Nigel S., Chambers S., Johnson R. Operations Management
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and expanding on the demand side is sometimes called ‘forward’ or ‘downstream’ vertical
integration.
2 The extent of vertical integration. How far should an operation take the extent of its vertical
integration? Some organizations deliberately choose not to integrate far, if at all, from
their original part of the network. Alternatively, some organizations choose to become
very vertically integrated.
3 The balance among stages. How exclusive should the relationship be between operations.
A totally balanced network relationship is one where one operation produces only for
the next stage in the network and totally satisfies its requirements. Less than full balance
allows each operation to sell its output to other companies or to buy in some of its supplies
from other companies.
Making the outsourcing / vertical integration decision
Whether it is referred to as do-or-buy, vertical integration or no vertical integration,
in-house or outsourced supply, the choice facing operations is rarely simple. Organizations
in different circumstances with different objectives are likely to take different decisions.
Yet the question itself is relatively simple, even if the decision itself is not: ‘Does in-house
or outsourced supply in a particular set of circumstances give the appropriate perform-
ance objectives that it requires to compete more effectively in its markets?’ For example,
if the main performance objectives for an operation are dependable delivery and meeting
short-term changes in customers’ delivery requirements, the key question should be: ‘How
does in-house or outsourcing give better dependability and delivery flexibility performance?’
This means judging two sets of opposing factors – those which give the potential to improve
performance and those which work against this potential being realized. Table 6.1 sum-
marizes some arguments for in-house supply and outsourcing in terms of each performance
objective.
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Table 6.1 How in-house and outsourced supply may affect an operation’s performance objectives
Performance objective
Quality
Speed
Dependability
Flexibility
Cost
‘Buy it in’ outsourced supply
Supplier may have specialized knowledge
and more experience, also may be motivated
through market pressures, but communication
more difficult.
Speed of response can be built into the
supply contract where commercial pressures
will encourage good performance, but there
may be significant transport/delivery delays.
Late-delivery penalties in the supply contract
can encourage good delivery performance,
but organizational barriers may inhibit in
communication.
Outsource suppliers may be larger with wider
capabilities than in-house suppliers and have
more ability to respond to changes, but may
have to balance conflicting needs of different
customers.
Probably the main reason why outsourcing
is so popular. Outsourced companies can
achieve economies of scale and they are
motivated to reduce their own costs because
it directly impacts on their profits, but costs
of communication and coordination with
supplier need to be taken into account.
‘Do it yourself’ in-house supply
The origins of any quality problems are usually
easier to trace in-house and improvement can
be more immediate but there can be some risk
of complacency.
Can mean synchronized schedules which
speeds throughput of materials and information,
but if the operation has external customers,
internal customers may be low-priority.
Easier communications can help dependability,
but, if the operation also has external
customers, internal customers may receive
low priority.
Closeness to the real needs of a business
can alert the in-house operation to required
changes, but the ability to respond may be
limited by the scale and scope of internal
operations.
In-house operations do not have to make the
margin required by outside suppliers so the
business can capture the profits which would
otherwise be given to the supplier, but relatively
low volumes may mean that it is difficult to gain
economies of scale or the benefits of process
innovation.
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Deciding whether to outsource
Although the effect of outsourcing on the operation’s performance objective is important, there
are other factors that companies take into account when deciding if outsourcing an activity is
a sensible option. For example, if an activity has long-term strategic importance to a company,
it is unlikely to outsource it. For example, a retailer might choose to keep the design and
development of its web site in-house even though specialists could perform the activity at less
cost because it plans to move into web-based retailing at some point in the future. Nor would
a company usually outsource an activity where it had specialized skills or knowledge. For
example, a company making laser printers may have built up specialized knowledge in the
production of sophisticated laser drives. This capability may allow it to introduce product or
process innovations in the future. It would be foolish to ‘give away’ such capability. After these
two more strategic factors have been considered the company’s operations performance can
be taken into account. Obviously if its operations performance is already too superior to any
potential supplier, it would be unlikely to outsource the activity. But also even if its perform-
ance was currently below that of potential suppliers, it may not outsource the activity if it feels
that it could significantly improve its performance. Figure 6.3 illustrates this decision logic.
