An-Najah National University Faculty of Engineering Industrial Engineering Department System Dynamics 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 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) State Variables: indicate system conditions at specific points in time
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 o o o Provide Optimum solution to a problem (Single Goal). Example: Linear Programming Do not allow random variables to be defined as input data (use averages) Assume constant conditions
Systems Analysis Techniques Operations Research Techniques Descriptive Techniques: o o o Static Analysis techniques such as queuing theory Provide good estimate for basic problems such as determining the expected average number of entities in a queue. 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- L q = Expected number of entities in a queue 3- W = Expected time in the system 4- W q = Expected time in the queue 5- P n = Prob. Of exactly n customers in the system
For M/M/1 system + FIFO L = Ρ/(1- Ρ) = λ/(µ-λ) L q = L-Ρ = Ρ 2 /(1-Ρ) W = 1/(µ-λ) W q = λ/{µ(µ-λ) P n = (1-Ρ)Ρ n LITTLE s LAW: L = λw L q = λw q
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