Using M/N/1 queue theory to evaluate the risk that a project will not complete on time. This uses a Poisson statistical approach to model project milestones waiting in line to be resolved by a project assigned resources inside an expected time. The assumed signal to noise ratio of both work to do and worker availability is 1 to 1.

Terms:

Ra = Rate of Arrival, Milestones per Time Unit

Re = Rate of Execution, Milestones per Time Unit

U = Utilization of workers

Ct = Total Cycle time. Average time to complete for each milestone in turn, waiting plus resolution. It generally makes better sense to consider this the lead time between each milestone followed by the work to complete each milestone.

P0 = Odds that staff will be 100% free from work and their will be no waiting for work on a milestone to begin.

P1+ = Odds that a milestone will wait before work begins for 1 or more milestones to complete first.

T = Actual completion time of the project, all milestones.

U = Ra/Re

Ct = 1/(Re – Ra)

P1+ = 1 – exp(-T/Ct)

Assuming each milestone represents equal amounts of known work, P1+ amounts to the odds that the project itself will complete in the expected time, Ct. With use of a simple metric, it is possible to consider the impact of milestone work load changes, waiting periods between milestones, staff work load planning to deal with variation in work load and more.

The cost of delaying a milestone:

This uses Net Present Value techniques. The amount of money placed at interest right now to earn/cost the value of an item in the future.

The original milestone has a target date and value. The Project is given a budget that needs to earn enough value for the firm to be worth the either literal or figurative loan of cash to pay for the project work. This will use continuously compounding interest to allow for easy estimation and Excel spreadsheet mathematical functions and notation.

Terms:

R = Return On Invested Capital %/yr required for loaned budget cash.

Tm = The expected completion time of the milestone from the start of the project.

Vm = The cash value of the milestone work for the project

T = The actual completion time of the milestone from the start of the project.

NPV0 = Original Net Present Value of the milestone

NPV1 = Changed Net Present Value of the milestone

Value of the milestone before a change in the expected completion time.

NPV0 = Vm*exp(-R*Tm)

Value of the milestone after a change in the expected completion time.

NPV1 = Vm*exp(-R*T)

Percent valuation change of the milestone by moving its completion time.

(NPV1 – NPV0) / NPV0 = Vm* (exp(-R*T) – exp(-R*Tm))/(Vm*exp(-R*Tm)) = exp(-R*(T-Tm)) – 1