System Dynamics

An-Najah National University

Faculty of Engineering

Industrial Engineering Department

Instructor: Eng. Tamer Haddad

Introduction

Knowing how the elements of a system

interact & how overall performance can

be improved are essential to the effective

use of simulation

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

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)

System Elements

Entities, Activities, Resources & Controls

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.)

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

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.)

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

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

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)

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.

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

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

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)

System Optimization

The Systems Approach

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

Systems Analysis Techniques

Spreadsheets

Adequate for some applications with little variability and component interaction.

Period driven rather than event driven (weakness point)

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

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.

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.

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.

Symbols

Arrival Rate: λ

Service Rate: µ What are the mean inter-arrival and service times???

Traffic intensity factor Ρ = λ/µ

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

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

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?

Summary

System Dynamic is essential to using any tool for planning system operations

Systems are made up of entities, resources, activities, controls

Summary

Characteristics of Systems: interdependencies & variability

Simulation is capable of imitating complex system which traditional analytical techniques cannot do it