Operations Management Homework: Decision Analysis, Networks

This document presents a comprehensive solution to an Operations Management assignment, addressing four key problems. The first problem focuses on capacity planning, analyzing the optimal production process based on demand and cost structures, using break-even analysis to determine the best alternative between buying components or in-house production using different processes. The second problem utilizes a decision tree to evaluate the expected net present value of different machine purchasing options. The third problem involves a project network diagram, identifying critical paths and project completion times using techniques like early start, early finish, late start, and late finish. The final problem calculates the mean and standard deviation to determine the probability of project completion within a given timeframe. The solution provides detailed calculations and explanations for each problem, offering a thorough understanding of the concepts.

Operations Management
Student Name
Institution Name
Date
Problem 1
a. Best alternative
When the demand is 7000 units, process II graph indicates the lowest cost of production.
It shows that the total production cost for process II will be $ 46,000 which is the lowest.
b. The intersection point B
Intersection point B is where the graph of buy and use process II meet.
The equation of the two graphs are
Process II : y =25000+3 x
Buy : y=7 x
Using the breakeven technique
25000+3 x=7 x
4 x=25000
x=6,250 units
Q=6,250units
c. Volume at intersection point A
Process II and Process I meet
Using breakeven technique
Process II : y =25000+3 x
process I : y=16000+ 5 x
25000+3 x=16000+5 x
9000=2 x
x=4500units
Volume at intersection point C
Process I and Buy meet

ProcessI : y =16000+ 5 x
Buy : y=7 x
Now
16000+5 x=7 x
2 x=16000
x=8000 units
Now A=4500 , B=6250 , c=8000
From 0 to 6250 units, he should choose the option to buy
Above 6250 units he should choose option of in-house production using process II.
d. The choice of in-house production using process I should never be selected. At the
intersection point B, buy and produce using process II have similar cost hence either can
be chosen. At this same intersection point in built production using process I is more
expensive hence is not an optimal choice.
Problem 2
a. Decision tree
b. Expected net present value
Buying one machine initially will have an expected net present value of $ 90,000
c. From the decision tree, buying two machines initially will have an expected net present
value of $113,500

d. The manager should purchase one machine initially. This will minimize the cost of the
machines to an expected net present value of $90,000.
Problem 3
a. Project network diagram
b. Length of each path
We have to get the paths from A, B to E
A to C to E; 4 +5+ 4=13
A to D to E: 4 +3+4=11
B to D to E: 9+3+ 4=16
The critical oath is B to D to E
c. Project completion time
From the table above the project completion time is 16 weeks
d. The graph can be used to fill the table

Activity Early Start Early Finish Late Start Late Finish Slack
A 0 4 3 7 3
B 0 9 0 9 0
C 4 9 7 12 3
D 9 12 9 12 0
E 12 16 12 16 0
e. The critical activities are the activities that have their ealy finish and late finish being the
same. These are activity B, D, and E.
Problem 4
a. Mean of the paths
N ¿ O¿ Q ¿ T ≔10+15+12+18=55 weeks
N ¿ P¿ R ¿ T ;10+ 8+20+18=56
b. Probability of project completion in 58 weeks
Mean is 56
Standard deviation 11
Using this information, the Z score is
Z=58−56
11 =0.1818
Pr (completion ≥ 58)=0.57 14
Hence probability of completion in 68 weeks or less is 0.4286