Quantitative methods in marketing 233
The linear programming model has been used
in solving distribution problems, particularly in
the transportation of finished goods to ware-
houses. The aims were to minimize transport
costs subject to certain constraints, such as
warehouse costs (Kotler, 1972). Other uses of LP
models in marketing include site location,
physical distributions and blending products.
Warehouse location
Chentnick (1975) discusses the various meth-
ods of locating warehousing systems which are
of interest as their usefulness is indicated, thus
suggesting the advantage of linear program-
ming in comparison to other methods. Broadly,
the function of a warehouse can be broken
down into five areas:
1 Storage.
2 Assembling of customer orders.
3 Service of customers.
4 Economies of scale by bulk buying and delivery.
5 Processing and final packaging.
There are two definable sets which characterize
the two methods of solution to the warehouse
location problem (Meidan, 1978):
1 The infinite set assumes that the warehouse
can be positioned anywhere on the map –
obvious slight adjustments can be made later
to allow for rivers, mountains, etc. A main
assumption is that transport costs are directly
proportional to distance (as the crow flies),
and this is questionable in many situations.
2 The feasible set assumes a finite number of
possible locations, and both costs of buildings
and haulage can be calculated with a high
degree of precision.
Media selection
One area in marketing where linear program-
ming models have been extensively used is in
advertising decisions, especially in media mix
decisions in a market segment. Higgins (1973),
for example, proposed the use of this model for
deciding on the optimum paging schedule for
colour supplements of newspapers.Marketing mix decisions and budget
allocations
The marketing mix refers to the amounts and
kinds of marketing variables the firm is using at
a particular time, and includes price, advertis-
ing costs and distribution expenditures, each of
which could be subdivided into further
variables.Product mix and the multi-product
marketing strategy problem
The problem of product mix, i.e. variety and
quantity of products produced, is commonly
encountered by almost all multi-product firms
during the planning period. Here the objective
is to maximize current profits subject to the
various constraints, such as capacity, demand
levels and quality. Such problems necessitate
the use of linear programming.Other marketing management
applications for LP
Wilson (1975) cites a number of potential
applications of LP, including new product
decisions, resolving conflict in market segmen-
tation and the choice of a new market from a set
of possible alternatives, and gives an example
of its use in allocating a salesforce to new
products. Goal programming, on the other
hand, may be used when a minimum knowl-
edge of the situation and realistic objectives are
available. Here the subjective constraints
placed on the model give direction to an
objective and hence an area of solutions, i.e.
constraints become goals.The transportation model
The transportation model is a specialized class
of linear programming model. Like the linear
programming models, its aim is to optimize the