A job completion time follows a triangular distribution and can be accurately es

Question

A job completion time follows a triangular distribution and can be accurately estimated for the project manager. The most likely completion time is 10 days (m), the most optimistic estimate of completiontime is 5 days (a), while the most pessimistic estimate is at 18 days (b).

C1: Compute the Expected completion time for this job:

C2: Compute the variance for this job:

C3: Determine the probability of completing the job between 3-8 days.

C4: The vendor earns $1,000 for a job completed within 8 days, but loses $250 for any job completed after 8 days. Compute the expected profit/loss for the vendor performing the same job 1000 times.

Explanation / Answer

Expected completion time for the job

= ( Optimistic completion time + 4 x Most likely completion time + Pessimistic completion time ) / 6

= ( 5 + 4 x 10 + 18 )/ 6

= 63/6

= 10.5

Standard deviation of completion time for the job

= ( Pessimistic completion time – Optimistic Completion time ) / 6

= ( 18 – 5 ) / 6

= 13/6

Therefore, Variance for the job

= ( Standard deviation for the job)^2

= ( 13/6)^2

= 4.694

EXPECTED COMPLETION TIME FOR THIS JOB = 10.5 DAYS

VARIANCE FOR THIS JOB = 4.694 DAYS

Let Z value corresponding to probability of completing the job in 3 days = Z1

Let Z value corresponding to probability of completing the job in 8 days = Z2

Hence,

Expected completion time + Z1 x standard deviation of completion time = 3

Or, 10.5 + 13/6 x Z1 = 3

Or, 13/6x Z1 = - 7.5

Or, Z1 = - 3.46

Probability corresponding to Z1 = - 3.46 as derived from standard normal distribution table= 0.00027

Similarly,

Expected completion time + Z2 x Standard deviation of completion time = 8

Or, 10.5 + Z2 x 13/6 = 8

Or, 13/6 x Z2 = - 2.5

Or, Z2 = - 1.15

Probability corresponding to Z2 = - 1.15 as derived from standard normal distribution table= 0.12507

Thus probability of completing the job between 3 – 8 days

= probability of completing the job in 8 days – Probability of completing the job in 3 days

= 0.12507 – 0.00027

= 0.1248

PROBABILITY OF COMPLETING THE JOB BETWEEN 3 TO 8 DAYS = 0.1248

Probability of completing a job within 8 days = 0.12507

Thus, probability of completing the job after 8 days = 1 – 0.12507 = 0.87493

Expected earning for completing the job within 8 days = $1000 x 0.12507 = $125.07

Expected loss for completing the job after 8 days = $250 x 0.87493 = 218.73

Thus, Net expected loss for performing the job once   = $218.73 - $125.07 = $93.66

Hence, Expected loss for vendor performing the same job 1000 times = $93.66 x 1000 = $93660

EXPECTED LOSS FOR THE VENDOR PERFORMING THE SAME JOB 1000 TIMES = $93660

EXPECTED COMPLETION TIME FOR THIS JOB = 10.5 DAYS

VARIANCE FOR THIS JOB = 4.694 DAYS

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