Monte Carlo

Wprowadzenie do technik symulacyjnych

W projekcie może być setki działań, z których każde posiada własne zasoby, ryzyka i inne czynniki wpływające na czas trwania. Różnice w tych źródłach mogą prowadzić do różnych rezultatów projektu. W tym celu wykorzystujemy techniki symulacyjne, aby sprawdzić, co się stanie, jeśli nastąpią zmiany w jednym lub kilku czynnikach.

Analiza Monte Carlo

Jedną z najczęściej stosowanych technik symulacyjnych jest analiza Monte Carlo. Choć w egzaminie nie będziesz musiał wykonywać obliczeń związanych z tą techniką, musisz zrozumieć jej działanie, ponieważ możesz napotkać to pojęcie w pytaniach.

W analizie Monte Carlo komputery wykonują obliczenia, bazując na wielu możliwych scenariuszach. Na przykład, technika trzech punktów szacowania, o której mówiliśmy wcześniej, wykorzystuje optymistyczne, najbardziej prawdopodobne i pesymistyczne oszacowania czasu trwania działań.

Przykład

Załóżmy, że mamy trzy działania z różnymi oszacowaniami czasu trwania. Na przykład, czas trwania działania A może wynosić od 3 do 6 dni, działania B od 4 do 7 dni, a działania C od 1 do 3 dni. Jeśli wszystko pójdzie idealnie, projekt może być ukończony w 8 dni. Jednak każde działanie ma szansę być wykonane w czasie mieszczącym się w zakresie między wartościami optymistycznymi a pesymistycznymi.

Komputer wykonuje obliczenia dla losowo wybranych możliwości czasowych i generuje wykres przedstawiający zakres możliwego czasu trwania projektu. Ten wykres nazywany jest krzywą S, ponieważ przypomina kształt litery „S”.

Analiza Monte Carlo nie ogranicza się tylko do czasu trwania projektu. Można jej użyć do szacowania kosztów projektu, ryzyka lub prawdopodobieństwa, że dane działanie znajdzie się na ścieżce krytycznej.

Analiza scenariuszy typu “What-if”

Kolejną techniką jest analiza scenariuszy typu “what-if”, która jest podobna do analizy Monte Carlo. Różnica polega na tym, że w analizie scenariuszy wybieramy konkretne scenariusze logicznie, a nie losowo, i sprawdzamy, co by się stało, gdyby dany scenariusz miał miejsce.

There may be hundreds of activities in a network diagram. Each activity has its own source. For example, resources are different for each activity. Differences in these sources may result in different results on the project.

We use simulation techniques to investigate the different results of different scenarios. In other words, we use simulation techniques to see what happens if there is a change in one or more activity sources. These sources may be the resources, risks, or anything that may affect the activities’ duration.

Monte Carlo analysis is a commonly used simulation technique. We use computers to apply this technique, and you will not calculate anything about this technique in the exam. But for the exam, you need to understand this technique since you may see this term in the questions.

So let’s talk about this technique. In some sources, they may use the term Monte Carlo simulation instead of Monte Carlo analysis. Both terms are the same.

To understand how the Monte Carlo analysis is done by computers, we will have a simple example. In the previous lectures, we mentioned the three-point estimation technique. We use this technique to estimate an activity’s duration or cost. As you will remember, in this technique, we use the optimistic, most likely, and pessimistic estimates to obtain more realistic estimations.

Let’s say we have only three activities here in this table. We see the optimistic, most likely, and pessimistic estimates for these activities. As you see, the duration of activity A may occur between 3 and 6 days. The duration of activity B may be between 4 and 7 days, and the duration of activity C may be between 1 and 3 days.

Let’s take the optimistic ones only and calculate the project duration accordingly. As you see, we find the project duration as eight days. This means if everything goes perfectly well for each activity, we can complete the project in eight days. This is only one of the probabilities of the possible different results. There are lots of other possibilities as well.

For example, activity A and B may be completed optimistically, but activity C’s duration may end up with its most likely duration. As you see, in this case, the project duration becomes nine days. In reality, all of the activities have a chance of being completed in any duration between their optimistic and pessimistic values.

For example, activity A may be completed in four days. Activity B may be completed in 5.5 days, and activity C may be completed in 1.3 days. The computer does the calculations for the randomly selected duration possibilities and calculates the possible amounts of the project duration. It does these calculations about 10,000 times for different scenarios and draws a graph about the range of the possible project duration. The traditional name of this graph is the S curve. This name comes from the S-shaped form.

Here, we can ask the computer the possibility of the project being completed in, for example, ten days, and it answers our questions. This is how the Monte Carlo analysis is done. Again, I would like to remind you that they will not ask you to do the Monte Carlo calculations on the exam, but to be able to comment on the questions, you need to know how it is done and what it is used for.

We can use Monte Carlo analysis for calculating the probabilities of not only the project duration but also the project cost. We can do similar calculations by using the cost information and get a range for the project budget. For example, as a result of the analysis, we can conclude the probability of completing the project between $20,000 and $30,000 as 80%. Similarly, we can use this simulation to calculate an activity’s possibility of being in the critical path or calculating the project risks.

Sometimes, what-if scenario analysis can also be helpful when developing the schedule. Since this is almost similar to the Monte Carlo simulation technique, I would like to mention this technique in this lecture. As I said, what-if scenario analysis is almost similar to Monte Carlo. There is only one difference: in the Monte Carlo simulation technique, we calculate the schedule by using randomly selected estimates from a determined range. But in the what-if scenario, we do the calculations for different scenarios that are determined logically. We don’t choose them randomly.

For example, we determine a scenario. Let’s say scenario A, and we calculate the schedule and investigate the answer to the “what if scenario A happens” question. Then we determine another scenario and calculate the schedule to find the answer to the “what if scenario B happens” question. We then use these results to determine the schedule resource, the feasibility of the project, and so on.