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**Process Analysis and Design**

Operations Strategy Process Analysis Manufacturing Services Service System Design Matrix Service Blueprinting Service Classifications Waiting Line Analysis 62 Process Analysis & Design - Manufacturing, Facility Layout, Services 62

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**Queues (Waiting Lines)**

People waiting to be served/machines waiting to be overhauled Can’t have inventory in services! The issue is the trade-off between cost of service and the cost of waiting Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Suggestions for Managing Queues**

Determine an acceptable waiting time Divert customer’s attention while waiting Inform your customers of what to expect Keep other employees out of sight Segment customers Train employees to be friendly Encourage customers during slack periods Adopt a long-term perspective Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Suggestions for Managing Queues**

For example, can control arrivals by: Restricting the line (short line) - e.g., Wendy’s drive-thru Post business hours Establishing specific hours for specific customers or price - e.g., run specials; increase price for adult haircuts Can also provide faster (or slower) servers, machines, layouts, set-up times, etc. Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Components of the Queuing Phenomenon**

Server(s) Waiting Line Servicing System Population Source? Infinite or Finite Service Rate? Constant or Variable Customer Arrivals Exit Finite: Number of machines needing repair when a company only has three machines. Infinite: The number of people who could wait in a line for gasoline. Constant: Items coming down an automated assembly line. Variable: People spending time shopping. Lamda = Arrival Rate Poisson Distribution - # arrivals in T If machine paced arrivals are constant Mu = service rate Follows Exponential Distribution Infinite Queue Length FCFS Balking or Reneging? 64 Process Analysis & Design - Manufacturing, Facility Layout, Services 64

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Queuing Components Arrivals from a finite population - Limited size customer pool (important distinction, as probabilities change after each customer) FCFS (First come, first served) - most common priority rule, but not only one - can have emergencies first, best customers first, triage, etc. Balking (look and then leave) vs. Reneging (wait for awhile and then decide to leave) Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Queuing Components (cont’d)**

Poisson Distribution: - The Poisson is the most common distribution used in queuing theory for arrivals - The Poisson distribution is discrete, as the number of arrivals must be an integer - The probability of n arrivals within a T minute period = PT(n)=(λT)n(e-λT)/n! Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Queuing Components (cont’d)**

Service Rates: - The capacity of the server (in units per time pd) (e.g., a service rate of 12 completions per hour) - Use the Exponential distribution when service times are random (as opposed to constant), where μ = avg # of customers served per time pd, and the probability the service time will be less than or equal to a time of length t: P = 1 – e-µt. Perceptions Management - What is an acceptable waiting time? - Install distractions and involve customers. - Get customer out of line. - Make conscious of time only if necessary - Keep unused resources out of sight Modify arrivals -Appointment Books, discounts Personality types - Express 63 Process Analysis & Design - Manufacturing, Facility Layout, Services 63

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**Line Structures Single Phase Multiphase One-person barber shop**

Car wash Hospital admissions Bank tellers’ windows Single Channel channel is number of servers phase is number of stops Multichannel (Also, “Mixed”; See text pages ) 65 Process Analysis & Design - Manufacturing, Facility Layout, Services 65

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**Properties of Waiting Line Models**

Source Model Layout Population Service Pattern 1 Single channel Infinite Exponential 2 Single channel Infinite Constant 3 Multichannel Infinite Exponential 4 Single or Multi Finite Exponential (See formulas for each model in text on page 253) These four models share the following characteristics: Single phase Poisson arrival FCFS Unlimited queue length 66 Process Analysis & Design - Manufacturing, Facility Layout, Services 66

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**Waiting Line Models Characteristics of a waiting line model:**

Lq = Average number in line Ls = Average number in system Wq = Average time in line Ws = Average time in system ρ = Utilization of Server Pn = Probability of exactly n in system nl ns tl ts Rho - Pn 67 Process Analysis & Design - Manufacturing, Facility Layout, Services 67

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**Characteris-tics of Waiting Lines Definition Model 1 (single channel, **

Characteris-tics of Waiting Lines Definition Model 1 (single channel, exp. service rate) Model 2 constant service rate) Lq Average number in line 2/[(-)] 2/[2(-)] Ls Avg. number in system /(-) Lq + (/) Wq Average time in line /[(-)] or Lq/ /[2(-)] Ws Average time in system 1/(-) or Wq +(1/) (“rho”) Utilization of server / - Pn Prob.of exactly n in system [1-(/)](/)n Po Prob. of exactly zero in system 1 - (/) Where = Arrival rate (e.g., = 2 would represent a mean arrival rate of 2 per minute), and = Service rate or avg number of customers served per time period (e.g., 1 per 3 mins =20 per hour). and must be in the same units. (corrected 5/3/05)

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**Example: Model 1 (worked problem)**

Drive-up window at a fast food restaurant. Customers arrive at the rate of 25 per hour. The employee can serve one customer every two minutes. Assume Poisson arrival and Exponential service rates. A) What is the average utilization of the employee? B) What is the average number of customers in line? C) What is the average number of customers in the system? D) What is the average waiting time in line? E) What is the average waiting time in the system? F) What is the probability that exactly two cars will be in the system? WP1 Process Analysis & Design - Manufacturing, Facility Layout, Services WP1

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**Example: Model 1 (worked problem)**

A) What is the average utilization of the employee? B) What is the average number of customers in line? WP2 Process Analysis & Design - Manufacturing, Facility Layout, Services WP2

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**Example: Model 1 (worked problem)**

C) What is the average number of customers in the system? D) What is the average waiting time in line? WP3 Process Analysis & Design - Manufacturing, Facility Layout, Services WP3

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**Example: Model 1 (worked problem)**

E) What is the average waiting time in the system? F) What is the probability that exactly two cars will be in the system (one being served and the other waiting in line)? WP4 Process Analysis & Design - Manufacturing, Facility Layout, Services WP4

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**Example: Model 2 (worked problem)**

An automated pizza vending machine heats and dispenses a slice of pizza in 4 minutes. Customers arrive at a rate of one every 6 minutes with the arrival rate exhibiting a Poisson distribution. Determine: A) The average number of customers in line. B) The average waiting time in the system. WP5 Process Analysis & Design - Manufacturing, Facility Layout, Services WP5

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**Example: Model 2 (worked problem)**

A) The average number of customers in line. Lq l 2 (10) 2 = = = .6667 2 m ( m - l ) (2)(15)(15 - 10) B) The average waiting time in the system. l 10 Wq = = = hr s = 4 mins 2 m ( m - l ) 2 ( 15 )( 15 - 10) 1 1 Ws Wq = + = hr s + = .1333 hrs = 8 mins m 15 / hr WP6 Process Analysis & Design - Manufacturing, Facility Layout, Services WP6

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**Approximating Customer Waiting Time**

A “quick and dirty” method has been developed to compute average waiting time for multiple servers (see text, pp ). No assumptions about the underlying distributions are required! All that is needed are 4 numbers – the average and standard deviation of the inter-arrival time and service time. 70 Process Analysis & Design - Manufacturing, Facility Layout, Services 70

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**Utilization and Time in System**

70 Process Analysis & Design - Manufacturing, Facility Layout, Services 70

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© The McGraw-Hill Companies, Inc., 1998 Irwin/McGraw-Hill 2 Chapter 7 TN Waiting Line Management u Waiting line characteristics u Some waiting line management.

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