Chapter 6 Supply network design
145
Figure 6.3 The decision logic of outsourcing
The market for notebook computers is a fast-evolving and
competitive one. Brands such as Dell, Sony, Fujitsu and
Apple as well as many smaller brands vie for customers’
attention. Yet few who buy these products know that the
majority of the world’s notebooks, including most of those
sold by the big names, are made by a small number of
Taiwanese and Korean manufacturers. Taiwanese firms
alone make around 60 per cent of all notebooks in the
world, including most of Dell, Compaq and Apple
machines. And this group of Taiwanese manufacturers is
dominated by Hon Hai, Quanta and Compal. In a market
with unremitting technological innovation and fierce price
competition, it makes sense to outsource production to
companies that can achieve the economies that come with
high-volume manufacture as well develop the expertise
which enables new designs to be put into production
without the cost overruns and delays which could ruin a
new product launch. However, the big brand names are
keen to defend their products’ performance. Dell, for
example, admits that a major driver of its outsourcing
Short case
Behind the brand names
4
policy is the requirement to keep costs at a competitive
level, but says that it can ensure product quality and
performance through its relationship with its suppliers.
‘The production lines are set up by Dell and managed by
Dell’, says Tony Bonadero, Director of Product Marketing
for Dell’s laptop range. Dell also imposes strict quality
control and manages the overall design of the product.
Outsourcing is a strategic
decision
Source: Rex Features
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Outsourcing and offshoring
Two supply network strategies that are often confused are those of outsourcing and offshoring.
Outsourcing means deciding to buy-in products or services rather than perform the activities
in-house. Off-shoring means obtaining products and services from operations that are based
outside one’s own country. Of course, one may both outsource and offshore as illustrated in
Figure 6.4. Offshoring is very closely related to outsourcing and the motives for each may be
similar. Offshoring to a lower-cost region of the world is usually done to reduce an operation’s
overall costs as is outsourcing to a supplier that has greater expertise or scale or both.
5
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Figure 6.4 Offshoring and outsourcing are related but different
In many instances there has been fierce opposition to companies outsourcing some of their
processes. Trade unions often point out that the only reason that outsourcing companies
can do the job at lower cost is that they either reduce salaries or reduce working condi-
tions, or both. Furthermore, they say, flexibility is only achieved by reducing job security.
Employees who were once part of a large and secure corporation could find themselves
as far less secure employees of a less benevolent employer with a philosophy of permanent
cost-cutting. Even some proponents of outsourcing are quick to point out the problems.
There can be significant obstacles, including understandable resistance from staff who
find themselves ‘outsourced’. Some companies have also been guilty of ‘outsourcing a
problem’. In other words, having failed to manage a process well themselves, they ship
it out rather than face up to why the process was problematic in the first place. There
is also evidence that, although long-term costs can be brought down when a process is
outsourced, there may be an initial period when costs rise as both sides learn how to
manage the new arrangement.
Critical commentary
The location of capacity
It was reputedly Lord Sieff, one-time boss of Marks and Spencer, the UK-based retail
organization, who said, ‘There are three important things in retailing – location, location and
location’, and any retailing operation knows exactly what he meant. Get the location wrong
and it can have a significant impact on profits, or service. For example, mislocating a fire
service station can slow down the average journey time of the fire crews in getting to the fires;
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locating a factory where there is difficulty attracting labour with appropriate skills will affect
the effectiveness of the factory’s operations. Location decisions will usually have an effect on
an operation’s costs as well as its ability to serve its customers (and therefore its revenues).
Also, location decisions, once taken, are difficult to undo. The costs of moving an operation
can be hugely expensive and the risks of inconveniencing customers very high. No operation
wants to move very often.
Reasons for location decisions
Not all operations can logically justify their location. Some are where they are for historical
reasons. Yet even the operations that are ‘there because they’re there’ are implicitly making a
decision not to move. Presumably their assumption is that the cost and disruption involved
in changing location would outweigh any potential benefits of a new location. Two stimuli
often cause organizations to change locations: changes in demand for their goods and services,
and changes in supply of their inputs.
Changes in demand. A change in location may be prompted by customer demand shifting.
For example, as garment manufacture moved to Asia, suppliers of zips, threads, etc. started
to follow them. Changes in the volume of demand can also prompt relocation. To meet
higher demand, an operation could expand its existing site, or choose a larger site in another
location, or keep its existing location and find a second location for an additional operation;
the last two options will involve a location decision. High-visibility operations may not
have the choice of expanding on the same site to meet rising demand. A dry cleaning service
may attract only marginally more business by expanding an existing site because it offers a
local, and therefore convenient, service. Finding a new location for an additional operation
is probably its only option for expansion.
