A Critical Path Method Example

When you, the project manager, need to make sure a project finishes on time, there is a science as well as an art form involved.  But the science tends to enhance the art, in other words, if you know the science you will be that much better at practicing the art form.

In yesterday’s post we outlined the critical path method which is the professional project manager’s techniques to ensuring project deadlines are met.  Today we will walk through an example with a complete solution.

Our example project is to build a new driveway.  We will be hiring our friend, Jon, who is a concrete worker and paying him an amount he has agreed to.  We will rent an excavator for a few days which we will operate ourselves.

The project will be scheduled using professional project management techniques without project management software, in other words, with MS Excel.

To rehash, the critical path method contains 6 steps:

1. Divide the project into tasks
2. Estimate each task
3. Create the network diagram
4. Draw initial Gantt (bar) chart
5. Perform resource levelling
6. Compress the schedule (if necessary)

Step 1:  Divide the Project into Tasks

The first step is to divide the project into tasks, also known as activities.  Ideally, each task should have one responsible party and be easy to estimate.  For example, excavation and pouring concrete might have separate responsible parties (contractors, etc.) and should therefore be separate tasks.  Here’s the task list I came up with:

Task List
Task No.	Name	Predecessors
110	Excavation
120	Build Forms	110
130	Place Rebar	110
210	Pour Concrete	120, 130
310	Setting & Curing	210
320	Strip Forms	310

 

A graphical style is sometimes helpful, but not a necessity.  This one was done in 5 minutes with MS Excel using the SmartArt feature:

The task list can also contain “activity attributes,” which identify meta-level information about the task. For example, there could be a column called “Subcontractor”:

 

Task List
Task No.	Name	Dependencies	Subcontractor
110	Excavation
120	Build Forms	110	Jon’s Concrete
130	Place Rebar	110	Jon’s Concrete
210	Pour Concrete	120, 130	Jon’s Concrete
310	Setting & Curing	210
320	Strip Forms	310

 

Step 2:  Estimate Tasks

Let’s get into the meat & potatoes.  Once the project has been divided into tasks, each task must be estimated.  Two things need to be determined:

1. Task Resources
2. Task Duration

I’ll show you the result and then explain it.  Here are the final estimate tables:

110 Excavation
Type	Average Use	Total
Mini-excavator	4 days @ $450/day	$1,800
Sweat Equity	12 hours @ $0/hr	$0
TOTAL		$1,800
Duration		4 days

120 Build Forms
Type	Average Use	Total
Lumber	Lump Sum	$100
Sweat Equity	8 hours @ $0/hr	$0
TOTAL		$100
Duration		2 days

130 Place Rebar
Type	Average Use	Total
Rebar	Lump Sum	$200
Jon	24 hours @ $25/hr	$600
Sweat Equity	24 hours @ $0/hr	$0
TOTAL		$800
Duration		6 days

210 Pour Concrete
Type	Average Use	Total
Concrete	12 yd3 @ $45/yd3	$540
Jon	6 hours @ $25/hr	$150
Sweat Equity	6 hours @ $0/hr	$0
TOTAL		$690
Duration		1 day

310 Setting & Curing
Type	Average Use	Total
Tarps	Lumps Sum	$50
Heater	4 days @ $50/day	$200
Sweat Equity	5 hours @ $0/hr	$0
TOTAL		$250
Duration		5 days

320 Strip Forms
Type	Average Use	Total
Sweat Equity	5 hours @ $0/hr	$0
TOTAL		$0
Duration		5 days

The overall project budget is therefore:

ID	Task	Budget
110	Excavation	$1,800
120	Build Forms	$100
130	Place Rebar	$800
210	Pour Concrete	$690
310	Setting & Curing	$250
320	Strip Forms	$0
TOTAL		$3,640

 

Here’s a checklist for resources:

• Labor.  Even if the cost to the project is $0, such as when a project member is borrowed from a technical department (or you’re doing it yourself, like above), they should be entered as resources because their availability can affect the project deadlines.
• Equipment.  Often equipment is sourced at hourly rates, or internally owned equipment has an hourly rate applied to it.
• Materials.  If the project needs to purchase materials, their cost is often easy to estimate from published rates, or quotes can be obtained from suppliers.
• Fixed cost items, such as a subcontractor.  This is a double edged sword, as a subcontractor’s costs are fixed, but they take responsibility for the schedule and quality of work away from you.  Also, you must know the fine print, or else the costs might not nearly be as “fixed” as you think.

