Waiting Line Management

Operations Management

Tapas MahapatraTapas Mahapatra

WAITING LINE MANAGEMENT

Waiting Time Everyday we encounter waiting lines in one or the other form. Line for railway ticket, waiting for a bus, waiting for canteen to open, waiting for turn in ATM, hold on telephone etc.Service mangers need to properly manage these customer waiting time to ensure both efficiency and that customers are not negatively affected by waiting to the point to taking their future business to elsewhere. There are two components of waiting time:1. actual waiting time2. Perceived waiting time by customer

Waiting Lines• Waiting lines occur in all sorts of systems• Wait time is non-value added

– Wait time range from the acceptable to the emergent• Short waits in a drive-thru• Sitting in an airport waiting for a delayed flight• Waiting for emergency service personnel

– Waiting time costs• Lower productivity• Reduced competitiveness• Wasted resources• Diminished quality of life

Waiting time and Good Service Customer satisfaction is key to success and providing customer satisfaction through managing customer’s perceived waiting time is an important parameter in taking competitive advantage. Factors to good service:1. Friendliness2. Knowledge of service provider3. Fast service

Waiting time pays a major role in fast service. Time is more valuable in more highly developed countries, customers are less willing to wait. Even willing to pay more for premium service.

Waiting time and good Service

Providing fast service does not mean providing service in specified time (e.g. boards displaying service time in bank for various service) but to satisfy the customer with a level of service to create a customer loyalty.

Queuing Theory

• Queuing theory– Mathematical approach to the analysis of waiting

lines– Applicable to many environments

• Call centers• Banks• Post offices• Restaurants• Theme parks• Telecommunications systems• Traffic management

The Difference Between Manufacturing and Service

TransformationProcess

Finished Goods

Manufacturing:

Customer

Efficiency versus F. G. Inventory

F. G. Inventory versusLevel of Service

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The Difference Between Manufacturing and Service

TransformationProcess

Services:

Customer

Efficiency versus Customer Service

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Why Is There Waiting?

• Waiting lines tend to form even when a system is not fully loaded– Variability

• Arrival and service rates are variable– Services cannot be completed ahead of time

and stored for later use

Waiting Lines: Managerial Implications

• Why waiting lines cause concern:– The cost to provide waiting space– A possible loss of business when customers leave the line

before being served or refuse to wait at all– A possible loss of goodwill– A possible reduction in customer satisfaction– Resulting congestion may disrupt other business operations

and/or customers

Efficiency and Customer Waiting time

Cost of waiting

Cost of service

cost

Waiting Time

Classical operations Management model

Efficiency and Customer Waiting time –Trade off in waiting line management

Waiting of customer is taken as inventory in manufacturing. If process efficiency is increased by making the customer to wait, it is like increasing in process inventory cost.

If waiting time is reduced, the cost of service is increased as more workers are engaged to provide the service and they would be idle if customer is not available.

Proper design of the service delivery process, workers an often be productive during idle time.

Level of Service versus Process Efficiency

Cost

Level of Service

Good (Fast) Poor (Slow)

Fast Service (Expensive)

Slow Service (Cheap)

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Waiting Line Management• The goal of waiting line management is to minimize total

costs:– Costs associated with customers waiting for service– Capacity cost

Customer Satisfaction

Customer satisfaction is related to the comparison between customer’s expectation of a service performance and his perception of that performance.

If perceived performance meets the expectation, customer would be satisfied, if performance falls it results in customer dissatisfaction and if exceeds expectation , it results in delighted customer.

In marketing terminology, satisfaction is said to be related to disconfirmation (i.e. difference) between expected and perceived performance.

The Role of Satisfaction in a Customer Behavior Model

Expectations

SATISFACTION

Performance Disconfirmation

IntentionsAttitudes Future Behavior

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The Role of The Role of Satisfaction Satisfaction in a in a Customer Customer Behavior Behavior ModelModel

Exhibit 16.3

SATISFACTION

Customer Expectations It is defined as customers’ preconceived notion

of what level of service he or she should receive from a particular business or organisation ( varies from organisation to organisation like expectation from dhaba and five star hotel)

Source of expectations :

1.Advisement

2.Prior experience

3.Word of mouth

4.Overall service delivery package (high price service –less or no waiting)

Perceived Waiting Time

Perceived waiting time is the amount of time a customer believes he or she has waited before receiving the service.

