Section Three Overhead Masters

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Section ThreeOverhead Masters
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Usefulness of Models (Historically)

• --Benefits--
• Understand Relationships
• Facilitate Experimentation
• --Drawbacks--
• Managing Many Calculations
• Time Element Difficult

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Computers Make Modeling Easier

• Perform calculations faster
• Manage Interdependencies
• Handle time element (dynamic)
• Reduce overall cost

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Challenging Questions

• What is to be the scope of the model?
• What level of detail will be included?

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Simulation Tools

• General Purpose Programming Languages
• Simulation Languages
• Simulators
• Simulators with Language Features

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Why Simulate ?

• Foster Creative Problem Solving
• Predict Outcomes
• Account for System Variances
• Promote Total Solutions
• Can be Cost Effective

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Creative Problem Solving

• Simulation can help-
• define a concept for improvement
• test the concept with known system parameters
• sell the idea to those who must support it.
• The risk involved in modeling is low compared to
  trial and error with the system.

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Prediction Capabilities
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Ability to AnalyzeStochastic Dynamic Systems

• Model Type
• Opinion Models
• Static Mathematical
• Simulation Models

• Analytical Capability
• Low
• Medium
• High

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Promotes Total Solutions

• Bring together diverse inputs
• Illuminates interdependencies
• Highlights assumptions
• Suggest investigation of specific areas
• Encourages a systems approach

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Cost Effective

• Flexible evaluation tool
• Base model reusable
• Effective training tool
• Reduced risk of implementation

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How Simulation Works

• Metrics
• Variables
• Instructions

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Typical (Internal) Instructions

• Determine next event type
• Set simulation clock to next event time
• Update any statistical variables
• Perform calculations for current event
• Schedule time for next occurrence

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Simulation Terminology

• System state
• Discrete Event vs Continuous Event
• Static Model vs Dynamic Model
• Steady-State vs Terminating Simulations
• Warm-up Period (Initialization bias)
• Random Seed and Random Stream
• Runs and Replications

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ProModel Overview

• Menu Driven
• Text format (ASCII files)
• Automatic Model Build
• Modular Model Construction
• Integrated Animation
• Statistical Reporting

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Model Elements in MedModel 3.5

• Locations
• Path Networks
• Arrivals
• Variables
• Attributes
• Files

• Entities
• Resources
• Processing
• Routing
• Graphic Icons
• Subroutines

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Other Useful MedModel 3.5 Features

• Model Merging
• Shift Editor
• Expression Builder
• SimRunner

• Submodels
• Graphic Editor
• Costing
• Run Time Interface
• StatFit

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The Simulation Project

• Problem Definition and Statement of Objectives
• Model Formulation and Planning
• Data Collection
• Model Development
• Verification
• Validation
• Experimentation and Optimization
• Results Analysis and Presentation
• Implementation

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Problem Definition

• Current need
• Consider only relevant parts of system
• Consensus, if possible

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Statement of Objectives

• Flow from problem statement
• Evaluation of proposed improvements
• Generation of new ideas
• Milestones
• Financial Justification

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Model Formulation and Planning

• Conceptual Framework
• Sketch or Layout Drawing
• Data Collection (identify requirements and
  sources)

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Data Collection

• Varying Quantity Quality (even within same
  organization)
• Importance of Assumptions
• Macro Data
• Micro Data
• Ongoing Process

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Model Development

• Coding (model building)
• Modular in ProModel
• Often Several Approaches
• Start with General Abstraction...
• Then add Detail

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Verification

• Does it work as intended?
• Animation
• Use of Variables and Counters
• Review by another Modeler
• Data Output Consistent with Objectives
• Trace Function

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Validation

• Does it reflect the real system?
• Structured walk-through
• Animation
• Response to Input Data Changes (sensitivity
  analysis)
• Turing Test
• Comparison with Equipment Specs

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Experimentation

• Testing of Proposed Changes
• Identification of New Alternatives
• Importance of Run Length and Replications
• PMI as a Scenario Builder

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Results Analysis and Presentation

• Document Each Experiment Configuration
• Note Assumptions Made
• Use Graphics to Emphasize (animation, charts,
  etc.)
• Include only Practicable Alternatives
• Include Financial Impacts When Possible

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Implementation

• Support may depend on who had input during the
  simulation study
• Proper documentation of model and scenarios
  tested is essential
• Use an after-action review or post-mortem to
  generate support and improved methods for future
  projects

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Probability Distributions

• Empirical Data
• Relative Frequency Histogram
• Probability Density Function
• Discrete vs Continuous Distributions
• Statistical Parameters of a Distribution

