Information about the personnel of teaching staff of an educational organization. Initial data for performing laboratory work
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Department 504
Specialties:
Applied informatics (in economics)
Economics and management at mechanical engineering enterprises
(specialization Electronic business)
Areas of bachelor's training:
Applied Informatics"
Management"
METHODOLOGICAL MATERIALS AND TASK OPTIONS
by discipline:
"Information Management", "E-Business Project Management", "Management information systems», « Information Technology
In Economics", "Information Technologies in Management"
with the participation of graduates of the department. 504
specialty 080801
Borodina V.A. and Romanova S.M.
Approved at the meeting of department 504
« 31 » August 2011 city, protocol No. 1
Moscow – 2011
| p. | |
| 1. Purpose laboratory work………………………………………………………………. | |
| 2. Assignment for laboratory work……………………………………………………….. | |
| 3. Recommended order of procedures for generating a stochastic network model using Microsoft Project………………………………………………………………………………... | |
| 4. Composition of the laboratory work report……………………………………. | |
| Appendix 1. Initial data for performing laboratory work in accordance with the assignment options.………………………………………………………………………………….. | |
| Appendix 2. Methodology for calculating some time indicators and forming the main versions of the stochastic network model when conducting analysis using the PERT method...................................... ........................................................ ........................................................ ..... |
Purpose of laboratory work
The purpose of the laboratory work is to obtain practical skills in drawing up a network implementation model design work(tasks) based on probabilistic estimates of their duration using the problem-oriented tool Microsoft Project. The network formed in this case is characterized as stochastic in terms of the duration of individual works and the project as a whole. As an example, a website development project is considered.
The main feature of the laboratory work is that during its implementation, the PERT network technology, within the framework of which a stochastic network model of the “arc-work” type (PERT-diagram) is formed, is simulated using the Microsoft Project tool, which implements a network model of the “vertex-to-work” type. work" (precedence diagram). For this purpose, the tools provided in the software product for analysis using the PERT method are used.
Laboratory assignment
Based on the list of project work to create a website and probabilistic estimates of their duration (Table 1 of Appendix 1 to these methodological materials), as well as information on the composition of the project team (Table 2 of Appendix 1), corresponding to the number of the assignment option assigned by the teacher, it is necessary formulate a stochastic network model, including a network version of the Gantt chart (a time-based network) and a canonical node-to-job network graph (precedence chart). The structure of the results generated during the development of the network model of project work, presented in the report on the implementation of laboratory work, is discussed in more detail in Section 4 of these methodological materials.
When performing laboratory work, the formation of an initial network model is provided. If necessary, in agreement with the teacher, procedures for optimizing the network model by resources are performed. The implementation of procedures for monitoring the implementation of the network diagram when performing this laboratory work is not provided.
For all project tasks, the “fixed duration” task type is used. When setting a specific start date for a website development project, you need to keep in mind that the project cannot start before the current date.
The methodology for calculating some time indicators and forming the main versions of the stochastic network model when conducting analysis using the PERT method is presented in Appendix 2 to these methodological materials.
Rice. 1. Dashboard for PERT analysis
12) Checking the Microsoft Project settings for calculating the mathematical expectation of the task duration in accordance with the formula adopted in the PERT method (see formula (1) in Appendix 2 to these Methodological materials). For this purpose, on the toolbar PERT Analysis(Fig. 1) you need to press the button Exercise weighting coefficients PERT method .
In the form that opens, the value of the weight coefficient in the field Optimistic must be equal to 1, in the field Expected– 4 and in the field Pessimistic– 1. If necessary, you can change the values of the weighting coefficients, keeping in mind that in all cases the sum of the weighting coefficients should be equal to 6.
13) Go to the data entry table for analysis using the PERT method: PERT input sheet(far right button on the panel for analysis using the PERT method, Fig. 1) and then filling it out.
It is necessary to fill in the columns with optimistic, expected and pessimistic duration estimates according to the data in Table. 1 of Appendix 1, corresponding to the assignment option. The information in the “Duration” column will be generated directly by Microsoft Project when performing procedure 14 (see below). Initially, this column contains single duration values.
14) Carrying out analytical calculations using the PERT method. To do this, click the button PERT calculations, located in the middle of the PERT analysis panel (see Fig. 1 above). Calculations will be performed after the user clicks the button Yes in the dialog box that appears, will confirm the intention to carry out calculations.
Evidence of the calculations performed is the appearance of the results in the “Duration” column in the data entry table for analysis using the PERT method instead of the initial single duration values entered in it, as well as the summary data for each of the local network models. It is possible to immediately view and analyze the results obtained.
15) Initiating the formation and viewing of the structural elements and indicators of the generalized network model generated by Microsoft Project.
15.1) Viewing the Gantt chart (Gantt Chart View), network diagram (Network graph view).
15.2) Initiating the formation and viewing of a resource loading schedule ( View Resource Graph), “Project Statistics” tabs ( Project Project Information Statistics).
15.3) Initiating the formation and viewing of the table Calendar plan : Right-click in the upper left corner of the Gantt chart and select the “Schedule” option in the menu that opens.
