The Hindu Business Line : Partition theory of numbers and project crashing

The basic idea of crashing a project is to reduce the time duration and maintain a trade-off between crash cost and indirect cost. The recent CA (Final) examination had a question on crashing of a network consisting of 11 activities and four critical paths. The problem makes interesting reading if one were to find all the combinations.

Conceptually, where multiple critical paths emerge, the combinations will be through independent activities, activities common to all the paths and activity common to few of the paths along with independent and/or activities common to other paths.

Further, the maximum number of activities forming a combination will always be less than or equal to the total number of paths

To find the various combinations, the application of Partition Theory of Numbers would be quite useful. Here, weights on the basis of natural numbers forming an arithmetic progression are assigned to the various paths individually.

If the total number of paths is four, the weight assigned is in the order 1, 3, 5, 7 respectively.

Based on these weights, the weight of each of the activity is computed. Where the total number of the weights of the activities equal the square of the number of paths a combination emerges.

In the CA (Final) problem, since the number of paths is four the weights of the activities put together should equal 16. The weights of the activity as well as the number of paths are partition of the numbers 16 and 4 respectively.

The total number of combinations is found to be 15. For example, activity 8-9 is common to all the paths, hence, its individual commonality weight is 4 and total weights of all the paths, 16. Therefore, it will be a combination.

For further details, refer Chartered Accountant Journal (November 2006, page 779) of the Institute of Chartered Accountants of India.

R. SIVAKUMAR

More Stories on : Accountancy | Quant-at-Ease

Article E-Mail :: Comment :: Syndication :: Printer Friendly Page

Stories in this Section
Partition theory of numbers and project crashing

Chinindia ties

Service tax on bank loan

Know the tax benefit of higher education loan

The art of negotiation

Corus: CSN versus Tatas

Just Do IT

Number Crunch

A burning question on PAN

Fate of neighbourhood shops when giant retailers march in

Have an open mind

In mathematics there is no ignorabimus