It is not the actual time ???

Waiting time for tea is different from waiting for exams result …

Factors Affecting Customer Satisfaction with Waiting

• Firm-Related–Unfair versus fair waits

–Uncomfortable versus comfortable waits

–Unexplained versus explained waits

–Initial versus subsequent waits

• Customer-Related–Solo versus group waits

–Waits for more valuable versus less valuable services

–Customer value systems

–Customer’s current attitude

Factors Affecting Customer’s satisfaction with Waiting

Categories:

1.Firm related Factors

2.Customer related Factors

3.Both firm and customer related factors

Firm Related Factors

1.Unfair versus Fair waits – depends on queue

design, service system design and contact hours. If first come first serve basis is followed, customer feels fairness like if many service points are available, same queue can be made and which ever station is free takes next customer like in Railways booking office.

Giving importance to telephone call than physically present customer also creates unfairness.


2. Uncomfortable versus comfortable waits- if a person is uncomfortable, time passes more slowly. Comfort by lights, music, air-conditioners, seating etc. can be used.

Restaurants provide lounges for waiting.

3. Unexplained Versus explained waits – if waiting time is explained to customer for example train late arrival times informed to customer, customer feels more satisfied.

Unused capacity in terms of idle workers or idle workstations is a form of unexplained waits. Waiting for unknown duration is also causes feeling of long waiting.


4. Initial versus subsequent waits

Customer feels more dissatisfied with initial waits prior to entering a service delivery system rather than subsequent waits as see them outside of system.

Initial waiting must be minimized.

Customer Related Factors

These can not be controlled by the firm.

1.Solo versus group waiting

2.Waits for more valuable versus less valuable services

3. Customer value system - customers who place a premium on obtaining fast service do not mind paying for it and do not want to waste time in waiting.

4.Customer’s current attitude – customers attitude just prior to entry impact on their satisfaction. If he is upset, he will be dissatisfied.

Both Firm an customer Related Factors

1.Occupied versus unoccupied waits – reading materials, interesting displays, mirrors, and music, gambling casinos in night clubs to entertain during waiting, create win-win situation. Also customers can be made busy in useful activities like Availability of internet, Fax, PC etc for customers to do their jobs.

2.Anxious versus calm waits – Customer’s anxiety regarding the nature of the service or the uncertainty of the wait may effect customer satisfaction. Like waiting in emergency room, waiting for lab. Report etc. It may be reduced by explaining the procedures or reading materials.

A Focus On Providing Fast service

This can be brought by :

1.System design concept – by adopting split core strategy by having first core – front –of-the house – interact directly with customer and adopt chase strategy and Second core – backroom – accomplish all the activities which can be done without customer’s presence adopting level-type strategy.

By reducing set up time, worker can switch from one job to other and use idle time.

2. Cross Training of Employees to perform variety of jobs.

Waiting line Characteristics

Waiting line phenomenon has Six components :

1.Population

2.Arrival characteristics

3.Physical features of the line

4.Customer Selection

5.Service facility structure

6.Exit


PopulationI

Arrival

II

Service System

Physical

Features

III

Selection

IVServiceFacility

Exit

VI


1. Population source – finite population or infinite population (finite population – when customer leaves population reduces)

2. Arrival characteristics – arrival pattern (controllable like controlling by prices or uncontrollable like emergency medical demand), size of arrival units (one at a time or in batch like shares) , distribution pattern (time between arrival is constant or follow statistical distribution- Exponential or Poisson, Erlang others) and degree of patients (patient and impatient)

Balking Behaviour – customer comes, surveys the facility and waiting line and decide to leave

Reneging Behaviour – Customer comes, surveys, joins the line for some time and leaves

Jockeying – customer switches from one queue to other queue thinking that that queue is fast moving

Poison distribution :is a discrete probability distribution of number of customers arriving in some time interval

In many practical situations, the inter arrival time is approximated by an exponential distribution

Exponential Probability density function

t

F(t) F(t)

tExponential cumulative Probability density function

λ= arrival rate λ= arrival rate

Erlang distribution

F(t)

t

K=2

K=3

K= phases of services , without completion of all phases service is not completed


3. Physical features of line

a) length – infinite potential length like line of vehicles backed up for miles at a bridge or limited line capacity like in gas station, loading docks and parking lots.

b) No. of lines – single line or single file or multiple lines


4. Customer Selection

Queuing discipline – A queuing discipline is priority rules to determine the order of service to customer in waiting line these are First cum first serve or first in first out Shortest processing time reservations firstEmergencies firstLimited needs like single transactions only in a bank or cash only in a market Others – highest profile customers first, largest orders first, best customers first etc.


