While traditional CPM have been upgraded to consider resource leveling the calculations for resource leveled float have not. The only software I know that can correctly determine Resource Leveled Critical Path floats is Spider Project. A few might claim they can but Spider tests have prove them wrong.

Still they resource level the jobs into feasible schedules though not necessarily the most efficient. They get the feasible results without calculating resource leveled floats and therefor is why I suggested the use of Ron Winter Logic League.

The following link is a Power Point presentation reduced for purpose of our discussion. 

http://www.slideshare.net/davilara11/resource-lev

For the full presentation follow next link.  http://www.spiderproject.ru/library/rlpm.ppt With resource constraints and date constraints the longest path notion that the critical path runs from start to finish is no longer valid. You might have a schedule for a building that will take you to build 8 months but the contract finish date is 12 months, here only the last activity [contract finish] is critical while all others have float, out of possible hundreds of activities only one will belong to the critical path. Contractual milestones create similar conditions with multiple critical paths.

Yes, depending on software it is possible your client have no way to determine correct critical float values along with the implications this have on the identification of critical path. I would not be surprised if they try to force you to use soft links, this could yield substandard and even erroneous schedules as resource dependencies usually change as the schedule moves with time. 

What differentiates Critical Path Methods to Bar Charts is Float, if you do not care about float you do not care about critical path and what is driving your schedule.

100% resource driven schedules are very rare, usually on short sample jobs used for illustration purposes, in any case 100% resource driven, 100% logic driven or a combination of both, float is at the center of it. Resource leveling algorithms are dependent on  the calculation of float and if wrong it might reduce the effectiveness of the algorithm. Still some software are notorious for poor computations of float under resource leveling and some do not even attempt to compute resource leveled float.

There is much more to float than the simple calculations of the 60's, more in depth analysis is needed.

From: http://www.spiderproject.ru/library/pmie01_rcp.pdf

• Resource assignments can be also characterized by floats. Assignment float can be defined as the amount of time that resource assignment may be delayed without delaying the project finish date. In case of complicated resource assignments when resource teams can execute the same activity independently of each other, resource assignments may be critical even on non-critical activities.

Serious scheduling such as the development of the Dreamliner or the construction of a battleship require advanced scheduling techniques, otherwise the plans might be inefficient with a substantial increase in cost and duration. It is not enough for plans to be feasible to be considered a good schedule, they got to be efficient. The goal shall be to make it right, not to make it easy at the expense of making it right. 

The construction of a house is so simple that even a hand drawn Gantt will do it but not all jobs are so simple, if this is your target you do not need advanced scheduling software. 

What Olivia is asking makes all the sense, along the critical path some segments are driven by logic while other segments  are driven by resource dependencies, at other times the critical path is interrupted by other constraints such as date constraints. 

Resource links are temporary and traditional CPM cannot handle them. Few software such as Spider Project can display resource dependencies but not P6 off the shelf, therefore you can consider using Logic League Resource Links.

http://scheduleanalyzer.com/ll_resource.htm

Maybe then after transferring resource dependencies you can be able to get what you are looking for.

It is not unusual for many activities in parallel using the same resource to delay some activity, a delay on any would delay the activity but only one resource dependency is needed for the resource leveling algorithm to work, usually only one of the resource dependencies will be displayed. Therefore I am more interested on what resource delayed the activity rather than a single resource dependency. I see resource dependencies as a marker and a mathematical trick for the resource leveling algorithm.

Resource dependencies are good to transfer resource leveled jobs using more robust engines than the available in P6 that is considered by many very poor.

http://www.stottlerhenke.com/product/products/aurora-ccpm/

BTW using Spider Project off the shelf I could get the optimum solution of the Aurora sample job, a solution Aurora could not get. For such simple job finding some prioritization rule rather than using optimization algorithm yielded the optimal result. This is very unusual and using this as representative would be unfair to Aurora advanced resource leveling algorithm. I believe on complex jobs Aurora as well as Spider will yield very good results close to optimum.

The links shown in dashed lines are not logic links but resource dependencies. You can try the sample job using P6 without the resource dependencies as links, then you can add the resource dependencies as links in order to get the optimum schedule.

Spider Project can also model Spatial Resources using Consumable [Material] Resources consumption and production, that would be another interesting comparison. 

Hope the reference will be of help.