From: https://docs.oracle.com/cd/E17462_01/Web_Access/Help/en/Projects/Tasks/pm_cpm.htm
The longest path is broken when activities are no longer driven by relationships; that is, when activity dates are driven by constraints or resource leveling.
Most construction jobs have resource limitations, consumable resources limitations, contractual constraints and some have spatial resource constraints as well as financial constraints. Current Longest Path calculations do not take into consideration all these real constraints that can drive/delay your schedule and therefore not suitable under these circumstances.
http://www.mediafire.com/view/u16g8w3wy9o12dz/Bricks_Installation_Job.pdf
The above reference provides a short example of how lack of construction materials can delay a construction job. It is simple if there are not enough materials the activities are stopped and until there are enough materials to continue.
It is a job at Culebras Island, the deliveries are limited to space available on the Ferry, you got a preliminary schedule but it might be delayed, even if not delayed you still must plan for limited deliveries, you must level non-renewable resources.
Another scenario in which Longest Path Theory fails is when financial constraints drive your schedule.
"No ticky, no laundry"
Once again Longest Path Theory breaks down. An outdated theory good for the schedules of the 1960's. Of course schedules of the 1960's with no computer assisted resource leveling, otherwise we shall move back to the 1950's.
If it is so limited then why insist on it? To make money on it?
Can you tell me what activities are in the Longest Path?
All these actions either will delay the schedule or worst make it unfeasible if a delivery activity is deleted and not enough bricks are delivered.
While these activities are not linked by logic they are resource dependencies that can change as the work progress and things do not happen as planned.
By making these outdated procedures mandatory the institutions that promote them are favoring a few software interests at the expense of ruling out more advanced models.