Lecture Introduction to Management Science with Spreadsheets: Chapter 14 - Stevenson, Ozgur

Chapter 14 Simulation, after completing this chapter, you should be able to: Explain what the term simulation means and how simulation differs from analytical techniques; explain the difference between discrete and continuous simulations, between fixed-interval and next-event simulations, and between discrete and probabilistic simulations; list and briefly describe the steps in simulation;...

Stevenson and Ozgur

First Edition

Introduction to Management Science

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Learning Objectives

1 Explain what the term simulation means and how

simulation differs from analytical techniques

2 Explain the difference between discrete and

continuous simulations, between fixed-interval and next-event simulations, and between discrete and probabilistic simulations

3 List and briefly describe the steps in simulation

4 Use the Monte Carlo method to generate random

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Learning Objectives (cont’d)

6 Conduct simulation with Excel using various

distributions

7 Conduct simple waiting-line simulation using Excel

8 Conduct inventory management simulation using

Excel

9 List the advantages and limitations of simulations

After completing this chapter, you should be able to:

–A descriptive tool for the study of the behavior of a

system under various conditions

–The goal in simulation is to create a model that will

reflect the behavior of some real-life system in order to

be able to observe how it may behave when certain inputs or parameters are changed

–Unlike analytical techniques, it is not an optimizing

technique

–Experimental situations in which outcome variables

are discrete and are described by a count of the

number of occurrences.

• Continuous Simulations

–Experimental situations in which the variable of

interest is continuous in that it can assume both

integer and noninteger values over a range of values

that are measured rather than counted.

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Types of Simulations (cont’d)

Types of Simulations (cont’d)

• Fixed-Interval Simulations

–Experiments simulating the value of a variable over a

given or fixed interval of time, distance or area.

–Interest is centered on the accumulated value of a

variable over a length of time or other interval

• Next-Event Simulations

–Experiments focused on when something happens, or

how much time is required to perform a task.

–Interest is centered on an occurrence of an event and,

perhaps, how much time or effort is required for the event

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Types of Simulations (cont’d)

Types of Simulations (cont’d)

• Deterministic Simulations

–Cases in which a specific outcome is certain, given a

set of inputs

• Probabilistic Simulations

–Cases that involve random variables and, therefore,

the exact outcome cannot be predicted with certainty, given a set of inputs

–Cases that incorporate some mechanism for

mimicking random behavior in one or more variables

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Define the problem Set objectives

Develop model

Gather data

Validate model

Design experiments

Run simulations

Analyze and interpret results

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The Monte Carlo Method

The Monte Carlo Method

• Monte Carlo Simulation

–A commonly used approach for achieving randomness that derives its name from its similarity to games of

chance

• Characteristics of random numbers

–All numbers are equally likely

–No patterns appear in sequences of numbers.

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Example

Example

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20 and 100

20 and 100

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Andersen Quick Oil and Lube Example

Andersen Quick Oil and Lube Example

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Waiting-Line Problem

Waiting-Line Problem

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Company Inventory Problem Where Quantity =12, ROP =5

Company Inventory Problem Where Quantity =12, ROP =5

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Plumbing Company Inventory Problem Where Quantity = 10, ROP = 7

Plumbing Company Inventory Problem Where Quantity = 10, ROP = 7

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Problem 1 (Fire Station)

Problem 1 (Fire Station)

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Problem 2

Problem 2

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Problem 3 (Emergency Repairs)

Problem 3 (Emergency Repairs)

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Problem 3 (Emergency Repairs)

Problem 3 (Emergency Repairs)

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Advantages of Simulation

Advantages of Simulation

1 It is particularly well-suited for problems that are difficult

or impossible to solve mathematically

2 It allows an analyst or decision maker to experiment

with system behavior in a controlled environment

instead of in a real-life setting that has inherent risks

3 It enables a decision maker to compress time in order

to evaluate the long-term effects of various alternatives

4 It can serve as a mode for training decision makers by enabling them to observe the behavior of a system

under different conditions

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Limitations of Simulation

Limitations of Simulation

• Probabilistic simulation results are approximations,

rather than optimal solutions

• Good simulations can be costly and time-consuming to develop properly; they also can be time-consuming to run, especially in cases in which a large number of

trials are indicated

• A certain amount of expertise is required in order to

design a good simulation, and this may not be readily available

• Analytical techniques may be available that can provide better answers to problems