© 2007 Pearson Education Simulation Supplement B.

Slides:

Advertisements

Similar presentations

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. A PowerPoint Presentation Package to Accompany Applied Statistics.

Advertisements

© 2007 Pearson Education Simulation Supplement B.

Chapter 15: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1 Chapter 15. Simulation.

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Simulation.

Module F: Simulation. Introduction What: Simulation Where: To duplicate the features, appearance, and characteristics of a real system Why: To estimate.

Introduction to Simulation. What is simulation? A simulation is the imitation of the operation of a real-world system over time. It involves the generation.

1 Simple Linear Regression Chapter Introduction In this chapter we examine the relationship among interval variables via a mathematical equation.

Chapter 14 Simulation. Monte Carlo Process Statistical Analysis of Simulation Results Verification of the Simulation Model Computer Simulation with Excel.

Project 2: ATM’s & Queues

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 14-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 14.

1 1 Slide Chapter 6 Simulation n Advantages and Disadvantages of Using Simulation n Modeling n Random Variables and Pseudo-Random Numbers n Time Increments.

Operations Management

Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. Waiting Line Models.

©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin Probability Distributions Chapter 6.

©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin Probability Distributions Chapter 6.

Spreadsheet Simulation

Verification & Validation

B – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Simulation B For Operations Management, 9e by Krajewski/Ritzman/Malhotra ©

The AIE Monte Carlo Tool The AIE Monte Carlo tool is an Excel spreadsheet and a set of supporting macros. It is the main tool used in AIE analysis of a.

Advanced Waiting Line Theory and Simulation Modeling Chapter 6 - Supplement.

Section 8.1 Estimating  When  is Known In this section, we develop techniques for estimating the population mean μ using sample data. We assume that.

F Simulation PowerPoint presentation to accompany Heizer and Render

B – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Simulation Supplement B.

F - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall F F Simulation PowerPoint presentation to accompany Heizer and Render Operations Management,

Introduction to Modeling Introduction Management Models Simulate business activities and decisions Feedback about and forecast of outcomes Minimal risk.

Project 2: ATM’s & Queues. ATM’s & Queues  Certain business situations require customers to wait in line for a service Examples:  Waiting to use an.

Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Discrete Distributions The values generated for a random variable must be from a finite distinct set of individual values. For example, based on past observations,

SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-1 Chapter 19 Supplement Simulation.

1 QUEUES. 2 Definition A queue is a linear list in which data can only be inserted at one end, called the rear, and deleted from the other end, called.

Outline of Chapter 9: Using Simulation to Solve Decision Problems Real world decisions are often too complex to be analyzed effectively using influence.

Advance Waiting Line Theory and Simulation Modeling.

Simulation OPIM 310-Lecture #4 Instructor: Jose Cruz.

Simulation is the process of studying the behavior of a real system by using a model that replicates the behavior of the system under different scenarios.

Transparency Masters to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc.,

Monté Carlo Simulation  Understand the concept of Monté Carlo Simulation  Learn how to use Monté Carlo Simulation to make good decisions  Learn how.

Supplement E Simulation Copyright ©2013 Pearson Education, Inc. publishing as Prentice HallE- 01.

PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J F-1 Operations.

NCTM Series Navigating through Navigating through Probability in Grades 9-12 AATM State Conference September 27, 2008 Shannon Guerrero Asst Professor,

Computer Simulation. The Essence of Computer Simulation A stochastic system is a system that evolves over time according to one or more probability distributions.

Waiting Lines and Queuing Theory Models

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Supplement.

Simulation. Introduction What is Simulation? –Try to duplicate features, appearance, and characteristics of real system. Idea behind Simulation –Imitate.

4.3 More Discrete Probability Distributions NOTES Coach Bridges.

Technical Supplement 2 Waiting Line Models McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

Simulation Chapter 16 of Quantitative Methods for Business, by Anderson, Sweeney and Williams Read sections 16.1, 16.2, 16.3, 16.4, and Appendix 16.1.

Simulation in Healthcare Ozcan: Chapter 15 ISE 491 Fall 2009 Dr. Burtner.

 Simulation enables the study of complex system.  Simulation is a good approach when analytic study of a system is not possible or very complex.  Informational,

MODELING AND SIMULATION CS 313 Simulation Examples 1.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 15-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Prepared by.

©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin Probability Distributions Chapter 6.

Introduction to Simulation Chapter 12. Introduction to Simulation  In many spreadsheets, the value for one or more cells representing independent variables.

Simulation Modeling.

FREQUENCY DISTRIBUTION

Simulasi sistem persediaan

Probability Distributions

Computer Simulation Henry C. Co Technology and Operations Management,

Chapter Eight Estimation.

Prepared by Lloyd R. Jaisingh

Modeling and Simulation CS 313

Probability Distributions

Simulation Meaning Types The Monte Carlo Methodology.

Prepared by Lee Revere and John Large

Simulation Modeling.

RANDOM VARIABLES Random variable:

Probability Distributions

Simulation Supplement B.

Simulation Supplement B

Presentation transcript:

© 2007 Pearson Education Simulation Supplement B

© 2007 Pearson Education Simulation Simulation: The act of reproducing the behavior of a system using a model that describes the processes of the system. Time Compression: The feature of simulations that allows them to obtain operating characteristic estimates in much less time than is required to gather the same operating data from a real system. Monte Carlo simulation: A simulation process that uses random numbers to generate simulation events.

