Download - Introduction to System Simulation
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System Dynamics
An-Najah National University
Faculty of Engineering
Industrial Engineering Department
Instructor: Eng. Tamer Haddad
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Introduction
Knowing how the elements of a system
interact & how overall performance can
be improved are essential to the effective
use of simulation
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System Definition
What is a system? System is a collection of elements that functions
together to achieve a desired goal
A system consists of multiple elements
Elements are interrelated & work in cooperation
A system exists for achieving specific objectives
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System Definition
Processing Systems:
artificial (man-made), dynamic (interact with time) & stochastic (random behavior)
Service Systems (restaurants, banks)
Manufacturing Systems (job shops, production facilities, assembly lines, warehousing, distribution)
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System Elements
Entities, Activities, Resources & Controls
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System Elements(1)
Entities: Items processed through the system(e.g Products, Customers, Documents.)
Types of Entities: Human or animate (customers, patients, etc.)
Inanimate (parts, documents, etc.)
Intangible (calls, emails, etc.)
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System Elements(2)
Activities: tasks performed in the system involved in the processing of entities (e.g Cutting parts, Servicing customers, Repairing machines.)
Activities consumes time and involve the use of resources
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System Elements(3)
Resources: means by which activities are preformed. They provide facilities, equipments and personnel for activities
Characteristics: capacity, speed, cycle time, reliability
Types of Resources: Human or animate (operators,doctors, etc.) Inanimate (equipment, tooling, floor space, etc.) Intangible (information, electronic power, etc.)
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System Elements(4)
Controls: dictate how, when & where activities are preformed.
Highest Level: schedule, plans & policies
Lowest level: take written procedure, machine control logic
Examples: Route sequencing
Production Planning
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System Complexity
Elements of a system operate in concert with one another in ways that often results in complex interactions.
Bounded Rationality- Our limited ability to grasp real-world complexity
Factors Interdependencies : the behavior of one element to
affect other elements in the system
Variability: produced uncertainty
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Interdependency
Interdependency tight or loose
System with tightly coupled interdependency have greater impact on system operation and performance
Eliminating interdependency is preferred but not entirely possible for most systems
Dedicate resources to single machine (excessive inventories,
underutilized resources)
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Variability
Variability: System involving Human & Machinery which is inevitable ,e.g. Supplier delivery, Equipment failure, Unpredictable absentee
Type of Variability (see p.30, Table 2.1 ) Activity times: Operations times, repair times, move
times.
Decisions: To accept or reject the part, which task to perform next.
Quantities: Lot sizes, arrival quantities.
Event Intervals: Time between arrivals, time between equipment failures.
Attributes: Part size, skill level.
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Performance Metrics
Flow/Cycle/Throughput/lead Time
Utilization
Value-added time (or processing time)
Waiting time
Flow rate ( production/processing/throughput rate)
Inventory (queue) levels
Yield ( Reject rate)
Customer responsiveness
Variance
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System Variables
Decision Variables (Input Factors): define how a system works
Controllable /Uncontrollable
Controllable Variable
1. # of Operators
2. # of Work Shifts
Un-Controllable Variable
1. Service Time
2. Reject Rate at a cost
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System Variables
Response Variables (Performance/Output): indicate how a system performs
State Variables: indicate system conditions at specific points in time
Examples of Response Var.:• # of Entities Performed• Average Utilization• Performance Metric
Examples of State Var.:• Current # of Entities waiting
to be performed• Status of Teller (busy or idle)
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System Optimization
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The Systems Approach
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Systems Analysis Techniques
Hand Calculations
Example: If a requirements exists to process 200 items per hour, and the processing capacity of a single resource unit is 75 work items per hour.
The needed number of resources = 200/75 = 2.666667 ≈ 3 resources
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Systems Analysis Techniques
Spreadsheets
Adequate for some applications with little variability and component interaction.
Period driven rather than event driven (weakness point)
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Systems Analysis Techniques
Operations Research Techniques
Prescriptive Techniques:
o Provide Optimum solution to a problem (Single Goal).
o Example: Linear Programming
o Do not allow random variables to be defined as input data (use averages)
o Assume constant conditions
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Systems Analysis Techniques
Operations Research Techniques
Descriptive Techniques:
o Static Analysis techniques such as queuing theory
o Provide good estimate for basic problems such as determining the expected average number of entities in a queue.
o Look at many system characteristics.
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Queuing Theory
The science of waiting lines.
Consists of: Queues & Servers.
Serving Criteria: FIFO, LIFO, and others.
Different inter-arrival time distributions may be analyzed.
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How to classify queuing system?
The Form: A/B/s A: Inter-arrival distribution type.
B: Service time distribution type
s: # of servers
M: Markovian or exponential distribution.
G: General Distribution.
D: Deterministic of constant value.
Example: M/D/1, explain it.
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Symbols
Arrival Rate: λ
Service Rate: µ What are the mean inter-arrival and service times???
Traffic intensity factor Ρ = λ/µ
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Queuing System Performance Measures
Based on steady–state expected values
1- L = Expected # on entities in the system
2- Lq = Expected number of entities in a queue
3- W = Expected time in the system
4- Wq = Expected time in the queue
5- Pn = Prob. Of exactly n customers in the system
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For M/M/1 system + FIFO
L = Ρ/(1- Ρ) = λ/(µ-λ)
Lq = L-Ρ = Ρ2/(1-Ρ)
W = 1/(µ-λ)
Wq = λ/{µ(µ-λ)
Pn = (1-Ρ)Ρn
LITTLE’s LAW: L = λW
Lq = λWq
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Example
Suppose customers arrive to use an ATM at an inter-arrival time of 3 min exponentially distributed and spend an average of 2.4 min exponentially distributed at the machine.
What is the expected number of customers in the system and in the queue?
What is the expected waiting time for customers in the system and in the queue?
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Summary
System Dynamic is essential to using any tool for planning system operations
Systems are made up of entities, resources, activities, controls
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Summary
Characteristics of Systems: interdependencies & variability
Simulation is capable of imitating complex system which traditional analytical techniques cannot do it