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The solutions to assignment # 01 for the operations research course mth601, offered in spring-2012. The assignment includes three questions related to project management and network flow diagrams. Students are expected to have a good understanding of the concepts covered in lectures 4 to 10.
Typology: Exercises
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Assignment: # 01 (Spring-2012) Mth601 (Operations Research) Lecture: 04– 10 Total Marks = 30
Please read the following instructions before attempting to solve this assignment
1. In order to attempt this assignment you should have full command on Lecture # 04 to Lecture # 10 2. Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in Lecture # 04 to Lecture # 10 3. You should concern recommended books for clarify your concepts as handouts are not sufficient. 4. Try to make solution by yourself and protect your work from other students. If we found the solution files of some students are same then we will reward zero marks to all those students. 5. You are supposed to submit your assignment in Word format any other formats like scan images, PDF format etc will not be accepted and we will give zero marks to these assignments.
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Question- A manager notes that when his clerk uses the telephone, he takes no less than 10 minutes for a call and sometimes as much as one hour. Twenty minutes calls are more frequent than calls of any other duration. If clerk’s phone call were an activity in a PERT project: i) What would be the phone call’s expected duration? ii) What would be its variance? iii) In scheduling the project, how much time would be allocated for the phone call?
Solution: Here Optimistic Time = t0 =10 min Most likely Time = tm = 20 min Pessimistic Time = tp =60 min
i) expected duration = 0
25 min 6 6
n p e
t t t t
ii) Variance =
2 ( ) 0 69. 6
p e
t t V t
iii) In scheduling the project, the time to be allocated to the phone call is 25 minutes.
Question-
Tasks A,B,…,H,I constitute a project. The notation X<Y means that the task X must be completed before Y is started. With the notation, A<D, A<E,B<F,D<F,C<G,C<H,F<I,G<I. i) Draw the network flow diagram. ii) Calculate all the floats. iii) Find the minimum time of completion of the project. Time of completion of each project is as follows; Task A B C D E F G H I Time(Days) 8 10 8 10 16 17 18 14 9 Solution:
The project length variance = 2 = 4+16+16 = 36 Standard deviation = =√36 = 6 The probability of completing the project within 31 days is given by
P(Z≤D) and
D T^ s^ Te
So,
= 0.253 i-e 25.3%
So it can be concluded that if the project is performed 100 times under the same conditions, then there will be 25.3 occasions when the job when the job will be completed in 31 days.