© 2007 Pearson Education Specialty Steel Products Company produces items such as machine tools, gears, automobile parts, and other specialty items in small quantities to customer order. Demand is measured in machine hours. –Orders are translated into required machine-hours. Management is concerned about capacity in the lathe department. Assemble the data necessary to analyze the addition of one more lathe machine and operator. Specialty Steel Products Co. Example B.1

© 2007 Pearson Education Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Total1.00 Specialty Steel Products Co. Example B.1 Historical records indicate that lathe department demand varies from week to week as follows:

© 2007 Pearson Education Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Specialty Steel Products Co. Example B.1 Average weekly production is determined by multiplying each production requirement by its frequency of occurrence. Average weekly production requirements = 200(0.05) + 250(0.06) + 300(0.17) + … + 600(0.02) = 400 hours

© 2007 Pearson Education Specialty Steel Products Co. Example B.1 Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 The average number of operating machine-hours in a week is: 320(0.30) + 360(0.40) + 400(0.30) = 360 hours

© 2007 Pearson Education Specialty Steel Products Co. Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Total1.00 Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines) (10 machines)0.30 The average number of operating machine-hours in a week = 360 Hrs. RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (10 machines) (11 machines) (11 machines)0.30 Experience shows that with 11 machines, the distribution would be: Example B.1

© 2007 Pearson Education Specialty Steel Products Co. Assigning Random Numbers Random numbers must now be assigned to represent the probability of each demand event. Random Number: A number that has the same probability of being selected as any other number. Since the probabilities for all demand events add up to 100 percent, we use random numbers between (and including) 00 and 99. Within this range, a random number in the range of 0 to 4 has a 5% chance of selection. We can use this to represent our first weekly demand of 200 which has a 5% probability.

© 2007 Pearson Education Event Weekly Demand (hr)Probability Random numbers in the range of 0-4 have a 5% chance of occurrence. Random numbers in the range of 5-10 have a 6% chance of occurrence. Random numbers in the range of have a 17% chance of occurrence. Random numbers in the range of have a 5% chance of occurrence. Specialty Steel Products Co. Assigning Random Numbers

© 2007 Pearson Education Event Existing Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – – – – –99 If we randomly choose numbers in the range of enough times, 5 percent of the time they will fall in the range of 00-04, 6% of the time they will fall in the range of 05-10, and so forth. Specialty Steel Products Co. Assigning Random Numbers

© 2007 Pearson Education Specialty Steel Products Co. Model Formulation Formulating a simulation model entails specifying the relationship among the variables. Simulation models consist of decision variables, uncontrollable variables and dependent variables. Decision variables: Variables that are controlled by the decision maker and will change from one run to the next as different events are simulated. Uncontrollable variables are random events that the decision maker cannot control.

© 2007 Pearson Education Specialty Steel Products Co. Example B.2 1.Using the Appendix 2 random number table, draw a random number from the first two rows of the table. Start with the first number in the first row, then go to the second number in the first row. 2.Find the random-number interval for production requirements associated with the random number. 3.Record the production hours (PROD) required for the current week. 4.Draw another random number from row three or four of the table. 5.Find the random-number interval for capacity (CAP) associated with the random number. 6.Record the capacity hours available for the current week. Simulating a particular capacity level

© 2007 Pearson Education 7.If CAP > PROD, then IDLE HR = CAP – PROD 8.If CAP < PROD, then SHORT = PROD – CAP If SHORT < 100 then OVERTIME HR = SHORT and SUBCONTRACT HR = 0 If SHORT > 100 then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT – Repeat steps until you have simulated 20 weeks. Specialty Steel Products Co. Example B.2 Simulating a particular capacity level

© 2007 Pearson Education Specialty Steel Products Co. 20-week simulation 10 Machines Existing DemandWeeklyCapacityWeeklySub- RandomProductionRandomCapacityIdleOvertimecontract WeekNumber(hr)Number(hr)HoursHoursHours Total Weekly average

© 2007 Pearson Education Comparison of 1000-week Simulations 10 Machines11 Machines Idle hours Overtime hours Subcontract hours Cost$1,851.50$1, Specialty Steel Products Co week simulation A steady state occurs when the simulation is repeated over enough time that the average results for performance measures remain constant.

© 2007 Pearson Education Monte Carlo Simulation Application B.1 Famous Chamois Car Wash Car Arrival Distribution (time between arrivals) Famous Chamois is an automated car wash that advertises that your car can be finished in just 15 minutes. The time until the next car arrival is described by the following distribution. MinutesProbabilityMinutesProbability

© 2007 Pearson Education Famous Chamois Car Wash: Random Number Assignment Assign a range of random numbers to each event so that the demand pattern can be simulated. Minutes Random Numbers Minutes Random Numbers 100– –  – – –  –  –58 Monte Carlo Simulation Application B.1

© 2007 Pearson Education Monte Carlo Simulation Famous Chamois Car Wash: Simulation Simulate the operation for 3 hours, using the following random numbers, assuming that the service time is constant at 6, (:06) minutes per car. Random Number Time to Arrival Arrival Time Number in Drive Service Begins Departure Time Minutes in System 5070:070 0:136 63?

© 2007 Pearson Education

Computer Simulation  The simulation for Specialty Steel Products demonstrated the basics of simulation.  However it only involved one step in the process, with two uncontrollable variables (weekly production requirements and three actual machine-hours available) and 20 time periods.  Simple simulation models with one or two uncontrollable variables can be developed using Excel, using its random number generator.  More sophisticated simulations can become time consuming and require a computer.