Parallel and Series Tasks and Merge Bias

Parallel and Series Tasks and Merge Bias

Had a recent conversation with a colleague about probabilistic modeling of cost, schedule, and the impact on risk management. Lots of topics were touched on, but one was the concept of Merge Bias.

Merge Bias is the impact of parallel tasks on the probability of completing?on or before?a needed date. I've talked in the past about?Schedule Margin?using Monte Carlo. The notion of a?Deterministic versus Probabilistic Schedule?is the starting point for Merge Bias.

In the management of projects, the important points along the path to completion are usually where several parallel paths come together. At these merge points, the paths must all be completed before a milestone can be achieved. An inspection is done, sub-assemblies are integrated for testing, and initial flight testing is complete – activities like these.

The Fallacy of the Critical Path and PERT Methods

There are several critical factors in the use of standard scheduling techniques.

  • The project duration calculated by the critical path method is accurate only if everything goes according to plan. This is rare in real projects.
  • In many cases, the completion dates the critical path method produces are unrealistically optimistic and highly likely to be overrun, even if the schedule logic and duration estimates are accurately implemented.
  • The critical path method completion date is not even the most likely project completion date, in almost all cases.
  • The path identified as the critical path using traditional critical path method techniques may not be the one that will be most likely to delay the project and which may need management attention. This?near-critical path?is the "killer" path, not shown in static assessment methods.

Extreme Parallel and Serial Task Example

Here's an example where all the work is performed in parallel and all the work is performed in series. This extreme example is used to show that when we encounter project schedules where?merge points?are used, there is a hidden effect -?merge bias?that will result in unpleasant outcomes if we don't understand and deal with the probabilistic aspects of this type of structure.

In the next figure, all the work is in series. We plan to finish on 1/25/2013. The work is a series of 10-day activities that have a total of 100 days of work.

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When we run the Monte Carlo Simulation (MCS) using Risk+ and look at the final outcome, Series Tasks Complete, we get this curve.

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This graph tells us there is a 55% probability of completing?on or before?our target date of 1/25/13. This is a cumulative probability curve for all the 1,000 samples taken in the model. That's OK since there is a 90% probability of completing?on or before?1/30/13, 5 calendar days after our target date. The schedule has no slack, so this is another topic about having margin in all schedules.

The extreme Parallel example looks like this. Here there are two sets of parallel activities, whose total durations to the same 100 days. How they do this is not an issue here, maybe fewer resources, maybe just different work periods, but the parallel aspects are the point of the model.

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The MCS for this parallel case, for the same?Period of Performance,?looks like this. The target date of 1/25/13 is not even in the realm of possibilities. 1/31/13 of only 5% probability. The 80% probability date – the common confidence level of a planned date is 2/13/13, 3 weeks late. This?lateness?is from the parallel aspects of the network of activities.

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So What Does This Tell Us?

It doesn't mean don't have parallel work. It means that when there is parallel work, the standard PERT style estimating is no good. It means:

  • The network should not be developed at too high a level of detail. This creates or may even mandate parallel flows.
  • The schedule should show clearly the parallel paths that could cause the project to be late if not coordinated.
  • The network should not be developed in such great detail that it requires too much information and create more opportunities for parallel flows.

Here's the killer concept that is little understood

When we think of statistical processes, say an estimate of cost, the variability of these numbers will tend to the Mean. That is, when there is an estimated cost with a higher than planned cost, that will be (or could be) offset by an estimate with a lower than planned cost. This is the notion of the Central Limit Theorem. Sets of random numbers tend to be the mean when the sample size grows large.

In a schedule, when the work is in parallel when the duration of a work activity along a path experiences a higher than planned result, and another work activity experience a lower than planned result, it is the higher than planned duration activities that impact the schedule. If both are higher than the highest one is the result. If both are lower than the highest, the lower one is the result.

Without a Monte Carlo Simulation of the network, any credible confidence in completing on or before a date with a budget at or below that planned value is not there.

Here's a collection of resources for applying Monte Carlo Simulation in the project management domain.

I re-read the original posts from 2006. What is the scale of a one of the 5000 activities in your representative project? My guestimate is you are talking about activities on the order of an FTE month.

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Sasho Andonov

Aviation, Quality, Safety, Audits, Education&Training, Project Management, etc.

2 年

The Monte Carlo method has meaning only if it is executed to not less then 100 000 samples.

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Alex Lyaschenko

Portfolio Planning & Delivery | PMP | P3O Practitioner | AgilePM Practitioner | Six Sigma | Project Data Modelling | PredAptivePM

2 年

Glen Alleman With appreciation I agreed with the analysis but disagreed with your concussions. 1. Performing activities in parallel instead of in sequence create an opportunity to speed up delivery and it has to be considered when it is only possible. 2. Yes, it creates an additional risk that if only one of the parralel activities is late, the whole work package is late. However, it still will be quicker to perform all these activities in parallel than in sequence, even with the delay. 3. MCS analysis (or alternative Quantitative Risk Analysis methods) performed based on a very detailed schedule allows the identification of these scheduling risks and it creates an opportunity to measure the size of time buffers correctly. 4. If work is going to be performed in parallel but the schedule doesn't have that level of detail results of MCS analysis are going to be misleading.

Santosh B.

Independent Consultant for Project Planning and Scheduling, Schedule Risk Analyses and also Co-Founder of Turbo-Chart

2 年

Merge bias, along with work period availability (calendar risks) are unique to schedule risk that doesn't occur in cost risk.

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Good article. A simple way to understand the gravity of the problem is with non-parametric statistics and the last horse under the wire metaphor. Stipulating unbiased plan estimates, for any merge, you are waiting for the last one to finish. The race isn't over when the first horse finishes, nor when the median horse completes. It's over only after the last horse crosses the finish line. Each task has a 50% chance of finishing early, and a 50% chance of finishing late. The chance that both of two tasks finish early is, therefore, only 1 in 4. The chance of 3 of 3 tasks finishing early is 1in 8. (only a 12.5% chance you won't be late!) This means that estimating a schedule of network with merge points using average (median) estimates will be optimistic, because 75% of the simplest merges will complete later than the ,best estimate of task times would predict.

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