Colour coding:
# comments
> user commands
computer output
# view the example portfolio:
> portfolio
| name | needs | finish | sofar | commit | |
| 1 | accountant | 20 | 8 | 15 | y |
| 2 | architect | 40 | 10 | 35 | y |
| 3 | bizlogo | 10 | 12 | 0 | y |
| 4 | shopkeeper | 20 | 15 | 12 | y |
| 5 | mathwiz | 20 | 20 | 5 | y |
| 6 | doctor | 40 | 25 | 0 | n |
| 7 | mailsystem | 20 | 40 | 0 | n |
| 8 | athlete | 20 | 40 | 0 | n |
| 9 | mapreader | 50 | 45 | 0 | n |
| 10 | composer | 60 | 60 | 0 | n |
# Interpretation of the columns:
# name: the name of project i .
# needs: estimated total time, in person-days, required for completion
of project i
from start to finish.
# finish: deadline for project i , measured in number of days from now.
# sofar: amount of effort, in person-days, expended on project i
up to now.
# commit: whether or not the deadline for project i is a firm commitment:
#
`y' denotes a committed deadline, `n' denotes a deadline under consideration.
# The syntax is:
# distname should be one of:
# EXAMPLE:
# Now apply the PROJMAN function to find the probability of portfolio success
# with the deadlines stated in the finish column of portfolio.
#
#
projman(projdat, E, Ntimes, distname, dispersion)
#
# projdat is the portfolio information (here stored with name portfolio);
# E is the number of employees available to work on the portfolio;
# Ntimes is the number of simulations to perform
#
(the default Ntimes=10000 gives maximum margin of error of 1% on all estimated probabilities);
# distname is the selected distribution name (must be in quotes);
# dispersion is the dispersion associated with the selected distribution, if required.
# "pois" (Poisson), "norm" (Normal), "chisq"(Chi-squared), "gamma" (Gamma),
# "lnorm" (Lognormal), or "lnorm.med" (Lognormal, median specification).
# A dispersion value is required for the Normal, Gamma, and Lognormal options, but can be
# left blank for the Poisson and Chi-squared options.
# dispersion is the variance for the Normal option, the variance/(mean
squared) for the Gamma
# and Lognormal options, and the variance/(median squared) for the
Lognormal-median option.
# find the probability of portfolio success for the example data portfolio,
# for a company employing E=4 workers,
# assuming that the effort of each project is Gamma with common dispersion 0.4
# and mean given by the needs column in portfolio.
# Compile results from Ntimes=10000 simulations.
> projman(portfolio, E=4, Ntimes=10000, distname="gamma", dispersion=0.4)
Projects in order from earliest deadline to latest:
[1] accountant architect bizlogo shopkeeper mathwiz
doctor
[7] mailsystem athlete mapreader composer
Starting Monte Carlo simulations... please wait:
| name | pc.fail | pc.firstfail | finish | finish.95 | finish.99 | |
| 1 | accountant | 6.78 | 6.78 | 8 | 9 | 13 |
| 2 | architect | 36.10 | 29.95 | 10 | 21 | 29 |
| 3 | bizlogo | 39.40 | 5.47 | 12 | 24 | 32 |
| 4 | shopkeeper | 43.10 | 7.39 | 15 | 28 | 36 |
| 5 | mathwiz | 39.26 | 3.61 | 20 | 33 | 42 |
| 6 | doctor | 62.18 | 16.29 | 25 | 47 | 58 |
| 7 | mailsystem | 25.97 | 0.04 | 40 | 52 | 64 |
| 8 | athlete | 42.61 | 0.92 | 40 | 59 | 69 |
| 9 | mapreader | 66.11 | 8.79 | 45 | 75 | 88 |
| 10 | composer | 62.40 | 4.06 | 60 | 96 | 112 |
pc.success
16.7
# The columns are interpreted as follows:
# finish.95 and finish.99 are included as guidelines, but are not used further
# pc.success is the overall probability of portfolio success:
#
here, only 16.7% of the 10000 simulations were successful for all projects.
# pc.fail is the percentage of the 10000 simulations for which the deadline for project
i was missed.
# pc.firstfail is the percentage of simulations for which the deadline for project
i was the first to be missed.
# finish is the stated deadline for project i from the portfolio data.
# finish.95 gives the deadline for project i that would ensure 95% of the
10000 simulations
#
would meet the deadline for project i.
# finish.99 gives the deadline for project i that would ensure 99% of the
10000 simulations
#
would meet the deadline for project i.
# because they don't take into account the interactions between projects.
# The syntax is:
# Only projects with commit=`n' in the portfolio information will be given a modified deadline.
# The function works by finding the probability of failure on the set of committed projects,
# Note that setdates chooses a prioritization on projects so that:
# EXAMPLE:
# Now apply the SETDATES function to find a set of deadlines to achieve
# some stated level of portfolio success.
#
#
setdates(projdat, E, Ntimes, distname, dispersion, psuccess)
#
# projdat, E, Ntimes, distname, and dispersion are as above.
# psuccess is the required probability of portfolio success: a number between 0 and 1 (default=0.9).
# and sharing out any remaining allowed failure equally among the uncommitted projects.
# Thus deadlines on the uncommitted projects are selected so that pc.firstfail is about
# the same for each one.
# (a) committed projects are ordered first, by their deadlines;
# (b) uncommitted projects are ordered next, by their
estimated size (the needs column in portfolio).