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Standard Distributions

• Includes Possible Values Not Observed During
  Short Data Collection Period
• Easier to Manipulate in a Model than Empirical
  Data
• Each Distribution May be Useful for Different
  Applications

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EXPONENTIAL

• Queuing Systems
• Task Times
• Time to Failure

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GAMMA

• Task Times
• Groups of Task Times
• Exponential is a Special Case of the Gamma

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NORMAL

• Measurement of Error
• Most Familiar (possibly over used)

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UNIFORM

• Basis for Obtaining Values from Standard
  Distributions
• Task Times
• Starting Point if Little Data Available

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WEIBULL

• Time to Failure
• Average Life
• Task Time

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TRIANGULAR

• Often Used in Absence of Data
• Approximation May be Obtained Directly from
  Operators

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LOGNORMAL

• Task Times
• Quantities that are Products of Other Quantities
• Useful if Many Observed Values are Near Zero

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ERLANG

• Service Time Distributions (queuing systems)
• Special Case of Gamma

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BETA

• Proportions
• Task Times
• Used Often in Absence of Data

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POISSON

• Arrival Rates
• Random Batch Sizes
• Demand on Inventory

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BINOMIAL

• Number of Items (in a batch)
• Number of Defects (in a batch)
• Number of Successes in Independent Trials

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DISCRETE UNIFORM

• Random Occurrence of Several Possible Outcomes
• First Trial model where Outcome is an Integer
  Value (in the absence of better data)

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Goodness-Of-Fit Tests

• Chi-Square
• Kolmogorov-Smirnov (K-S)
• Anderson Darling
• Turing

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Chi-Square Test

• Level of Significance
• Degrees of Freedom
• Expected Frequencies
• Computed Value vs Critical Value

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Extracting Values from Distributions

• Cumulative Probability Distribution
• Cumulative Distribution Function
• Random Number Generators
• Uniformly Distributed Values 0-1 (y)
• Unique Random Value (x) for Each (y)

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Types of Output

• Throughput
• Makespan
• Utilization
• Queuing Data (length, average wait time,
  etc.)
• Other

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Warm-Up Period

• Remove Initialization Bias
• Bring to Steady State (before collecting
  statistics)
• Moving Average Method (one of several)

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Replications

• Data Generated from Stochastic Models is Itself
  Stochastic
• Level of Accuracy Required
• Statistical Inference
• Central Limit Theorem

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Comparing Evaluating Alternatives

• Which is better?
• How much better is it? (Is the difference
  significant?)

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Paired-t Test

• Equal Number of Replications
• Same Random Number Streams Used

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Two-Sample Test

• Unequal Number of Replications
• Common Random Streams Not Used

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The Financial Perspective

• Budget may be ultimate constraint
• Organizational Objectives
• Time Horizon

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Important Financial Questions

• What cost and revenue information is required?
• Where can it be obtained?
• How can financial information be processed?
• How will financial results be interpreted?

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Comparison of Alternatives

• Total Costs and Benefits
• Criteria Dependent
• Often No Clear Winner

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Hierarchy of Financial Integration

• Full - all cost information processed within the
  simulation model.
• Partial - some cost information processed in the
  simulation.
• External - all cost information processed
  externally

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Carrying Costs

• Part of total cost picture, but often hidden
• Wait time a key factor
• Sensitivity Analysis

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Healthcare Applications

• Capacity Planning Facility Design
• Emergency Services Planning
• Shared Service Analysis
• Resource Allocation
• Patient Scheduling
• Logistical Analysis
• Personnel Planning
• Equipment Purchasing
• Staff Planning Scheduling
• Interdepartmental Patient Flows

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Service Industry Applications

• Staffing Level Evaluation
• Facility Layout
• Equipment Levels
• Capacity Planning
• Resource Allocation
• Service Level Decisions
• Queuing and Waiting Times
• Office Improvement Projects
• Support Levels
• Logistics

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Manufacturing Applications

• Capital Equipment Evaluation
• Work-In-Process Reduction
• Maintenance Planning
• Material Handling
• Plant Layout
• Just-In-Time
• Capacity Planning
• Job Shop Scheduling
• Production Line Balancing
• Technology Assessment (and more)

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Logistics Applications

• Inventory Materials Management
• Distribution Warehousing
• Transportation Planning
• Order Processing
• Packaging
• Product Support
• Quality Assurance
• Maintenance Planning
• Customer Service Levels
• Reliability Availability