Longest path vs critical path — where theory breaks down

A month ago, I challenged the LinkedIn PM community with a simple scheduling quiz: calculate the duration of two parallel tasks and analyse the critical path.

It was deliberately designed to expose the gap between scheduling theory and real delivery. Surprisingly, no one attempted to model it properly. Most tried to solve it manually or asked GenAI system for a solution. Maybe it looks too simple to bother even trying? 

Let’s revisit it and see where common scheduling thinking falls apart.

Two parallel activities each ideally require 3 resources (6 total), but only 5 are available. We must assign resources, calculate durations, Total Float, and identify Critical and Longest paths.  

This is a common scenario for any project. The full quiz conditions are below.
 

A practical (though not optimal!) solution is:
• Start both activities in parallel
• Assign 3 resources to one activity and 2 to the other
• When the first activity finishes, move the freed resource to the second
Outcome:
• Activity 1 finishes in 10 days
• Activity 2 receives a third resource from day 11 and accelerates from 15 days to ~13.3 days

Detailed quiz requirements (for those who want to model it):
• 2 parallel activities
• Each can use 1, 2, or 3 resources
• Resources can move between tasks but can’t multitask

Resource-driven durations:
• 3 resources → 10 days
• 2 resources → 15 days
• 1 resource → 30 days
• All resources share the same calendar and productivity rate
• Total available resources: 5

Tip: It is easier to model the scenario if we assume that the volume for each activity is 240 units, that a day has an 8h calendar, and that each resource has a 1 unit per hour productivity rate.

1. CPM gives the wrong project duration
Depending on assumptions, CPM-based planning is likely to produce 10-day or 15-day estimation. Neither reflects reality.

2. Critical path vs longest path
Activity 1 is on the critical path, but not on the longest path. Activity 2 is on the longest path, but not on the critical path. 

3. Float tells the real story
Start of Activity 1 (even though it is on the longest path (!)), can be delayed by ~3.3 days without impacting completion but start of shorter Activity 2 can’t be delayed at all.

So, which one is truly critical?

In real projects, once we introduce:
• complex logic
• dynamic assignments
• resource limits
• calendars
• external constraints
• deadlines
• lags/leads
longest path is often meaningless. What matters is whether an activity has float under existing constraints.

When projects apply Resource Critical Path method, the true critical tasks and real acceleration options become visible.

If we analyse the solution, we will see that the assignment is not optimal, as two resources are idle for the last 3.3 days. The optimal solution is to move the 3rd resource from Activity 1 to Activity 2 on day 7. In this case, each activity will be completed in 12 days!

This optimisation opportunity is far from intuitive.

No one in the LinkedIn discussion identified it. Some proposed a theoretical 50/50 allocation but couldn’t explain how such a split would actually be implemented in practice. And this is a very simple scenario. Real projects involve thousands of activities and hundreds of resources. Finding a truly optimal allocation becomes a complex mathematical problem that requires advanced, resource-driven project data modelling approaches.

Many guidelines claim that activities on longest path can’t be delayed without delaying the project delivery date. This example demonstrates that the assumption doesn’t hold when real-life project complexity is taken into account.

If we want schedules to support project decisions, not just inform reporting, we need to move beyond Critical Path Method and adopt resource-driven scheduling approaches.