Waiting Lines CrossChek Sporting Goods’ Golf Division gets requests-for- quotes for custom-made golf clubs at a rate of about 4 per hour. Each of these.

Slides:

Advertisements

Similar presentations

Chapter 7 EM Math Probability.

Advertisements

Sampling Distributions

Multiplication and division as arrays 1) 2)3) 4)5) 7) 6) 8) 9) Use each array to write 2 multiplication and 2 division sentences ©

Part 3 Probabilistic Decision Models

Using Graphs and Tables to Solve Linear Systems 3-1

+ 7.3B The Central Limit Theorem 1/16/ Section 7.3 Sampling Distributions & The CLT After this section, you should be able to… APPLY the central.

Chapter 7 Sampling Distributions

Stats for Engineers Lecture 5

Problem1; Admission Flow

Discrete Distributions

Department of Engineering Management, Information and Systems

Introduction Queuing is the study of waiting lines, or queues.

Process Analysis and Design

Waiting Line Management

Chapter 5: Service Processes

Least Common Multiple (LCM)

EXAMPLE 4 Solve a multi-step problem SHOPPING

Using Graphs and Tables to Solve Linear Systems 3-1

Chi-Square and Analysis of Variance (ANOVA)

Capacity Planning and Queuing Models

Capacity Planning Chapter 14.

Operations Management

Three Key Process Measures: Flow Rate

HOW TO COMPARE FRACTIONS

Created by Susan Neal $100 Fractions Addition Fractions Subtraction Fractions Multiplication Fractions Division General $200 $300 $400 $500 $100 $200.

© 2007 Pearson Education Waiting Lines Supplement C.

Lesson Menu Five-Minute Check (over Lesson 5–7) Main Idea and Vocabulary Key Concept: Percent of Change Example 1:Real-World Example: Find Percent of Change.

Introduction to Queuing Theory

An Investment Planning In a barber shop business Paxton Zhou Paul Kim.

Queuing Analysis Chapter 13.

Julian Archer Shannon Cummings Ashley Green David Ong.

ST3236: Stochastic Process Tutorial 9

Active Learning Lecture Slides For use with Classroom Response Systems Sampling Distributions.

1 3. Process Flow Measures Problem 1 (a) 1. Time Travelers Insurance Company (TTIS) processes 12,000 claims per year. The average processing time is 3.

Module C8 Queuing Economic/Cost Models. ECONOMIC ANALYSES Each problem is different Examples –To determine the minimum number of servers to meet some.

INDR 343 Problem Session

Waiting Lines Example Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their request take on average 10.

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Capacity Planning and Queuing Models.

Queuing Theory Worthmore Department Store

QUEUING MODELS Based on slides for Hilier, Hiller, and Lieberman, Introduction to Management Science, Irwin McGraw-Hill.

1 Ardavan Asef-Vaziri Jan-2011Operations Management: Waiting Lines 2 Bank of San Pedro has only 1 teller. On average, 1 customer comes every 6 minutes,

Waiting Lines CrossChek Sporting Goods’ Golf Division gets requests-for- quotes for custom-made golf clubs at a rate of about 4 per hour. Each of these.

S. Chopra/Operations/Managing Services1 Operations Management: Capacity Management in Services Module u Why do queues build up? u Process attributes and.

1 Ardavan Asef-Vaziri Jan-2011Operations Management: Waiting Lines 2 The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution.

Waiting Lines Example-1

Operations research Quiz.

Queuing Models Economic Analyses. ECONOMIC ANALYSES Each problem is different Examples –To determine the minimum number of servers to meet some service.

Waiting Lines Students should be able to:

Queuing. Elements of Waiting Lines  Population –Source of customers Infinite or finite.

Waiting lines problems

Problem 8.4 K = ∞ R i = 60/4 = 15 /hr T p = 3 min = 0.05 hour c= 1 R p = c/Tp = 20 /hour Both Ti and Tp exponential Server $20 /hr Phone $5/hr Wait cost.

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3  Terminology: The characteristics of a queuing system is captured by five parameters:

MNG221 - Management Science –

Introduction to Management Science

Production and Operations Management An area of management concerned with overseeing, designing, and controlling the production of goods or services It.

A spinner from a board game randomly indicates a real number between 0 and 50. The spinner is fair in the sense that it indicates a number in a given interval.

CrossChek Sporting Goods CrossChek Sporting Goods is a manufacturer of sporting goods, including golf clubs, hockey equipment, bats, balls and all things.

4/11: Queuing Models Collect homework, roll call Queuing Theory, Situations Single-Channel Waiting Line System –Distribution of arrivals –Distribution.

Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Waiting Line Analysis for Service Improvement Operations Management.

Chapter 16 Capacity Planning and Queuing Models

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3  Mean inter-arrival time = 1/Ri = 1/R  Probability that the time between two arrivals.

