232 The Marketing Book
Linear programming
Linear programming (LP) is a mathematical
technique for solving specific problems in
which an objective function must be maximized
or minimized, considering a set of definite
restrictions and limited resources. The word
‘programming’ stands for computing or calcu-
lating some unknowns of a set of equations
and/or inequalities, under specific conditions,
mathematically expressed.
Before the LP technique can be employed
in the solution of a marketing problem, five
basic requirements must be considered
(Meidan, 1981):
1 Definition of the objective. A well-defined
objective is the target of the solution and the
answer to the problem must satisfy the
requirements. Objectives such as reduced
costs, increased profits, matching of salesforce
effort to customer potential or improved
media selection can be handled.
2 Quantitative measurement of problem elements. A
quantitative measurement is needed for each
of the elements described in the problem,
which is an essential condition for applying
mathematical models such as hours, pounds
(£), etc.
3 Alternative choice. It must be possible to make a
selection for reaching a solution which satisfies
the objective function.
4 Linearity. The term ‘linearity’ describes the
problem and its restrictions. Equations and
inequalities must describe the problem in a
linear form.
5 Mathematical formulation. Information must be
compiled in such a manner that it is possible
to translate the relationships among variables
into a mathematical formulation capable of
describing the problem and all the relations
among variables.
A number of techniques are available for
solving a formulated linear programme. A
graphical solution is possible when there are
three variables only. An example showing the
use of LP in determining the best allocation and
mix of marketing effort is presented in detail by
Meidan (1981).
One is faced with four kinds of difficulties
in using linear programming models:1 The first difficulty is in describing the problem
mathematically. In an industrial situation one
must know exactly how much one can use the
production resources, such as manpower, raw
materials, time, etc.
2 The second problem lies in the interpretation
and proper use of the objectively obtained
optimum solution. One may need to analyse
additional business considerations, over and
above the ones used in describing and
formulating the problem.
3 Even if the problem has been correctly stated
and formulated, technical limitations may exist,
such as the amount of data a computer can
handle or that no solution exists (for example,
the number of constraints and/or variables may
be too large).
4 A further limitation lies in the reliability of the
proposed solution. This could arise when a
linear assumption is taken for real non-linear
behaviour of the component.Physical distribution
Designing an optimal physical distribution
system is dependent on choosing those levels of
services that minimize the total cost of physical
distribution, whose objective function might
read: C= T +F+ I + L, where C = total
distribution cost, T= total freight cost, F= total
fixed warehouse cost, I= total inventory cost
andL= total cost of lost sales.
Given the objective function, one seeks to
find the number of warehouses, inventory
levels and modes of transportation that will
minimize it, subject to at least three
constraints:1 Customer demand must be satisfied.
2 Factory capacity limits must not be exceeded.
3 Warehouse capacity cannot be exceeded.