Changes in supply. The other stimulus for relocation is changes in the cost, or availability,
of the supply of inputs to the operation. For example, a mining or oil company will need to
relocate as the minerals it is extracting become depleted. A manufacturing company might
choose to relocate its operations to a part of the world where labour costs are low, because
the equivalent resources (people) in its original location have become relatively expensive.
Sometimes a business might choose to relocate to release funds if the value of the land it
occupies is worth more than an alternative, equally good, location.
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Finding a suitable site for any operation can be a political
as well as an economic problem. It certainly was when
Tata, the Indian company, unveiled its plans for the
Nano in 2007. Named the ‘1 lakh car’ (in India one lakh
means 100,000), it would be the cheapest car in the
world, with the basic model priced at 100,000 rupees,
or $2,500, excluding taxes. The price was about half
of existing low-cost cars. And the site chosen by Tata
was equally bold. It was to be made at Singur, in the
Indian state of West Bengal, a populous state with
Calcutta (now called Kolkata) as its capital. Although the
Communist Party had ruled the state for four decades,
the West Bengal government was keen to encourage
Short case
The Tata Nano finds a
new home
6
the Nano plant. It would bring much-needed jobs and
send a message that the state welcomed inward
investment. In fact, it had won the plant against stiff
competition from rival states.
➔
Source: Getty Images
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The objectives of the location decision
The aim of the location decision is to achieve an appropriate balance between three related
objectives:
● the spatially variable costs of the operation (spatially variable means that something
changes with geographical location);
● the service the operation is able to provide to its customers;
● the revenue potential of the operation.
In for-profit organizations the last two objectives are related. The assumption is that the
better the service the operation can provide to its customers, the better will be its potential
to attract custom and therefore generate revenue. In not-for-profit organizations, revenue
potential might not be a relevant objective and so cost and customer service are often taken
as the twin objectives of location. In making decisions about where to locate an operation,
operations managers are concerned with minimizing spatially variable costs and maximizing
revenue and customer service. Location affects both of these but not equally for all types of
operation. For example, with most products, customers may not care very much where they
were made. Location is unlikely to affect the operation’s revenues significantly. However,
the costs of the operation will probably be very greatly affected by location. Services, on the
other hand, often have both costs and revenues affected by location. The location decision for
any operation is determined by the relative strength of supply-side and demand-side factors
(see Fig. 6.5).
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Controversially, the state government had
expropriated land for the factory using an old law dating
from 1894, which requires private owners to sell land
for a ‘public purpose’. The government justified this
action by pointing out that over 13,000 people had
some kind of claim to parts of the land required for the
new plant. Tata could not be expected to negotiate, one
by one, with all of them. Also financial compensation was
offered at significantly above market rates. Unfortunately
about 2,250 people refused to accept the offered
compensation. The political opposition organized mass
protests in support of the farmers who did not want to
move. They blocked roads, threatened staff and even
assaulted an employee of a Tata supplier. In response,
Ratan Tata, chairman of the Tata group, threatened to
move the Nano plant from the state if the company
really was not wanted, even though the company
had already invested 15 billion rupees in the project.
Eventually, exasperated with being caught in the
‘political crossfire’, Tata said it would abandon its
factory in the state. Instead, the company selected a
location in Gujarat, one of India’s most industrialized
states, which quickly approved even more land than
the West Bengal site.
Figure 6.5 Supply-side and demand-side factors in location decisions
Spatially variable costs
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Supply-side influences
Labour costs. The costs of employing people with particular skills can vary between different
areas in any country, but are likely to be more significant when international comparisons
are made. Labour costs can be expressed in two ways. The ‘hourly cost’ is what firms have to
pay workers on average per hour. However, the ‘unit cost’ is an indication of the labour cost
per unit of production. This includes the effects both of productivity differences between
countries and of differing currency exchange rates. Exchange rate variation can cause unit costs
to change dramatically over time. Yet in spite of this, labour costs exert a major influence on
the location decision, especially in some industries such as clothing, where labour costs as a
proportion of total costs are relatively high.
