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WEEK-16
WAITING LINE MANAGEMENT
Waiting lines abound in all sorts of service systems. And they
are non-value-
added occurrences. For customers, having to wait for service can
range from being acceptable (usually short waits), to being
annoying (longer waits), to being a matter of life and death(e,g.,
in emergencies). k?,- businesses, the costs of waiting comes from
lower productivity and competitive
disadvantage) For society, the costs are wasted resources
(e.g.., fuel consumption of cars stuck in traffic) and reduced
quality of life. Hence, it is important for system designers and
managers of existing service systems to fully appreciate the impact
of waiting lines.
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i() 527 hecorne.,s temporarily overloaded, giving. rise to
Waiting lines; at other times,
4 the system is idle because there are no customers: It follows
that in systems where variability is minimal or nonexistent
,waiting lines do not ordinarily
form. Managerial Implications of Waiting Lines Managers have a
number of very good reasons to be concerned with waiting
tines. Chief among those reasons are the following;
1. The cost to provide waiting space.
2. A possible loss of business should customers leave the line
before
being served or refuse to wait at all.
3. A possible loss of goodwill.
4. A possible reduction in customer satisfaction.
5. The resulting congestion that may disrupt other business
operatiosn
and/or customers.
Goal of waiting-line Analysis: '
The goal of queuing is essentially to minimize -total costs. 'i
here are two
basic categories of cost in queuing situation: those associated
with customers waiting for service and those associated with
capacity. Capacity costs are the
costs of maintaining the ability .to provide service. Examples
include the number of b-ayktrat a car wash, the number of checkouts
at a supeunarket, the n__..----- . . ).-)'S number of repair people
to handle equipment breakdowns, and the number
of lanes on a highway. en a service _ e ca acity is lost since
it
C) cannot be stored The customer waiting include the salaries
paid to
---- .._.
employees while they waitfor service (mechanics waiting for
tools, the drivers of trucks waiting to unload), the cost of the
space for waiting ( size of doctor's waiting room, length of
driveway at a car wash, fuel consumed
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by planes waiting to land), and any loss of business due to
customers refusing to wait and possibly going elsewhere in the
future.
A practical difficulty frequently encountered is pinning down
the cost of
' ,_customer waiting time, especially since major portions of
that cost are not a part of.accouniing data. One approach often
used is to treat waiting times or the line lengths as a policy
variable: A manager simply specifies an acceptable level of waiting
and directs that capacity be'established to
Lachieve that level.
Characteristics of waitin: Lines
There are numerous m ear from which an analyst can choose.
Naturally, much of the success of the anal is will depend on
choosing an appropriate model. Model choice is affected by the
characteristics of the system under investigation. The main
characteristics are
1. Population source 2. Number of servers (channels) 3. Arrival
and service patterns 4. Queue discipline (order of service)
Population Source "),4
" The approach to use in analyzing a queuing problem depends on
whether
the potential number of customers is limited. There are two
possibilities: infinite-source and finite-source populations. In an
infinite-source
situation, the potential number of customers greatly exceeds
system
capacity. Infinite-source situations exist whenever service is
tinrestricld.
Examples are supennarlcets, drugstores, banks, restaurants,
theatres, amusement centers, and toll bridges. Theoretically, large
numbers of
customers from the "calling population" can request service at
any time.
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When the poter.tial number.of customers is limited, .d
finite-source.
situation exists. An examples is the repairman responsible for a
certain number of machines in a company. The potential number of
machines
that might need repairs at any one time cannot .exceed the
number of
machines assigned to the repairer.
Number of Servers (Channels) 1 The capacity of queuing systems
is a function of the'Capacity of each
t\_/ server and the number of servers being used. The terms
server and
\,_,. channel are synonymous, and it is generally assumed that
each channel
v can handle one customer at a time. Systems can be either
single- or i-` ,,cf multiple-channel. Example of single-channel
systems are small grocery
---....,
stores with one checkout counter, some theatres, single-bty car
washes, and chive-in banks with one teller. Multiple-channel
systems (those with more than one server) are commonly found in
banks, at airline ticket counters, at auto service centers, and at
gas stations.
A related distinction is the number of stepS or phases in a
queuing system:For example, at theme parks, people go from one
attraction to
c.. ;) another. Each attraction constitutes a separate phase
where queues can form. Arrival and Service Patterns Waiting lines
area direct result of arrival and service variability. They
) ,, occur because random, highly variable arrival and service
patterns cause systems to be temporarily overloaded.
.1_14,1=fratry--___imst-ainces-tla.:abilities-
c-carrbe_clesr-i-13-ed:_-b-_y_-2theavetical-clistvilautiens.
- ,_-: Queue Discipline (`" Queue discipline refers to the order
in which customers are processed.
A11.1 but one of the models to be described shortly assume that
service is \-___
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t51.1 is TITS:- cane f7)=-. Ti-tr .7nIt theatres,
17.:StatUlailt.=. 10111--17,./ay stop 5ibis, reg ti 0,7";
Examples of systems that do not serve on a first-comc-- basi- d
e .., rn (----)
---,2 03,84y 0;,.R... 0-40--t..7614 hospital ernergeey, rush
ordbf-i-in a factory, and main a 3.44 ompute-T
processing of jobs. In these and similar situations, customers
do not all - --
represents the same waiting costs-;--those_with the hig.hest
C.O.StS4, e.g., the
most seriously ill) are_processed first, even
tlIol(),_ther_customers may have arrived earlier.
Measures of waiting Line Performance
The Operations manager typically looks t five measures when
evaluating existing or proposed service systems: 1. The average
number of customers waiting, either in line or in the
system.
2. The average time customers wait, either in line or inthe
system. 3. System utilization
-which refers to the percentage of capacity utilized. 4. The
implied cost of a given level of capacity and its related
waiting
line. 5. The probability that an arrival will have to wait for
service.
Of these measures, system utilization bears some elaboration. It
reflects the extent to which the servers are busy rather than idle.
On the surface, it
might seem that the operations manager would want to seek 100
percent
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