First, if you have not yet tried this past weekend’s PM Puzzler, it’s not too late. Just scroll down through my blog to the next article before you read the answers below.

Next, my congratulations to all who even attempted to answer the questions on this PM Puzzler. Knowing how to figure out these types of answers is important! And those who tried but got it wrong have demonstrated a willingness to try to compute new and valuable information. I will be only too delighted to help you master these calculations.

Of course, this information is *exactly *what project management software should calculate – that’s why those things are called “computers”! Again, if your company’s software doesn’t currently compute drag and drag cost (not to mention expected project profit and the DIPP), urge your provider to start including this functionality.

**Answers**

Of course, I don’t know how many people actually tried the puzzle, but just didn’t enter their answers in the forms below the exercise. However, as of 3:30pm US East Coast Time:

- Thirteen people entered an answer for the first question “1. On which ONE activity would you spend the extra $100K?” and five of them got it correct. Congrats, you five!
- Eleven people entered an answer for the second question “ How much more expected project profit (EPP) will the project have as a result of your decision to spend that $100K (or not to)?” No one got it correct.
- Nine people entered an answer for the third question “ The Starting DIPP for the project with the 54 day schedule was $800K divided by $400K = 2.0. What will the Starting DIPP be if you made the correct decision?” And nobody got this one correct.

**Explanations**

Question 1: “On which ONE activity would you spend the extra $100K?”

Solving this problem (like almost any problem that involves shortening a project schedule!) should start with computing the drag of the critical path activities. I have computed each in the network diagram shown below.

- Activity A, with nothing else in parallel, has drag of 2W due to its duration. Cutting its duration by 50% would therefore reduce the project duration by just
**one week**. - Activity D has drag of 4W, constrained by the total float of the parallel activity with the least total float, i.e., Activity E with total float of 4W. Cutting Activity E’s duration of 8W by 50% would therefore reduce the project duration by the full
**four weeks**of its drag. - Activity I has drag of 6W due to the sum of the lag-plus-total float (0 + 6) of its start-to-start successor Activity H, which is
*less than*the total float of any of the parallel activities. Cutting Activity I’s duration of 12W by 50% would therefore reduce the project duration by the full**six weeks**of its drag. - Although all of Activity M’s parallel activities have either 8W or 10W of float, (note that E and H are not parallel but ancestors and P is a descendant, all sharing a path with Activity M), its duration of 4W constrains its drag to 4W. Cutting Activity M’s duration of 4W by 50% would therefore only reduce the project duration by
**two weeks.** - Activity Q, despite its duration of 24W, has drag of only 2W due to the TF of parallel Activity P. Therefore even though Q’s duration could be cut by 12W, only two of those weeks would be drag. The impact of such a reduction in Q’s duration would be merely to give it 10W of float! Cutting its duration by 50% would therefore reduce the project duration by just
**two weeks**despite its juicy duration being twice as long as that of any other critical path activity. - Finally, Activity S, with nothing else in parallel, has drag of 4W due to its duration. Cutting its duration by 50% would therefore reduce the project duration by just
**two weeks.**

Question 2: How much more expected project profit (EPP) will the project have as a result of your decision to spend that $100K (or not to)?”

At the original schedule of 54 weeks duration, the project’s expected monetary value (EMV) was $1M minus $200,000 for the delay cost of two weeks beyond 52 weeks, or $800,000 on a budget of $400,000, for an EPP of $400,000. By spending an additional $100,000 on Activity I, the project’s expected completion will be pulled in by six weeks, from Week 54 to Week 48. The first two of those weeks will erase the delay costs of $100,000 per week, or $200,000. The remaining four weeks of acceleration will result in increased value of $50,000 per week, or an additional $200,000. Thus the EMV will increase by a total of $400,000 to $1.2M, while the cost increases by $100,000, from $400,000 to $500,000. Increased EMV of $400,000 for a cost of $100,000 means an increase in EPP of $300,000, from $400,000 with the 54 week schedule to $700,000 with the 48 week schedule. (No one got this correct, which, considering the extensive knowledge and experience of many of the folks reading this blog, surely says that this sort of analysis just isn’t being done very often.)

Question 3: The Starting DIPP for the project with the 54 day schedule was $800K divided by $400K = 2.0. What will the Starting DIPP be if you made the correct decision?

The DIPP is simply (EMV plus or minus acceleration premium or delay cost) divided by cost estimate-to-complete. If the EMV at 52 weeks is $1M and the acceleration premium for finishing four weeks earlier (48 weeks) is $50,000 per week, the EMV of the project with its new 48 week schedule will be $1.2M. At the start of the project, the Cost ETC is the budget, now $500,000. The Starting DIPP with the new schedule will therefore be $1.2M divided by $500,000, or 2.4.

Notice that this is up from the 2.0 before assigning the additional $100,000 to resources for Activity I. This is how we can now justify additional resources on specific items if we know the value/cost of time. And during project execution, we should track and attempt to maximize the DIPP as the prime metric of our project investment.

If there are any comments or questions about this exercise and the answers, I will be delighted to answer them here. And if you found this whole exercise interesting, please pass the URL along to other people at work who might find it interesting.

Fraternally in project management,

Steve the Bajan