Land costs. The cost of acquiring the site itself is sometimes a relevant factor in choosing
a location. Land and rental costs vary between countries and cities. At a more local level,
land costs are also important. A retail operation, when choosing ‘high-street’ sites, will pay a
particular level of rent only if it believes it can generate a certain level of revenue from the site.
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Tesco is an international retailer with sales in excess of
£50 billion, operating around 4,000 stores worldwide,
employing almost half a million people and serving millions
of customers each week. It sells a wide range of items
including groceries, petrol, financial services, electrical
goods, household items, toys and even furniture. Although
based in the UK Tesco now trades all over the world. One
of its big successes is Thailand, where it has 476 stores
and employs over 36,000 people. Tesco’s expansion
strategy is founded on the need to provide quality products,
convenient locations and opening hours and value for
money. The company has come to realize that international
markets need differing local approaches, with local supply
chains, different store formats and sensitivity to local
traditions. So how does Tesco (branded ‘Tesco Lotus’ in
Thailand) adapt its operating practice to local conditions?
Some things are relatively straightforward. For
example, those stores with limited opening hours open at
9.09 precisely, as Thais believe these numbers bring good
fortune. Other things are based on a thorough understanding
of local customers. They discovered that around 5% of
their customers were actually small family-run stores
taking advantage of Tesco’s lower prices. Rather than
discourage this they developed their ‘Club Pack’ products
that shopkeepers could break up and sell in their own
stores at a good profit. They also investigated the shopping
experience their Thai customers really want. ‘We started
out by asking our customers what they want our stores to
sell and look like. From the responses that we received, we
realized that the optimal solution would be best delivered
by Tesco Lotus constructing its own malls’ (Mrs Veena
Arunyakasem, Mall and Media Director, Tesco Lotus).
So, they developed two new concepts, the Lifestyle
Shopping Mall and Community Mall. Lifestyle Shopping
Short case
Tesco Thailand
7
Malls contain the flagship hypermarket stores and other
shops, including restaurants and banks, promoting
high-quality local brands rather than expensive imported
brands. ‘These “lifestyle shopping malls” provide better
service and increased convenience to our customers.
The biggest beneficiaries will be our upcountry customers
who have previously lived a long way from the nearest
cinema’ (Gwyn Sundhagul, Tesco Lotus Director and
Chief Marketing Officer).
Community Malls are smaller and emphasize easy
access to local neigbourhoods.
Other local developments take account of cultural
sensitivities. Thais greatly admire individuals and
organizations that help the poor. So Tesco set up
‘Tesco for Thais’, a non-profit charitable foundation.
The green agenda is also important in Thailand and
large organizations are expected to lead the way. In 2004
Tesco opened its first ‘green’ superstore in Bangkok.
This store includes a range of energy-saving initiatives
including recycling and the use of rainwater, with its air
conditioning run by solar panels, the size of three football
pitches, on the roof.
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Energy costs. Operations which use large amounts of energy, such as aluminium smelters, can
be influenced in their location decisions by the availability of relatively inexpensive energy.
This may be direct, as in the availability of hydroelectric generation in an area, or indirect,
such as low-cost coal which can be used to generate inexpensive electricity.
Transportation costs. Transportation costs include both the cost of transporting inputs
from their source to the site of the operation, and the cost of transporting goods from the
site to customers. Whereas almost all operations are concerned to some extent with the
former, not all operations transport goods to customers; rather, customers come to them
(for example, hotels). Even for operations that do transport their goods to customers (most
manufacturers, for example), we consider transportation as a supply-side factor because as
location changes, transportation costs also change. Proximity to sources of supply dominates
the location decision where the cost of transporting input materials is high or difficult. Food
processing and other agriculture-based activities, for example, are often carried out close to
growing areas. Conversely, transportation to customers dominates location decisions where
this is expensive or difficult. Civil engineering projects, for example, are constructed mainly
where they will be needed.
Community factors. Community factors are those influences on an operation’s costs which
derive from the social, political and economic environment of its site. These include:
● local tax rates
● capital movement restrictions
● government financial assistance
● government planning assistance
● political stability
● local attitudes to ‘inward investment’
● language
● local amenities (schools, theatres, shops, etc.)
● availability of support services
● history of labour relations and behaviour
● environmental restrictions and waste disposal
● planning procedures and restrictions.