A note of caution.  It is not only important to know what resources you need, but what their minimum specifications are.  For example, you might know you need a crane, but how big of a crane?  (I’ve seen the wrong size crane arrive at a site – I’m sure that cost the project some monopoly money).  It’s not always so obvious though, so make sure your resources are up to the task.

Step 3:  Create the Network Diagram

Since we’re not using project management software for this exercise, this network diagram will be produced with MS Excel.  Here is the original network, which is taken solely from the task list, above.  Click each image to enlarge it.

The Critical Path is defined as the longest path through the network, which means it defines the minimum completion date of the project.  A four step process is employed which determines the critical path, as well as the floats of non-critical path items.

1. Enter durations for all activities (previously calculated).
   
2. Perform a Forward Pass, which identifies the Early Start (ES) and Early Finish (EF) dates for each task.  These are entered into the top corners of the boxes, respectively.  Starting with the first task, ES = 1.  Then, EF = ES + Duration – 1.  Note that both dates are inclusive to the task duration so the EF always requires the subtraction of 1 day.  When passing through two parallel tasks, the highest EF is passed forward.
   
3. Perform a Backward Pass, which identifies the Late Start (LS) and Late Finish (LF) dates for each task.  These are entered into the bottom corners of the boxes, respectively.  Starting with the last task, LF = EF.  Then, EF = LF – Duration + 1.  When passing through two parallel tasks, the lowest LS is passed forward.
   
4. Calculate float for each task.  Float = LS – ES.
   

The minimum project duration is the EF (top right corner) of the final task, or 21 days.

Step 4:  Draw Initial Gantt (bar) Chart

To complete the scheduling process, a horizontal bar chart called a Gantt Chart is created.  This can be done in MS Excel as well although you need to have a good working knowledge of it.  It does not show the critical path but is the nicest, cleanest way to show the schedule.  It also allows for the final step in the process, which is resource levelling.  Here is the schedule:

The tasks are plotted on their ES dates, in other words as far as possible to the left.  At this point it is a coincidence if the resources do not contain spikes such as 12 hours of Jon’s time one day and 0 hours the next.  Therefore, we proceed to the next step called Resource Levelling.

Step 5:  Resource Levelling

In week 1, you are needed for 8 hours on friday, and 8 hours the following monday.  Since you have a full time job you are not available for 8 hours on those days.  In project management terminology, your resource calendar shows that you are not available.  Therefore, we need to move things around.

The gantt chart makes it clear that the building of forms (task 120) cannot start until the following week.  Also, you will need to work place rebar on saturday to avoid more than 4 hours of work per day.  Thus, we will move task 120, Build Forms, ahead by 3 days and ensure that both saturdays have 4 hours of work on task 130, Place Rebar.

 

When there are unacceptable spikes in resources, you have three options:

1. Keep the task duration constant and move the task forward or backward along its float.  The resources simply move to the new place in the schedule.
2. Increase the task duration within the float.  This will spread out the resources, for example, reducing a laborers hours on a task from 4 hours to 2 hours per day might eliminate overtime, but increase the duration of the task.  If that’s within the float, this is an acceptable solution.
3. Change the task end date past the end of its float.  This is the least desirable situation and it requires the rest of the schedule to be adjusted accordingly.  But sometimes it is necessary.

Step 6:  Schedule Compression

The last step applies only if you have to shorten the schedule.  Let’s say Jon decides he is leaving for a tropical vacation and the concrete must be poured on the friday prior to the regularly scheduled monday.

In this case, you have two options for each task:

1. Crashing.  This involves adding resources to the task.  Increasing Jon’s hours or getting the neighbor to help would be methods of crashing the schedule.
2. Fast tracking.  This involves performing tasks in parallel that are otherwise performed in sequence.  Building concrete forms before the excavation is done would be a type of fast tracking.  There is a risk of rework due to incorrect assumptions which must be made to account for incomplete predecessor tasks.

You also have three options which involve the overall project:

1. Change the scope.  Eliminate non-essential tasks from the project.  Maybe you can place less rebar.
2. Reduce quality.  Rent the excavator for one less day and don’t make the excavation lines as smooth.
3. Outsource.  Hire a laborer to complete tasks 120, Build Forms, or 130, Place Rebar.  This replaces the resource Sweat Equity (i.e. you don’t have to do it) and changes the durations of the tasks.

Good luck with your schedule.  Drop us a note in the comments to let us know how this process works for you!