Dimensional analysis, also known as the factor-label method, is a problem-solving technique used for comparing site costs in inventory control by considering both tangible and intangible costs. The approach involves calculating relative merits of different sites using cost ratios and weighted factors to aid in site selection for new factories and facilities. The Brown & Gibson model further elaborates on location factors by categorizing them into critical, objective, and subjective measures, ensuring site selection considers both measurable and qualitative aspects.

1. DIMENSIONAL ANALYSIS
MOHD HARIS
PM/2014/407
NIPER, HYDERABAD

2. WHAT IS IT?
Dimensional Analysis (also called Factor-Label
Method or the Unit Factor Method) is a problem-
solving method that uses the fact that any
number or expression can be multiplied by one
without changing its value. It is a useful technique.
The only danger is that you may end up thinking
that it is simply a math problem - which it definitely
is not.
Unit factors may be made from any two terms that
describe the same or equivalent "amounts" of
what we are interested in.

3. Dimensional Analysis in inventory control
• The problem of location of a site within the region
can be approached with the following cost-
oriented non-interactive model, i.e., dimensional
analysis.
• If all the costs were tangible and quantifiable, the
comparison and selection of a site is easy. The
location with the least cost is selected.
• In most of the cases intangible costs which are
expressed in relative terms than in absolute terms.
Their relative merits and demerits of sites can also
be compared easily.

4. • Since both tangible and intangible costs need to
be considered for a selection of a site, dimensional
analysis is used.
• Dimensional analysis consists in computing the
relative merits (cost ratio) for each of the cost items
for two alternative sites.
• For each of the ratios an appropriate weightage
by means of power is given and multiplying these
weighted ratios to come up with a comprehensive
figure on the relative merit of two alternative sites,
i.e.,
C1M, C2M, …, CzM are the different costs
associated with a site M on the ‘z’ different cost
items.

5. • C1N, C2N, …, CzN are the different costs
associated with a site N and W1, W2, W3, …, Wz
are the weightage given to these cost items, then
relative merit of the M and site N is given by:
If this is > 1, site N is superior and vice-versa.

6. • When starting a new factory, plant location
decisions are very important because they have
direct bearing on factors like, financial,
employment and distribution patterns. In the long
run, relocation of plant may even benefit the
organization.
• But, the relocation of the plant involves stoppage
of production, and also cost for shifting the
facilities to a new location.

7. • In addition to these things, it will introduce some
inconvenience in the normal functioning of the
business.
• Hence, at the time of starting any industry, one
should generate several alternate sites for
locating the plant.
• After a critical analysis, the best site is to be
selected for commissioning the plant.
• Location of warehouses and other facilities are
also having direct bearing on the operational
performance of organizations.

8. • The existing firms will seek new locations in order to
expand the capacity or to place the existing
facilities.
• When the demand for product increases, it will give
rise to following decisions:
Whether to expand the existing capacity and
facilities.
Whether to look for new locations for additional
facilities.
Whether to close down existing facilities to take
advantage of some new locations

9. Brown & Gibson Model:
• This model is more elaborate & considers three
classes of site location factors:
• Critical… e.g. water for refinery
• Objective … e.g. labour costs, raw material costs.
• Subjective…e.g. recreational facilities, union
activities
• For each site ‘I’ a location measure 1m is defined

10. • In order to ensure compatibility between objective
& subjective factor measures, objective factor
costs are converted to dimensionless indices.
• The rationale is:
• site with minimum cost must have the maximum
measure
• Relationship of total objective fa tor cost &
corresponding objective factor measure must be
maintained, a site with half the objective factor
cost is assigned twice the objective factor measure
of the other site.

11. • For each plant site I a location measure is
calculated :-
• CFMI specifies the measure of critical factors for
the plant site I
• OFMI specifies the measure of objective factors for
the plant site I
• SFMI specifies the measure of subjective factors for
the plant site I
• D specifies the objective factor decision weight

12. • The sum of objective factor measure for all
sites must equal to 1
• The subjective factor measure is given by:
• SFMI = (SFWJ * SWIJ )
• Where SFWJ signifies the weight of factor J
relative to all subjective factors and
• SWIJ signifies the weight of plant site I relative
to all potential plant sites for subjective
factor J