## The shopping project – contingency time

Do you go on weekly or fortnightly supermarket shopping expeditions? Either way, this blog item might help you determine your shopping contingency time (or contingency time for any other project) – that’s the extra time needed to allow for possible delay-causing incidents during project implementation. This blog item shows us how to determine contingency time somewhat more scientifically than merely thinking of a number and doubling it or throwing dice.

Part of the solution is to apply what’s called the PERT formula (Program Evaluation and Review Technique). This formula allows us to determine a project’s best estimated time (BET) or duration – depending always on the accuracy of our input data. (*PERT is a weighted-average estimate, heavily weighted towards the most likely duration (ie, 68.3%), which is one standard deviation (sd) either side of the norm – for those interested in such stuff.*)

While an “exact estimate” is clearly an oxymoron, an “accurate estimate” of project duration is that duration that gives us a 50% chance of early completion and a 50% chance of late completion. Such an estimate occupies the middle ground, where there is just as much chance of the project taking longer as there is of it taking a shorter time to complete. However, many projects are time-driven (the principal parameter is time) when on-time or very near on-time project completion is required. For such projects we need to add contingency time to help ensure we have a project duration that gives us a realistic chance of on-time completion, this contingency time being in recognition of Murphy’s Law – “Whatever can go wrong, will go wrong.”

This diagram shows a typical beta frequency distribution for project duration, where there is a limit to how early a project can be completed (optimistic estimate = 10), but practically no limit to how long the project might take (pessimistic estimate = 25). Usually there are many more negative risks (or threats) that can delay project completion than there are positive risks (or opportunities) that can cause the project to be completed ahead of schedule – hence the lop-sided shape to this distribution curve, rather than the more common symmetrical bell-shaped distribution curve. So, modern thinking is that risks can also have a positive impact. They aren’t just bad things. In fact, project risk has been defined as uncertainty that impacts project parameters (time, cost, quality, scope and benefits) for better or for worse. Risk management aims to avoid or reduce threats and enhance or exploit opportunities. In this example, where O is the Optimistic duration (10), L is the Most Likely duration (13.75) and P is the Pessimistic duration (25), the best estimated time (BET) 15 has been determined thus:

**BET = {O + (4 x L) + P}/6 = {10 + (4 x 13.75) + 25}/6 = 15 (weeks)**

Incidentally, should we ever apply this formula, remember to complete the maths functions in the correct sequence, starting with inside brackets first. (*The “BEDMAS” sequence is explained at **http://math.about.com/od/glossaryofterms/g/What-Is-Bedmas.htm*.)

Anyway, back to my family’s supermarket shopping expedition. From experience, I know if it’s a straightforward job with all shopping-list items readily available and very few other shoppers cluttering the aisles, time spent in the supermarket can be as little as **22 minutes** – most welcome, but seldom happens. However, there have also been some rare occasions when supermarket-shopping time has blown out to an almost intolerable **100 minutes** caused by a combination of frustrations such as these:

- Shelve layout has changed since our last visit, such that items take longer to find.
- A shopping list with several indecipherable hand-written entries.
- Some items are out of stock, but this is only evident after time spent searching.
- Time-consuming comparison of product prices and content information.
- Many other shoppers slowing our progress, including shopping trolley logjams.
- Too few checkouts open, resulting in longer queues and wait times.
- Mum meets friends and has time-consuming (and seemingly frivolous) discussions.
- Delay caused by cheque (check) book use rather than credit cards or cash.
- Daughter selects too-expensive items that need to be put back.
- Some smart bugger beats us to the shortest or quickest checkout queue.
- Our queue is the slowest (seemingly whichever queue we join or when we join it).
- Checkout operator dawdles away to find the price of some items.

However, experience tells me that the most likely duration for our weekly shopping project is **40 minutes. **

Using our shopping scenario, we can determine that project contingency to provide us with our required level of confidence for on-time project completion. The higher our required level of confidence, the greater is the required contingency, and the longer will be our project’s planned duration. The following table provides the formula for different levels of confidence for on-time completion (applicable to all projects). (*The multipliers given in the table range from 0 for 50% confidence level up to 3 for 100% probability of on-time completion, and these are based on standard deviations of which there are three either side of the norm.)*

All this calculating tells us that to have a 80% likelihood of on-time completion we should allow 58 minutes for our shopping project, which includes a contingency of 11 minutes.

Another way to determine this contingency is by risk quantification. Thus, after identifying risk events, we assess the time delay that each of these events might cause our project and the probability or likelihood (based on historical frequency) that each of these risks will arise. The sum of the product of these two figures for each risk allows us to determine a time contingency for the project. In this example, we assume that these risks could all delay tasks on the project critical path. The critical path is that sequence of tasks, the sum of which individual task durations determine the project’s estimated duration. The following table may help you understand what I mean:

So using this method, the shopping contingency would be 24 minutes, providing a risk-adjusted estimated project duration of 71 minutes. Of course as our shopping project moves past exposure to each of these risks without mishap, the total contingency should be reduced in proportion to the reduced project risk, otherwise we there may be irresponsible time-wasting activities towards the end of the project simply to use up contingency. In other words, as Parkinson’s Law tells us, “Time to complete a project expands to fit the time available.” – another reason for this skewed frequency distribution.

Incidentally, the same types of calculations as those explained above can also be applied to project costs, where the potential impact of a risk is expressed as dollars loss caused by the risk should it occur, plus the dollars to put it right, and probability is again expressed as a percentage likelihood, determined mainly from previous experience. Expected monetary value (EMV) is a risk score derived from multiplying risk impact (dollars) by risk probability (eg, $2,000 x 30% = $600). Adding up the EMV for each risk provides us with contingency dollars for our project.

Complicated novel projects or pioneering endeavours that possess considerable uncertainty, about which we have no risk history, usually need bigger contingencies for time and cost than do our more familiar projects. They also need a significant management reserve, which is extra time or money to cater for unanticipated events. In fact, now that I think about it further, most supermarket expeditions are more likely to blow the budget than they are the duration, unless we rigidly adhere to our shopping list (yeah right), keep abreast of escalating prices and ignore those strategically-placed tempting items at the checkout where we invariably need to wait.

One such unanticipated event, verging on “black swan” risk status, might be a supermarket fight that further delays a shopping trip when guards attempt to retrieve stolen goods, a rather funny local example of which is shown here in this short video. Check the bag-wielding bum-crack chick. Turn up the sound for best effect. What would you do? http://www.youtube.com/watch?v=jwjW1Q0jowg

If you are interested in this risk stuff, my book “Managing Murphy” that comprehensively explores the subject of project risk management is available from jim_young@xtra.co.nz or from New Zealand Whitcoulls’ bookshops – see http://www.whitcoulls.co.nz. Also, here is a taster.