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170 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

MANAGEMENT SCIENCE IN ACTION

A Marketing Resource Allocation Model At Reckitt And Coleman
eckitt and Coleman is a world leader in the ties for each region; together with additional market-
R manufacture and marketing of household, toi- ing information such as market size, alternative mar-
letry, food and pharmaceutical products employing keting costs and so on. Interestingly, the model was
over 25 000 people worldwide and with its products built with 11 alternative marketing objectives, such
sold in over 40 countries. In the late 1990s it decided as sales volume growth, brand value share allowing
to adopt a more analytical and objective approach to management to explore and evaluate the impact of
decisions relating to the allocation of marketing marketing spend in different ways. The model esti-
funds to its industrial cleaning products. The com- mates the revenue derived from the cost of the
pany operated seven geographical regions globally marketing mix chosen (such as advertising and store
and the marketing Vice President requested a model displays) and incorporates both marketing and
to determine the amount of marketing funds to be budgetary constraints. The benefits reported from
spent on current business and on new business use of the model included improved profitability, a
opportunities within each region. The model was faster response to unexpected or unpredicted mar-
expected to be modified and used as management ket conditions, more consistency in marketing deci-
visited each region as part of their marketing plan- sions and the ability to explore alternative scenarios
ning. An LP model was developed covering the in detail.
seven geographic regions; three product groups
Based on R. J. Richardson, ‘A Marketing Resource Allocation Model’,
for each region (surface cleaners, disinfectants,
Journal of Business and Economic Studies 10 1 (2004): 43–53.
oven cleaners); up to five new business opportuni-

Portfolio Selection
Portfolio selection problems involve situations in which a financial manager must
select specific investments – for example, stocks and bonds – from a variety of
investment alternatives. Managers of mutual funds, credit unions, insurance compa-
nies and banks frequently encounter this type of problem. The objective function for
portfolio selection problems usually is maximization of expected return or minimi-
zation of risk. The constraints usually take the form of restrictions on the type of
permissible investments, company policy, maximum permissible risk and so on.
Problems of this type have been formulated and solved using a variety of mathe-
matical programming techniques. In this section we formulate and solve a portfolio
selection problem as a linear programme.
Consider the case of Welte Mutual located in Berlin. Welte just obtained
E100 000 by converting industrial bonds to cash and is now looking for other
investment opportunities for these funds. Based on Welte’s current investments,
the firm’s top financial analyst recommends that all new investments be made in the
oil industry, steel industry or in government bonds. Specifically, the analyst identi-
fied five investment opportunities and projected their annual rates of return. The
investments and rates of return are shown in Table 4.14.
Management of Welte imposed the following investment guidelines:
1 Neither industry (oil or steel) should receive more than E50 000.
2 Government bonds should be at least 25 per cent of the steel industry investments.
3 The investment in Pacific Oil, the high-return but high-risk investment, cannot
be more than 60 per cent of the total oil industry investment.

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