How to solve

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task, prone to a lot of errors. At this point, the need for a specific algorithm for crashing a schedule is needed, as well as a preliminary programmed sample.

Analysis And Algorithm

The Traditional Crashing Method

The most basic and correct crashing method is the manual method, where activities are crashed on a day$-$by$-$day basis. This method, although resulting in correct results, is very time$-$consuming and can create an obstacle for project managers with limited time. The basic information needed to perform this method are five items, along with the project network diagram. First, the project manager needs to prepare a list of the activities, with the following attributes for each activity: normal cost, normal duration, crash cost, and crash duration. To determine the normal duration and the crashed duration, he must determine the budgeted quantity of work as well as the normal rate of productivity and the maximum rate of productivity. Then, he calculates the durations according to the following formulas $(1)$ and $(2).$

Normal Duration $=\frac{\text{B}\text{u}\text{d}\text{g}\text{e}\text{t}\text{e}\text{d}\text{Q}\text{u}\text{a}\text{n}\text{t}\text{i}\text{t}\text{y}}{\text{N}\text{o}\text{r}\text{m}\text{a}\text{l}\text{R}\text{a}\text{t}\text{e}of\text{P}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{y}}$

Crahsed Duration $=\frac{\text{B}\text{u}\text{d}\text{g}\text{e}\text{t}\text{e}\text{d}\text{Q}\text{u}\text{a}\text{n}\text{t}\text{i}\text{t}\text{y}}{\text{M}\text{a}\text{x}\text{i}\text{m}\text{u}\text{m}\text{R}\text{a}\text{t}\text{e}of\text{P}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{y}}$

$3$

Afterward, the slope is calculated, which is the daily increase in an activity cost. This slope is calculated using the formula:

Slope $=\frac{\text{C}\text{r}\text{a}\text{s}\text{h}\text{e}\text{d}\text{C}\text{o}\text{s}\text{t}-\text{N}\text{o}\text{r}\text{m}\text{a}\text{l}\text{C}\text{o}\text{s}\text{t}}{\text{N}\text{o}\text{r}\text{m}\text{a}\text{l}\text{D}\text{u}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}-\text{C}\text{r}\text{a}\text{s}\text{h}\text{e}\text{d}\text{D}\text{u}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}}$

Furthermore, when crashing the project, a new set of critical paths may emerge and the crashing procedure needs to take those new critical paths into consideration. On the other hand, when crashing an ongoing project schedule, the project manager will follow the same instructions discussed above, but with one major difference. An ongoing schedule has completion percentages for activities, and therefore the originally schedule durations should be replaced by remaining durations, and the crash duration shall be multiplied by the remaining percentage till completion, and rounded up$.$ The completion percentage shall be determined using formula $(6),$ after determining the actual quantity of work performed.

Completion Percentage $=\frac{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{Q}\text{u}\text{a}\text{n}\text{t}\text{i}\text{t}\text{y}}{\text{B}\text{u}\text{d}\text{g}\text{e}\text{t}\text{e}\text{d}\text{Q}\text{u}\text{a}\text{n}\text{t}\text{i}\text{t}\text{y}}100$

$12$