5. Service Facility Structure

a) Single channel, single line

b) Single channel multiphase

c) Multi channels, single phase

d) Multi channel, multiphase

Service rate :

a) constant rate – machine controlled operations

b) Erlang distribution – single channel, multi –

service situation , practical applications are rare

c) exponential distribution – used to approximate

actual situations

Waiting line Characteristics 6. Exit – two scenario

a. Customer may return to the source population

– like machine with fast breakdown problem or

reoccurring common cold.

b. Low probability of Re-Service – machine with

less probability of breakdown or health problem

Waiting Line Equations There are seven different waiting line systems

and respective steady state equations

Model 1

Single channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Exponential service pattern, Unlimited permissible queue length.

Example : Drive –in teller at bank, One lane toll bridge

Population Source

• Infinite source– Customer arrivals are unrestricted– The number of potential customers greatly

exceeds system capacity• Finite source

– The number of potential customers is limited

Channels and Phases

• Channel– A server in a service system– It is assumed that each channel can handle

one customer at a time• Phases

– The number of steps in a queuing system

Common Queuing Systems

Arrival and Service Patterns• Arrival pattern

– Most commonly used models assume the arrival rate can be described by the Poisson distribution

• Arrivals per unit of time– Equivalently, interarrival times are assumed to follow the

negative exponential distribution• The time between arrivals

• Service pattern– Service times are frequently assumed to follow a negative

exponential distribution

Poisson and Negative Exponential

Waiting Line Equations

Equation for Model 1

nl= λ2 / µ(µ -λ )

ns= λ / (µ -λ )

tl= λ / µ(µ -λ )

ts= λ / µ(µ -λ )

Pn = ( 1-λ/µ)(λ/µ)n

ρ = λ/µ

Where

µ= service rate

λ= arrival rate

ρ = potential utilisation of service facilities

1/µ= Average service time

1/λ= Average time between arrival

nl= Average number waiting in line

ns= Average number in system (including any being served)

tl= Average time waiting in line

ts= Average total time in system (including time to be served)

Pn = probability of occurrence

Waiting Line Equations Model 2

Single channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Constant service pattern, Unlimited permissible queue length.

Example : Automatic car wash, roller coaster rides in amusement park

Waiting Line Equations Equation for Model 2

nl= λ2 / 2µ(µ -λ )

ns= nl+ λ/µ

tl= λ / 2µ(µ -λ )

ts= t1 + 1/µ

Where

µ= service rate

λ= arrival rate

ρ = potential utilisation of service facilities

1/µ= Average service time

1/λ= Average time between arrival

nl= Average number waiting in line

ns= Average number in system (including any being served)

tl= Average time waiting in line

ts= Average total time in system (including time to be served)


Single channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Exponential service pattern, limited permissible queue length.

Example : Ice cream stand, cashier in a restaurant


Single channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Discrete distribution service pattern, unlimited permissible queue length.

Example : Empirically derived distribution of flight time for a transcontinental flight


Single channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Erlang service pattern, unlimited permissible queue length.

Example : one person barber shop


Multi channel layout, single service phase, infinite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Exponential service pattern, unlimited permissible queue length.

Example : Parts counter in auto agency, two lane toll bridge


Single channel layout, single service phase, finite source population, Poisson arrival pattern, First come first serve (FCFS) queue discipline, Exponential service pattern, unlimited permissible queue length.

Example : Machine breakdown and repair in factory

Two Typical waiting line situations (single server queuing model M/M/1- Markovian or exponential)

Problem 1 : Consumer in line

A bank wants to know how many customers (or cars) are waiting for a drive in teller, how long they have to wait, the utilization of the teller

Problem 2 :Equipment selection

A franchisee for Robot car Wash must decide which equipment to purchase out of a choice of three. Larger unit cost more, but wash cars faster. To make the decision, costs are related to revenue.

