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more leeway； and may be slipped without affecting the end date of the
project。 This is called slack or float。
The steps in the critical planning method process are：
。 Identify the events。
。 Decide on the sequence in which they must be carried out。
。 Draw the network。
。 Calculate the pletion time for each event。
。 Identify the longest and hence critical path。
。 Keep the chart updated as events unwind。
Programme evaluation and review technique （PERT） and an activity network；
also known as an ‘activity…on…node diagram’； are more sophisticated
forms of CPM that allow for a degree of randomness in activity start and
pletion times。
Linear programming
In 1947； George Dantzig； an American mathematician； developed an algorithm
（a mathematical technique） that could help resolve problems involving
operational constraints。 His algorithm could； for example； help
with situations where several products could be produced； but materials；
labour or machine capacity is insufficient to make all that’s demanded – the
Start
Task 1
3 weeks
Task 2
3 weeks
Task 5
1 week
Task 4
2 weeks
Task 3
4 weeks End
This path is longest – takes 10 weeks – is critical path
This path takes 7 weeks
Tasks 4 or 5 could between them start or finish up to 3 days
late without delaying pletion – so critical path has 3 days slack in it
Figure 10。3 Critical path method applied
Operations Management 239
challenge in that last case being to decide what mix of products can be
produced that will make the maximum profit and then plan accordingly。
Unfortunately； the iterative nature of producing solutions using Dantzig’s
algorithm proved so tedious that until cheap puters arrived it remained
an academic idea of interest only to mathematics students。
The Dantzig algorithm prises an objective； the quantity to be optimized；
for example profit； nutrient content； water flow or production of one
particular product out of several； any variables and constraints on them； for
example a certain minimum amount of water must flow。
Excel incorporates a Solver add…in feature to solve standard linear programming
problems。 It is not usually installed when Excel is first loaded so
to add this facility：
。 Select the menu option Tools ｜ Add_Ins （you will need your original
installation disk）。
。 From the dialog box check Solver Add…In。
。 Access to the Solver option is now available from the new menu option
Tools ｜ Solver
These websites provide more information on using linear programming in
operations：
。 Economics Network （economicsnetwork。ac。uk/cheer/ch9_3/ch9_
3p07。htm） provides a detailed explanation and Excel worked example。
。 IBM （www…128。ibm/developerworks/linux/library/l…glpk1） has a
worked example。
Queuing theory
Agner Krarup Erlang； a Danish engineer who worked for the Copenhagen
Telephone Exchange； had the problem of estimating how many circuits
were needed to provide an acceptable telephone service。 He found out by
empirical observation that the relationship between the number of circuits
and the number of telephone customers who could be provided with an
acceptable level of service was not as obvious as it at first seemed。 For example；
in his experiments where one circuit was provided on a network；
adding just one more could reduce waiting time by over 90 per cent； rather
than just halving it as simple logic might suggest。 He published the first
paper on queuing theory in 1909 and this new operation scheduling technique
was born。
Queuing theory can help answer operational questions such as these
for a service business such as a restaurant； bank or call centre： Given the
present resources：
240 The Thirty…Day MBA
。 How long will a customer have to wait before they are served？
。 How long will it take for the service to be pleted？
。 How big a waiting area will be needed for the queue？
。 What is the probability of a customer having to wait longer than a
given time interval before they are served – the classic service standard
problem calling for； say； ‘all telephone calls to be answered within 10
rings’？
。 What is the average number of people in the queue？
。 What is the probability that the queue will exceed a certain length？ This
can cause congestion； say in a bank or supermarket。
。 What time period will the server be fully occupied for and how much
idle time are they likely to have； bearing in mind this is a cost to be
minimized？
The technique can be used for any operational problem where efficiency
is determined by calculating the optimal number of channels required
to meet a level of demand。 J E Beasley； formerly of the Tanaka Business
School （Imperial College） and currently Professor of Operational Research
at Brunel University； provides helpful notes on the subject at this web link
（h。。p：//people。brunel。ac。uk/~mastjjb/jeb/or/queue。html）。
INVENTORY MANAGEMENT
High inventory levels are popular with marketing departments； as having
them makes satisfying customers an easier task； they are less popular with
production departments who have to carry inventory costs in their budgets。
Finance departments insist on having the lowest possible stock levels； as
high stock pushes working capital levels up and return on investment
down。 （Look back to Financial ratios in Chapter 1 on accounting to see how
this works。） This tussle between departments is a strategic issue that has to
be resolved by top management。 The birth of Waterstone’s； the bookshop
business founded by Tim Waterstone； fortuitously a marketing visionary；
qualified accountant and the pany’s managing director； provides an
interesting illustration of the dimension of the stock control issue。 Until the
advent of Waterstone’s the convention had been to store books spine out on
shelves； in alphabetical order； under major subject headings – puting；
Sport； Travel。 This had the added advantage of making it easy to see
what books needed reordering and stock counts were a simple process。
Waterstone； however； knew that ‘browsers’； the majority （60 per cent；
according to his research） of people who go into bookshop