Introductory Material John Fowler, Gerald Mackulak, Jennifer McNeill

Edited by: Wandaliz Torres-Garcia 5/16/2014

IEE 475/545

Topics

What is modeling?

Benefits/Purposes of models

Types of models

Three Modeling Techniques - Strengths and Weaknesses

IEE 475/545

What is Modeling ?

A model is a representation (abstraction) of an “actual” system.

Can be physical (a “mini” Goldwater building made of legos) or mathematical (an LP to help Burger King decide which/how many employees to schedule in which shift)

Modeling is the process of developing and exercising a model.

Discrete event simulation (DES) is a subset of modeling in which we imitate the behavior of the system through time.

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Modeling Basics

A model is always an abstraction of reality

Simulation is a tool to help make decisions –- it does not make decisions itself!

Real World

Model

User

Model detail

(determined by

management)

Constraints

Model purpose

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What is a “good” model?

Definition

A “good” model is one which allows the user to make “good” decisions (within a given deadline) as a result of inferences from the model.

If you were asked to build a model of this room to determine how many desks could fit in it, would you build the same model if you had 60 seconds that you would if you had 2 days? Would your definition of a “good” answer change?

What is a “good” model?

Fundamental Goal

To provide as simple a model as possible which is “good”. This implies capturing the appropriate level of detail within the given time constraints.

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“All models are wrong, some are useful.”

George Box

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So why study modeling/problem solving?

Compare useful alternatives

Perform research on system to better understand its behavior

Why not just experiment with “the real world”?

Expensive

Time & Money

Destructive and/or disruptive

Real system may not actually exist

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Model Types and Objectives

Static vs. Dynamic

Deterministic vs. Probabilistic

Absolute vs. Relative

Descriptive vs. Optimization

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Static vs. Dynamic

Static Models

Consider the behavior of the system without regard to time.

Dynamic Models

Consider the time dependent behavior of the system.

DES models are dynamic.

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Deterministic vs. Probabilistic

Deterministic Models

Assume that the system inputs are known with certainty; i.e. determined.

Probabilistic (Stochastic) Models

Assume that the inputs and parameters possess a “random” nature which might be described by a probability distribution; i.e. random variables.

DES models can be probabilistic or deterministic.

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Example -- Distribution of Downtimes

100 Samples from an Exponential Distribution with Mean 200.

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Absolute vs. Relative

Absolute Model A model in which the outputs are meant to agree

precisely with the actual system.

Relative Model A model in which the outputs are only “relatively” correct

i.e. if an input variable is changed, the outputs move in the right direction and approximate proportion.

Reminder: Garbage In Garbage Out

DES models are relative

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Absolute vs. Relative

Real System Model

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Descriptive vs. Optimization

Descriptive Models

Provide a description of how the system behaves.

Optimization Models

Attempt to find the “best” solution according to a given criterion.

DES models are descriptive

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Descriptive vs. Optimization

Descriptive Models can be used:

To predict system behavior.

As an evaluator in an effort to find a solution that “satisfies” one or more goals or constraints.

As an evaluator in an optimization effort.

Optimization models typically must be simple enough for mathematical analysis or direct search.

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Selecting a Methodology/Tool

Decisions depend on:

Whether the model is for single or on-going use

Who will own and maintain the model

What types of questions will be asked of the model

The client should identify these

What types of tools are available for use

The analyst should have responsibility for selecting between them

Attention should be paid to what the client will be able to learn, use, and modify as needed

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Selecting a Methodology

Some possibilities:

Spreadsheets

Analytic models

Simulation models

Data driven (fill in the blank)

Simulation languages (require using simulation building blocks). Image Source: Simul8

nUtilizatioi.e.