Problem 1 : Consumer in lineA nationalized bank is considering opening a drive –in

window for customer service. Management estimates that the customers will arrive in their cars at a rate of 15 per hours. The teller who will staff the window can service customers at the rate of one every three minutes. Assuming Poisson arrival and exponential service, find

i) Utilisation of the teller

ii) Average number in the waiting line

iii)Average number in the system

iv)Average waiting time in line

v) Average waiting time in the system, including service.

Problem 1 : Consumer in linei) The average Utilisation of the teller is

Given average service rate is 3 minutes i.e. average service time = 1/ µ = 3 minutes = 1/20 hour

therefore, µ, service rate = 20 customers / hour

and arrival rate = 15 / hour

utilisation rate = ρ = λ /µ = 15 / 20 = 75 percent

ii) Average number in the waiting line

nl= λ2 / µ(µ -λ ) = 15 2 / 20(20-15) = 2.25 customer

iii) Average number in the system

ns= nl+ λ/µ = 2.25 + 15/20 = 3 customers

Problem 1 : Consumer in lineiv) Average waiting time in line

tl= λ / µ(µ -λ ) = 15/ 20(20-15) = 0.15 hrs. or 9 minutes

v) Average waiting time in the system, including service

ts= tl + 1/µ = 0.15 + 1/20 = 0.2 hrs. or 12 minutes

Problem 2 : Equipment SelectionThe robot company franchises combination of gas and car wash station throughout the united states,. Robot gives a free car wash for a gasoline fill-up, or, for a wash alone, charges $0.50. Past experience shows that the number of customers that have car washes following fill-ups is about the same as for a wash alone. The average profit on a gasoline fill-up is about $0.70 and the costs of car wash to Robot is $0.10. Robot works for 14 hours per day.

Robot has three power units and drive assemblies, and a franchisee must select the unit preferred. Unit 1 can wash cars at the rate of one every five minutes and is leased for $12 per day. Unit 2, a larger unit, can wash cars at the rate of one every four minutes but costs $ 16 per day. Unit 3, the largest, costs $22 per day and can wash a car in 3 minutes.

Problem 2 : Equipment SelectionThe franchisee estimates that customers will not wait in line more than five minutes for a car wash. A longer time will cause Robot to lose both gasoline sale and car wash sales. If the estimate of customer arrivals resulting in washes in 10 per hour, which was unit should be selected?

Unit 1 : service rate µ = 12 per hour ( 1 per 5 minutes)

arrival rate λ = 10 per hour

Average waiting time of customer (constant service pattern

Model 2)

tl= λ / 2µ(µ -λ ) = 10/ 2 x12(12-10) = 0.208 hours =

12 ½ minutes

Problem 2 : Equipment SelectionUnit 2 : service rate µ = 15 per hour ( 1 per 4 minutes)

arrival rate λ = 10 per hour

Average waiting time of customer (constant service pattern

Model 2)

tl= λ / 2µ(µ -λ ) = 10/ 2 x15(15-10) = 0.067 hours =

4 minutes

If waiting time is only criteria, unit 2 is to be selected as customer will not wait for more than five minutes while in unit 1 customer has to wait for 12 ½ minutes.

But we must look at the profit difference between two.

Problem 2 : Equipment Selection

With unit 1, some customers would leave because of longer wait. We can calculate the lost sales with unit one by inserting i=5minutes or 1/12hours (the average length of time customer will wait) and solve for λ (arrival rate) as this will be effective arrival rate.

tl= λ / 2µ(µ -λ ) or λ = 2 t l µ2 / (1 +2 t l µ )

λ = 2 (1/12) (12) 2 / ( 1 + 2(/120(12)) = 8 per hours

as original estimated arrivals are 10 customers per hours, there is a loss of 2 customers per hours

loss of profit = 2 customers per hour x 14 hours x average of fill up profit and car wash profit

= 2 x 14 x ½ ($0.70 + $0.50- $0.10) = $15.40 per day

Additional cost for unit 2 = $ 2 per day , Hence unit 2 is preferable. Unit 3 is not considered as five minute wait is satisfied by unit 2

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Waiting Line Management