Review 3-25 In 2003, the average stock price for companies making up the S&P 500 was $30 per share, with a standard deviation of $8.20. Assume stock prices.

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution.

 Recall your experience when you take an elevator.  Think about usually how long it takes for the elevator to arrive.  Most likely, the experience.

1 Ardavan Asef-Vaziri Jan-2011Operations Management: Waiting Lines 2 Example: The average arrival rate to a GAP store is 6 customers per hour. The average.

Managerial Decision Making Chapter 13 Queuing Models.

Module D Waiting Line Models.

18 Management of Waiting Lines

Queuing Models Economic Analyses.

PROBABILITY AND STATISTICS

Presentation transcript:

Waiting Lines CrossChek Sporting Goods’ Golf Division gets requests-for- quotes for custom-made golf clubs at a rate of about 4 per hour. Each of these requests is individually assessed by a sales clerk, who then answers with a quote. It takes a clerk an average of 10 minutes to answer a request for a quote. What is the probability of 3 requests arriving in an hour? What is the probability of at least 2 requests arriving in an hour? What is the probability that it will take less than 10 minutes to process a quote request? What is the probability that it will take between 10 and 12 minutes to process a quote request?

Poisson Distribution Models distribution of numbers of arrivals during a specified period Few possible outcomes less than the mean, but higher likelihoods

Exponential Distribution Models distribution of service times Low outcomes more likely, very high outcomes still possible

Back to CrossChek’s Problem… CrossChek Sporting Goods’ Golf Division gets requests-for-quotes for custom-made golf clubs at a rate of about 4 per hour. Each of these requests is individually assessed by a sales clerk, who then answers with a quote. It takes a clerk an average of 10 minutes to answer a request for a quote. What is the probability of 3 requests arriving in an hour? What is the probability of at least 2 requests arriving in an hour? What is the probability that it will take less than 10 minutes to process a quote request? What is the probability that it will take between 10 and 12 minutes to process a quote request?

Back to CrossChek’s Problem… CrossChek Sporting Goods’ Golf Division gets requests-for-quotes for custom-made golf clubs at a rate of about 4 per hour. Each of these requests is individually assessed by a sales clerk, who then answers with a quote. It takes a clerk an average of 10 minutes to answer a request for a quote. What is the probability of 3 requests arriving in an hour? What is the probability of at least 2 requests arriving in an hour? What is the probability that it will take less than 10 minutes to process a quote request? 0.63 What is the probability that it will take between 10 and 12 minutes to process a quote request? 0.07

More Questions What is the average number of requests waiting to be processed? What is the average number of requests in the system? What is the average waiting time? What is the average time spent in the system? What is the probability that a request needs to wait before being processed? What is the probability that there are no requests waiting in line? What is the probability that there are 4 requests in the system? 7?

Fomulas QuestionNotationFormula Average number of customers in the waiting line LqLq L q = 2 /[µ(µ - )] Average number of customers in the system L L = L q + /  Average waiting timeWqWq W q = L q / Average time in the systemWW = W q + 1/µ Probability that a customer has to wait PwPw P w = /  Probability that line is emptyP0P0 P 0 = 1 - /  Probability that there are n customers in the system PnPn P n = P 0 ( /  ) n

More Questions What is the average number of requests waiting to be processed? 1.33 What is the average number of requests in the system? 2 What is the average waiting time? 20 min What is the average time spent in the system? 30 min What is the probability that a request needs to wait before being processed? 0.67 What is the probability that there are no requests waiting in line? 0.33 What is the probability that there are 4 requests in the system? 7? 0.066, 0.020

In-Store Service Suppose that CrossChek Sporting Goods’ uptown location receives customers at an average rate of 10 per hour It takes CrossChek an average of 5 minutes to serve each customer CrossChek has observed that if the line at the checkout has 4 or more people (including the one being served), new arrivals will walk out the door without purchasing anything with 0.3 probability CrossChek estimates that the hourly cost associated with these customers leaving is equal to $100 times the probability of a customer leaving CrossChek is considering adding a new staff member at the cost of $12 per hour, that is expected to reduce the average service time to 3 minutes Should CrossChek hire?

In-Store Service Suppose that CrossChek Sporting Goods’ uptown location receives customers at an average rate of 10 per hour It takes CrossChek an average of 5 minutes to serve each customer CrossChek has observed that if the line at the checkout has 4 or more people (including the one being served), new arrivals will walk out the door without purchasing anything with 0.3 probability CrossChek estimates that the hourly cost associated with these customers leaving is equal to $100 times the probability of a customer leaving CrossChek is considering adding a new staff member, at the cost of $12 per hour, that is expected to reduce the average service time to 3 minutes Should CrossChek hire? Yes, costs are decreased by $12.50

Multiple Lines Another alternative that CrossChek is considering is adding a second cash. This would not improve service time, and would cost the company an extra $13.50 per hour. Is this a better option?