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Spreadsheet Models

Strengths

Fast, able to evaluate many scenarios quickly

Easy to understand and use

Easy to modify and maintain data

Results are in format that managers are used to

Potential Weaknesses

Static

Deterministic (usually)

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Analytic Models

Examples

Capacity analysis

Queueing analysis

Linear programming

Other math programming models

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Analytic Models

Strengths

Fast, can evaluate multiple scenarios quickly

Can include complexity beyond spreadsheets (rework, batch processing, re-entrant flows)

Queueing models can include variability

Results are easy to interpret

Potential Weaknesses

Most queueing results are for steady-state behavior

Simplifying assumptions may not be appropriate

What is Simulation?

Modeling methodology capable of “imitating” the behavior of a real/theoretical system over time

General Types of Simulation

Systems Dynamics

Discrete-Event Simulation (focus of this course)

Agent-Based Simulation

Characteristics of Discrete-Event Simulation

DES can be seen as a sampling process

inputs and outputs are random variables

Characteristics of DES:

Event-trigger model

State variables change only at the time of an event

Clock moves in irregular jumps (from event to event)

Can be deterministic, but most applications are stochastic

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Discrete Event Simulation

Strengths

Can capture virtually any level of factory detail

Potentially very accurate

Captures dynamic and stochastic behavior

Has intuitive appeal for managers

Potential Weaknesses

Takes much longer to run than analytic models

Results can be difficult to interpret

Statistical analysis of output is necessary

Can be expensive

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System Components

Simulation models generally consist of entities moving from location to location based on their attributes and the available resources. While moving, they change

the state(s) of the system.

Entity: object of interest in your system

Attribute: characteristic that uniquely identify an entity

Activities: time periods of specific duration

Resources: items used to perform activities (that restrict flow)

States: variables describing the system state

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System Examples

Manufacturing System

Entity: part

Attributes: features, part number, color, etc.

Resources: machines

Activities: processing times

States: Machine States = busy and idle

School

Entities: students

Attributes: GPA, major, name, student ID #, etc.

Resources: classrooms, instructors

Activities: class times

States: Classroom states = full or empty

Simulation models generally consist of:

Clock, entity, resource, variable, attribute, state variable, activity, event, event calendar

Time-based statistics, observation-based statistics

Source: Banks (2010)

Exercise

Name several entities, attributes, activities, events, resources and state variables for the following systems:

A small-appliance repair shop

A cafeteria

A grocery store

A laundromat

A fast-food restaurant

A hospital emergency room

A taxicab company with 10 taxis

An automobile assembly line

Simulation can be applied to Diverse Types Systems

Manufacturing facility Bank or other personal-service operation Transportation/logistics/distribution operation Hospital facilities (emergency room, operating room,

admissions) Computer network Freeway system Business process (insurance office) Criminal justice system Chemical plant Fast-food restaurant Supermarket Theme park Emergency-response system

Steps in a Simulation Study

Source:

Banks

(2010)

Steps in a Simulation Study

1. Problem Formulation Statement of the problem

2. Set Objectives & Project Plan Questions to be answered

Is simulation appropriate?

Methods, alternatives

Allocation of resources People, cost, time, etc.

Steps in a Simulation Study (cont’d.)

3. Model Conceptualization

Requires experience

Begin simple and add complexity

Capture essence of system

Involve the user

4. Data Collection

Time consuming, begin early

Determine what is to be collected

Steps in a Simulation Study (cont’d.)

5. Model translation Computer form

general purpose vs. special purpose lang.

6. Verification Does the program represent model and

run properly? Common sense

7. Validated? Compare model to actual system

Does model replicate system?

Steps in a Simulation Study (cont’d.)

8. Experimental Design

Determine alternatives to simulate

Time, initializations, etc.

9. Production & Analysis

Actual runs + Analysis of results

Determine performance measures

10. More Runs?

Steps in a Simulation Study(cont’d.)

11. Documentation & Reporting

Program & Progress Documents

Thoroughly document program – will likely be used over time

Progress reports are important as project continues – history, chronology – changes, etc.

12. Implementation