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Figure 6.6 A major influence in where businesses locate is the cost of operating at different
locations. But, total operating cost depends on more than wage costs, or even total labour
costs (which includes allowances for different productivity rates). The chart illustrates what
makes up the cost of shirts sold in France. Remember, the retailer will often sell the item for
more than double the cost
8
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Demand-side influences
Labour skills. The abilities of a local labour force can have an effect on customer reaction
to the products or services which the operation produces. For example, ‘science parks’ are
usually located close to universities because they hope to attract companies that are interested
in using the skills available at the university.
The suitability of the site itself. Different sites are likely to have different intrinsic character-
istics which can affect an operation’s ability to serve customers and generate revenue. For
example, the location of a luxury resort hotel which offers up-market holiday accommoda-
tion is very largely dependent on the intrinsic characteristics of the site. Located next to the
beach, surrounded by waving palm trees and overlooking a picturesque bay, the hotel is very
attractive to its customers. Move it a few kilometres away into the centre of an industrial
estate and it rapidly loses its attraction.
Image of the location. Some locations are firmly associated in customers’ minds with a
particular image. Suits from Savile Row (the centre of the up-market bespoke tailoring dis-
trict in London) may be no better than high-quality suits made elsewhere but, by locating its
operation there, a tailor has probably enhanced its reputation and therefore its revenue. The
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Similar companies with similar needs often cluster
together in the same location. For example, knitted
garment manufacturers dominate parts of Northern Italy.
Perhaps the most famous location cluster is in the area
south of San Francisco known as Silicon Valley,
acknowledged as the most important intellectual and
commercial hub of high-tech business. Yet Silicon Valley
is being challenged by up-and-coming locations, especially
in developing countries. Here are two examples.
Bangalore in India has for many years been attractive
in the computer industry. Back in the 1980s the area
attracted software code-writing business from Western
multinationals attracted by the ready availability of
well-educated, low-cost English-speaking software
technicians. Now the area has attracted even more, and
even more sophisticated, business. Companies such as
Intel, Sun Microsystems, Texas Instruments and Cisco
have a presence in the area and are using their Bangalore
development centres to tackle cutting-edge projects. The
biggest draw is still India’s pool of high-quality, low-cost
software engineers. Each year Bangalore alone graduates
25,000 computer science engineers, almost the number
who graduate in the entire USA. More significantly, the
average wage of a top-class graduate software engineer
is around one fifth of that in the USA. Nor is there any
lack of multinational experience. For years Western
(especially US) high-tech companies have employed
senior Indian-born engineers. Equipped with Silicon
Valley experience, some of these engineers are happy
to return home to manage development teams.
Short case
Developing nations challenge
Silicon V
alley
9
The high-tech research and development activities
around Shanghai in China do not have the pedigree
of those in India, but are increasingly seen as
significant in the global technology industry. ‘Over
the next ten years, China will become a ferociously
formidable competitor for companies that run the entire
length of the technology food chain’, according to
Michael J. Moritz, a Californian venture-capital firm
specializing in high-tech businesses. And although
most industry commentators admit that China has far
to go, the combination of the availability of a highly
skilled and well-educated workforce, often at even
lower cost than in India, together with the Chinese
government encouragement of joint ventures with
multinationals is seen as a big impetus to high-tech
growth. Multinationals such as Alkatel, the French
telecom giant, and Matsushita, Japan’s largest
consumer electronics company, as well as chip
manufacturer Intel are all investing in research and
development facilities.
Source: Getty Images/AFP
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product and fashion design houses of Milan and the financial services in the City of London
also enjoy a reputation shaped partly by that of their location.
Convenience for customers. Of all the demand-side factors, this is, for many operations, the
most important. Locating a general hospital, for instance, in the middle of the countryside
may have many advantages for its staff, and even perhaps for its costs, but it clearly would
be very inconvenient to its customers. Those visiting the hospital would need to travel long
distances. Because of this, general hospitals are located close to centres of demand. Similarly
with other public services and restaurants, stores, banks, petrol filling stations etc., location
determines the effort to which customers have to go in order to use the operation.
Locations which offer convenience for the customer are not always obvious. In the 1950s
Jay Pritzker called into a hotel at Los Angeles airport for a coffee. He found that, although
the hotel was full, it was also for sale. Clearly there was customer demand but presumably the
hotel could not make a profit. That is when he got the idea of locating luxury hotels which
could command high revenues at airports where there was always demand. He called his
hotel chain Hyatt; it is now one of the best-known hotel chains in the world.