# A different prioritization of projects would produce different results.
# find a set of deadlines for the uncommitted projects in portfolio, to achieve an overall probability
# of portfolio success of 0.9, if possible.
# Continue to assume the Gamma distribution with dispersion 0.4.
# Store the result with name dates.
> dates <- setdates(portfolio, E=4, Ntimes=10000, distname="gamma", dispersion=0.4, psuccess=0.90)
Ordered projects:
[1] accountant architect bizlogo shopkeeper mathwiz
mailsystem
[7] athlete doctor mapreader composer
Sorry: specified failure rate is already exceeded by commitments. Best success rate is 46.42 %
fail.ok (%): 0
# View the deadlines obtained:
> dates
| accountant | architect | bizlogo | shopkeeper | mathwiz | doctor | mailsystem | athlete | mapreader | composer |
| 8.00000 | 10.00000 | 12.00000 | 15.00000 | 20.00000 | 80.15481 | 40.68966 | 50.67344 | 109.96637 | 124.09037 |
# Interpretation:
# The deadlines obtained (dates) are equal to the deadlines stated in portfolio for all committed
# It is not possible to achieve 90% success rate on this portfolio, with the assumed probability distribution,
# because the projects with committed deadlines already exceed the allowed 10% failure rate.
# The best possible success rate is about 46%, and this requires deadlines for all the currently
# uncommitted projects to be set so that each one has a 100% success rate (fail.ok=0%).
# projects (the first five), and are designed to ensure approximately 100% success for the five currently
# uncommitted projects.
# Now test the new deadlines in projman, to check that the success rate of about 46% applies:
> projman(portfolio, E=4, Ntimes=10000, distname="gamma", dispersion=0.4, newfinish=dates)
Projects in order from earliest deadline to latest:
[1] accountant architect bizlogo shopkeeper
mathwiz mailsystem
[7] athlete doctor mapreader composer
Starting Monte Carlo simulations... please wait:
| name | pc.fail | pc.firstfail | finish | finish.95 | finish.99 | |
| 1 | accountant | 6.81 | 6.81 | 8.00000 | 9 | 13 |
| 2 | architect | 37.05 | 30.76 | 10.00000 | 21 | 29 |
| 3 | bizlogo | 40.53 | 5.23 | 12.00000 | 24 | 31 |
| 4 | shopkeeper | 43.67 | 7.16 | 15.00000 | 28 | 36 |
| 5 | mathwiz | 39.70 | 3.80 | 20.00000 | 33 | 41 |
| 6 | mailsystem | 3.65 | 0.00 | 40.68966 | 39 | 47 |
| 7 | athlete | 1.71 | 0.01 | 50.67344 | 45 | 53 |
| 8 | doctor | 0.19 | 0.00 | 80.15481 | 58 | 68 |
| 9 | mapreader | 0.06 | 0.00 | 109.96637 | 75 | 88 |
| 10 | composer | 0.23 | 0.01 | 124.09037 | 96 | 111 |
pc.success
46.22
# The achieved success rate on the portfolio with new deadlines is about 46% as expected.
# The five uncomitted projects have pc.firstfail close to 0%, in accordance with fail.ok=0%.
# The same experiment can be repeated assuming that effort follows a Chi-squared distribution.
# No dispersion parameter is required.
# The Chi-squared distribution assumes less variability in the effort distribution
# than the Gamma distribution with dispersion 0.4,
# so we expect a higher probability of portfolio success under this model.
> projman(portfolio, E=4, Ntimes=10000, distname="chisq")
# This gives pc.success=41% roughly (compare with 16.7% under the Gamma model).
# Now check whether it is possible to achieve 90% success rate:
> dates2 <- setdates(portfolio, E=4, Ntimes=10000, distname="chisq", psuccess=0.90)
Ordered projects:
[1] accountant architect bizlogo shopkeeper mathwiz
mailsystem
[7] athlete doctor mapreader composer
fail.ok (%): 1.086
# View the new deadlines obtained:
> dates2
| accountant | architect | bizlogo | shopkeeper | mathwiz | doctor | mailsystem | athlete | mapreader | composer |
| 8.00000 | 10.00000 | 12.00000 | 15.00000 | 20.00000 | 41.24688 | 24.92981 | 30.27718 | 55.11012 | 71.26495 |
# Interpretation:
# We can select deadlines for the five uncommitted projects so that the overall success rate is about 90%.
# The selected deadlines will have pc.firstfail = 1% (approx) on each uncommitted project
(fail.ok=1.086).
# Check the new deadlines in projman.func:
> projman(portfolio, E=4, Ntimes=10000, distname="chisq", newfinish=dates2)
Projects in order from earliest deadline to latest:
[1] accountant architect bizlogo shopkeeper
mathwiz mailsystem
[7] athlete doctor mapreader composer
Starting Monte Carlo simulations... please wait:
| name | pc.fail | pc.firstfail | finish | finish.95 | finish.99 | |
| 1 | accountant | 0.09 | 0.09 | 8.00000 | 4 | 6 |
| 2 | architect | 1.24 | 1.18 | 10.00000 | 8 | 10 |
| 3 | bizlogo | 2.75 | 1.63 | 12.00000 | 11 | 13 |
| 4 | shopkeeper | 2.64 | 0.99 | 15.00000 | 14 | 16 |
| 5 | mathwiz | 1.96 | 0.65 | 20.00000 | 18 | 21 |
| 6 | mailsystem | 3.08 | 1.00 | 24.92981 | 24 | 27 |
| 7 | athlete | 3.24 | 0.92 | 30.27718 | 29 | 32 |
| 8 | doctor | 3.60 | 1.21 | 41.24688 | 40 | 44 |
| 9 | mapreader | 3.58 | 1.30 | 55.11012 | 54 | 59 |
| 10 | composer | 3.47 | 1.00 | 71.26495 | 70 | 75 |
pc.success
90.03
# The achieved probability of portfolio success is about 90%, as expected.
# The deadlines on the uncommitted projects each have pc.firstfail close to 1%, as expected.