users to test various managerial policies and decisions
to evaluate their effect on the operating environment
• Models the dynamics of large systems
⚬ corporate operating system
⚬ urban government
⚬ economic system
• Allows what-if? questions to test the effects of various policies
Systems Simulation

46. Systems Simulation

47. Verification
and
Validation
Verification involves determining that
the computer model is internally
consistent and following the logic of the
conceptual model.
• answers the question, "Did we build
the model right?"
Validation compares a simulation model
to the real system it represents to make
sure it is accurate.
• check the assumptions of the model
• answers the question, "Did we build
the right model?"

48. • Computers are critical in simulating complex tasks
• General-purpose programming languages can be used
• Simulation software tools have been developed to make the
process easier
⚬ Arena, ProModel, SIMUL8, ExtendSim, Proof 5
• Excel and add-ons can also be used
⚬ @Risk, Crystal Ball, RiskSim, XLSim
Roles of Computers in Simulation

49. Thank you!

50. References
Quantitative Analysis for
Management (13th Edition)" by
Barry Render, Ralph M. Stair Jr.,
Michael E. Hanna, Trevor S. Hale
MI Buhari's Academic Channel
https://www.oreilly.com/library/vi
ew/quantitative-techniques-
theory/
https://www.lucidchart.com/blog
/business-process-simulation