DIMENSIONAL ANALYSIS

MOHD HARISPM/2014/407NIPER, HYDERABAD

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.

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.

• 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.

• 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.

• 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.

• 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.

• 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

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

• 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.

• 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

• 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