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What is the critical path in project management, critical path network terminal element is an element of sequence that has the longest total duration of the project and determine the shortest completion time.
duration of the critical path determines the project duration. Any critical path delay of the terminal elements of the project will directly affect the expected completion time (for example, do not float on the critical path time).
a project can have multiple, parallel critical path. Another critical path than the total duration of slightly less of a total duration of parallel paths is called sub-critical path.
Initially, the critical path method considered only the logic between the terminal element dependencies. Critical chain method to increase the resource constraints.
critical path method is invented by DuPont.
characteristics of the critical path critical path has the following characteristics:
1, the activities on the critical path determine the duration of the project duration, critical path duration of all activities add up to the project duration.
2, on the critical path activities are the key activities of any one, any delay will cause an activity to complete the entire project time delay.
3, the critical path is from the beginning to the end point of the project the longest route in the route, so in order to shorten the project duration, critical path must think of ways to the contrary, if the critical path takes longer, then completion of the entire project will be extended.
4, critical path time-consuming to complete the project is the shortest amount of time.
5, the activities on the critical path is the minimum total float activity.
explore the critical path, said the incident with the vertices, arcs activities, the weight of the arc that the duration of activity are directed graph called AOE (Activity On Edge Network) network. AOE network commonly used in the estimation of completion time. For example:
Figure 1 is a network. 9 of which event v1, v2, …, v9; 11 events a1, a2, …, a11. Before each event that the activities it has been completed, it can begin after the event. That the whole project started as v1, v9 that the end of the whole project. V5 that activity, a4, and a5 have been completed, activities, a7 and a8 can begin. Associated with the right of each activity that the time required to complete the activities. If the activity a1 takes 6 days to complete.
1) AOV network has the nature of the
only represented by a vertex incident, starting from the vertex of each edge represents the activities to be started. Only have access to the edge of a vertex represents activity has ended, the vertices represent events take place. AOE represents the actual net project should be no ring, and there is only the beginning of entry through the vertex 0 and the only complete out-degree 0 vertices. 2) from the earliest occurrence of the event vj time of occurrence time and the latest definitions, you can take the following steps to obtain the key activities:
A, starting from the beginning of vertices v 1, so that ve (1) = 0, according to the topology ordered sequence of the remaining vertices seeking the earliest possible time.
Ve (k) = max {ve (j) dut (j, k)} (1.1) j ∈ T where T is the vertex vk to all the arcs of the head end of the set of points (2 ≤ k ≤ n .)
topology if ordered by the number of vertices in the sequence is less than the net number of vertices n, is illustrated in a ring network and can not find the critical path, the algorithm ends.
B, starting from the completion of the vertex vn, so that vl (n) = ve (n), ordered by inverse demand topology allows the rest of the vertices of the latest time of occurrence:
vl (j) = min {vl (k)-dut (j, k)} k ∈ S where S is the vertex vj is the head of all the arc of the tail vertex set (1 ≤ j ≤ n-1).
C, ask each activity ai (1 ≤ i ≤ m) the earliest start time e (i) = ve (j); the latest start time:
l (i) = vl (k )-dut (j, k) if a certain arc to meet the e (i) = l (i), it is the key activity.
AOE for the network shown in Figure 1, according to the calculation of the above steps results in Table 1, available a1, a4, a7, a8, a10, a11 is the key activity.
3) Find all the key activities of AOE network, simply by deleting all of the AOE network non-critical activities, you can get AOE network critical path.
time to complete from start vertex to reach all the paths are vertex critical path. An AOE network can be more than one critical path, as shown in Figure 7.21 of the AOE network has two critical paths, (v1, v2, v5, v7, v9) and (v1, v2, v5, v8, v9) have their path length 16. Figure 2:
Note: not speed up any one of the key activities can reduce the time to complete the entire project, only to speed up those included in all key activities on the critical path to achieve this goal. AOE only network without changing the premise of the critical path to speed up included in the key activities on the critical path can shorten the project completion time.
From: MBAlib
Today in History:

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2008 January-June general machinery industry in good shape overall economic performance, production, sales, profits continue to maintain the rapid growth of more than 30%, 1 – June general machinery industry total industrial output value of 192.201 billion yuan, an increase of 34.25, higher than the national machinery industry in industrial output growth rate 4.64 percentage points year on year; accumulated industrial sales output value of 184.226 billion yuan, an increase of 33.19%, higher than the national machinery industry output value of industry sales growth rate 3.13 percentage points year on year.
The main features of economic performance:
a production steady and rapid growth. 1 – 6 April the month of statistics, general machinery industry, above-scale enterprises this year, 1 – 6 months total industrial output value and sales of the output growth continue to maintain rapid and steady growth, year on year growth rate of production of the first five months this year, the same as last year 2 – 3 percentage points, slightly down year on year growth in June, down 0.07 percentage point;
Second, the export delivery value of steady growth. 1 – 6 April the month of statistics, the export delivery value remains steady at 20% of growth rate, but year on year growth compared to last year, an increase of falling significantly.
three main products industry increased year on year growth rate slowed down. 1 – 6 月份 main products industry statistics, pumps, gas compressors, valves, gearbox reduction, separation machinery output up double-digit growth, year on year growth rate of the industry year on year growth over last year monthly decline. Where: fan industry fell by 51 percentage points year on year increase was due mainly in Shanghai, Zhejiang, Guangdong Province three fan industry output accounted for 80% of total output, which is three in June 2007 the cumulative increase of 42% this year June cumulative increase of -20.96%, the fan output in the statistics of cities in 28 provinces, 10 regions of negative growth. Separation machinery output showing a 116.69 percent year on year growth rate of the growth is due to be completed in Shandong Province in June 9490 separation of mechanical units, the industry-wide 1 – 6 of the total fish meal 49.55%, an increase of 851.17 percent increase, adjustment factors can not be compared with an increase of 19.96%.
four, the total profit to maintain rapid growth, an increase of somewhat lower. Statistics show that, 1 – May the whole industry realized a total profit of 9.068 billion yuan total, an increase of 35.68%, an increase over the same period last year, 3.45 percentage points over the year from January to February fell 6.12 percentage points.
five, industry loss increased slightly. 1 – 5 month, the industry loss 15.48%, the cumulative losses of 617 million yuan, an increase of 24.4% loss compared to same period last year 121 million loss.
From the above data and analysis can be seen: general machinery industry production, sales, profit growth higher than the increase in physical volume of products that the industry continues to increase overall competitiveness, in recent years, production technology and equipment updates, and product structure the optimization and upgrading, so that production capacity, technical equipment, improve product competitiveness, advantages corporate strength gradually. Homogeneous industry competition remains severe, leading to lower growth in the telling of loss and the increase in losses. With iron ore prices will trigger a new round of steel price increases this year steel industry will face a new round of price increases test the ability of mature products is weak to withstand price increases, it is difficult to pass down or self-digestion prices, there is an urgent need to accelerate the upgrading of industrial structure, growth pattern.
early this year the national macro-control measures taken will gradually appear, industry growth will slow down. Since the state domestic well, full of enterprise task orders, production and sales of the second half of the industry will maintain a growth rate of around 30%.

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