Location techniques
Although operations managers must exercise considerable judgement in the choice of altern-
ative locations, there are some systematic and quantitative techniques which can help the
decision process. We describe two here – the weighted-score method and the centre-of-gravity
method.
Weighted-score method
The procedure involves, first of all, identifying the criteria which will be used to evaluate the
various locations. Second, it involves establishing the relative importance of each criterion
and giving weighting factors to them. Third, it means rating each location according to
each criterion. The scale of the score is arbitrary. In our example we shall use 0 to 100, where
0 represents the worst possible score and 100 the best.
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An Irish company which prints and makes specialist packaging materials for the pharma-
ceutical industry has decided to build a new factory somewhere in the Benelux countries
so as to provide a speedy service for its customers in continental Europe. In order to
choose a site it has decided to evaluate all options against a number of criteria, as follows:
● the cost of the site;
● the rate of local property taxation;
● the availability of suitable skills in the local labour force;
● the site’s access to the motorway network;
● the site’s access to the airport;
● the potential of the site for future expansion.
After consultation with its property agents the company identifies three sites which
seem to be broadly acceptable. These are known as sites A, B and C. The company also
investigates each site and draws up the weighted-score table shown in Table 6.2. It is
important to remember that the scores shown in Table 6.2 are those which the manager
has given as an indication of how each site meets the company’s needs specifically.
Nothing is necessarily being implied regarding any intrinsic worth of the locations.
Likewise, the weightings are an indication of how important the company finds each
criterion in the circumstances it finds itself. The ‘value’ of a site for each criterion is then
calculated by multiplying its score by the weightings for each criterion.
Worked example
Weighted-score method
Centre-of-gravity method
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The centre-of-gravity method
The centre-of-gravity method is used to find a location which minimizes transportation costs.
It is based on the idea that all possible locations have a ‘value’ which is the sum of all trans-
portation costs to and from that location. The best location, the one which minimizes costs,
is represented by what in a physical analogy would be the weighted centre of gravity of all
points to and from which goods are transported. So, for example, two suppliers, each send-
ing 20 tonnes of parts per month to a factory, are located at points A and B. The factory must
then assemble these parts and send them to one customer located at point C. Since point C
receives twice as many tonnes as points A and B (transportation cost is assumed to be directly
related to the tonnes of goods shipped) then it has twice the weighting of point A or B. The
lowest transportation cost location for the factory is at the centre of gravity of a (weightless)
board where the two suppliers’ and one customer’s locations are represented to scale and
have weights equivalent to the weightings of the number of tonnes they send or receive.
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For location A, its score for the ‘cost-of-site’ criterion is 80 and the weighting of this
criterion is 4, so its value is 80 × 4 = 320. All these values are then summed for each site
to obtain its total weighted score.
Table 6.2 indicates that location C has the highest total weighted score and therefore
would be the preferred choice. It is interesting to note, however, that location C has the
lowest score on what is, by the company’s own choice, the most important criterion –
cost of the site. The high total weighted score which location C achieves in other criteria,
however, outweighs this deficiency. If, on examination of this table, a company cannot
accept what appears to be an inconsistency, then either the weights which have been
given to each criterion, or the scores that have been allocated, do not truly reflect the
company’s preference.
Table 6.2 Weighted-score method for the three sites
Criteria Importance Scores
weighting
Sites
AB C
Cost of the site 4 80 65 60
Local taxes 2 20 50 80
Skills availability 1 80 60 40
Access to motorways 1 50 60 40
Access to airport 1 20 60 70
Potential for expansion 1 75 40 55
Total weighted scores 585 580 605*
*Preferred option.
A company which operates four out-of-town garden centres has decided to keep all
its stocks of products in a single warehouse. Each garden centre, instead of keeping
large stocks of products, will fax its orders to the warehouse staff who will then deliver
replenishment stocks to each garden centre as necessary.
The location of each garden centre is shown on the map in Figure 6.7. A reference
grid is superimposed over the map. The centre-of-gravity coordinates of the lowest-cost
location for the warehouse, G and H, are given by the formulae:
G =
∑x
i
V
i
∑V
i
Worked example
➔
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