Three consecutive activities A, B and E (in that order) have their T—Duration (in days) vs. C—Direct Cost (in monetary units) relationship expressed in the following table: A B C T C T C T C 8 15 6 7 4 11 9 14 7 6 4 11 10 16 8 7 6 13   What is the optimum duration for the corresponding minimum total direct cost for all the three activities when taken up consecutively without pause or disruption?

Three consecutive activities A, B and E (in that order) have their T—Duration (in days) vs. C—Direct Cost (in monetary units) relationship expressed in the following table: A B C T C T C T C 8 15 6 7 4 11 9 14 7 6 4 11 10 16 8 7 6 13   What is the optimum duration for the corresponding minimum total direct cost for all the three activities when taken up consecutively without pause or disruption? Correct Answer 20 days

Concepts:

Optimum Duration: The duration which gives the most economic cost for completing a project.

Direct Cost:  The expenditures of a project which can be directly charged for an activity and which can be specifically identified with the activities of the project. This includes labour cost, material cost, equipment cost etc. A diagram for cost vs time is shown below for better understanding

[ alt="F1 A.M 1.8.20 Pallavi D3" src="//storage.googleapis.com/tb-img/production/20/08/F1_A.M_1.8.20_Pallavi_D3.png" style="width: 334px; height: 215px;">

As, indirect cost is always linearly increasing, hence to find out the optimum duration corresponding to minimum total direct cost for any given sequence of activities, first the duration corresponding to minimum direct cost for each activity have to identified and then those are added in sequential manner.

Calculations:

The duration corresponding to minimum direct cost for all three activities are identified and listed in the following table:

Activity

Duration (days)

Direct Cost (monetary units)

A

9

14

B

7

6

E

4

11

Total

20

31

 

Hence, minimum direct cost for those consecutive activities are 31 monetary units and optimum duration is 20 days. 

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