Elements of Crashing a Network

Considering the elements of crashing a network, every activity has mainly two types of completion time that include- normal time and crash time. Similarly, costs will also have two types of measures that include normal cost and crash cost.

Comparing both normal cost and crash cost, the crash cost will always higher than the normal cost. But in the case of different activities, normal time will be greater than crash time.

If there is a crash on network, this implies crash on the activities and direct cost gets increased.  So, there will be tradeoff between the direct cost and indirect cost and it will be there until total cost becomes economical.

Following assumptions are taken to carry out the calculation in such situations-

• Calculate CP (critical path) along with normal time
• Calculate slope of each activity by using the formula

Slope = Crashing Cost – Normal Cost/ Normal Time – Crash Time

• Lowest Slope will be identified suing critical activity
• Compress the activities within the crash limit

Here, the compression time is given by min (crash limit, free float limit). Two conditions will be found that include-

When more than one CP is there, choose the common CP and when no such activity is found, choose critical activity with least slope for each CP.

Now, compress them within crash limit.

• Do crashing till there is no possibility to crash
• Calculate TC (Total Cost) for each crash by-

Total Crash = Previous TC + Increase in Direct Cost – Decrease in Indirect Cost

Suppose the current TC is greater than previous. In such case, next crashing will be uneconomical. So, there is no need to perform anymore crashing and stop here. To get the result, the previous solution will be considered as optimal crashing solution.

Links of Previous Main Topic:-

• Introduction to statistics
• Knowledge of central tendency or location
• Definition of dispersion
• Moments
• Bivariate distribution
• Theorem of total probability addition theorem
• Random variable
• Binomial distribution
• What is sampling
• Estimation
• Statistical hypothesis and related terms
• Analysis of variance introduction
• Definition of stochastic process
• Introduction operations research
• Introduction and mathematical formulation in transportation problems
• Introduction and mathematical formulation
• Queuing theory introduction
• Inventory control introduction
• Simulation introduction
• Time calculations in network

Link of Next Statistics Topics:-

• Introduction of game theory