15.4) Initiating the formation and viewing of the table Summary data containing generalized results for the project: Right-click in the upper left corner of the Gantt chart and select the “Summary data” option in the menu that opens.
16) Initiating the formation and viewing of lists of critical and non-critical tasks: Set the "Critical Tasks" option in the Grouping menu(initially looks like) Right-click in the upper left corner of the Gantt chart in the menu that opens and select the “Schedule” option.
17) Ensuring printing of structural elements and indicators of the generalized network model generated by Microsoft Project. To do this you need to use standard "Print" button , standard "Preview" button , dialog box Page settings, its tabs (for example, the tab Page), and standard "Zoom in" buttons And "Decrease" .
Note 17.1. The output of tables can be replaced by the output of standard reports provided by the program ( View Reports).
Note 17.2. The “Project Statistics” tab is printed using the Print Screen procedure.
18) Viewing the network version of the Gantt chart and the corresponding indicators of local network models. To do this, on the toolbar PERT Analysis buttons need to be pressed Gantt chart - optimistic estimate , Gantt chart - expected estimate or Gantt chart - pessimistic estimate .
Printing of the relevant data must be carried out in accordance with the recommendations set out above in paragraph 17.
19) Determination of the spread of duration and completion dates of the project due to the influence of the uncertainty factor statistical method based on the calculation of the standard deviation of the duration of work and the variance of work and the project as a whole (if this is permissible) outside of Microsoft Project, for example, based on the use of a Microsoft Excel spreadsheet processor.
20) In agreement with the teacher, the initial network model is optimized by resources.
4. Contents of the laboratory work report:
1) Time-based network (network version of the Gantt chart) for a generalized network model.
2) Canonical network diagram of the “vertex-job” type (precedence diagram).
3) Charts of labor resource loading (selectively for two or three resources; presentation of charts for overloaded resources is mandatory).
4) Resource sheet after calculations.
5) Table “Summary data”.
6) Table “Schedule”.
7) List of critical and non-critical tasks.
8) Time-based networks (network versions of the Gantt chart) according to three local versions of the stochastic network model: optimistic, most probable, pessimistic.
9) Tables with time indicators for each of the local versions of the stochastic network model (duration of tasks, start and end dates of tasks, duration and timing of the project as a whole).
Note: specified in paragraphs. 8 and 9, diagrams and tables for each version of the network model can be combined into one form.
10) Data entry table for analysis using the PERT method with calculation results.
11) The main results of solving the problem according to the following scheme:
11.1) Generalized indicators for the project as a whole:
● duration of the project in working days (mathematical expectation) –
● project start date –
● project completion date (mathematical expectation) –
● labor intensity of the project in man-days –
● costs wages for the project in rubles –
11.2) Expert assessment of the spread of duration and timing of the project:
● optimistic duration in working days –
● pessimistic duration in working days –
● most likely duration in working days –
● expected duration in working days –
● expert spread of duration in working days and percentage of project duration –
● optimistic project completion date –
● pessimistic project completion date –
● most likely project completion date –
● expected completion date of the project ‒
● expert spread in calendar days –
● eccentricity in calendar days (the difference between the most probable and expected project completion dates) –
● conclusion about the correctness of the statistical assessment of the spread in the duration and timing of the project.
11.3) Statistical evaluation spread of project duration and deadlines:
● dispersion of the duration of tasks and the project as a whole (in tabular form).
● standard deviation of the duration of tasks and the project as a whole (in tabular form).
● “three sigma” value, working days –
● mathematical expectation of project duration, working days –
● statistical assessment of the optimistic duration of the project in working days –
● statistical assessment of the pessimistic duration of the project in working days –
● statistical spread of project duration in working days and percentage of project duration –
● optimistic project completion date based on statistical assessment –
● pessimistic project completion date based on statistical assessment –
● statistical spread of project duration in calendar days –
● conclusions on the procedure for comparing expert and statistical estimates of the spread of project duration and completion dates.
The composition of additional final forms in the case of network optimization by resources is agreed upon with the teacher.
ANNEX 1
Initial data for performing laboratory work
in accordance with the task options
Option 1.
Table 1
Composition of the project team
Option 2.
Table 1
Composition of the project team
Option 3.
Table 1
Composition of the project team
Option 4.
Table 1
Composition of the project team
Option 5.
Table 1
Composition of the project team
Option 6.
Table 1
Composition of the project team
Option 7.
Table 1
Composition of the project team
Option 8.
Table 1
Composition of the project team
Option 9.
Table 1
Composition of the project team
Option 10.
Table 1
Composition of the project team
Option 11.
Table 1
Composition of the project team
Option 12.
Table 1
Composition of the project team
Option 13.
Table 1
Composition of the project team
Option 14.
Table 1
Composition of the project team
Option 15.
Table 1
Composition of the project team
Option 16.
Table 1
Composition of the project team
Option 17.
Table 1
Composition of the project team
Option 18.
Table 1
Composition of the project team
Option 19.
Table 1
Composition of the project team
Option 20.
Table 1
Composition of the project team
Option 21.
Table 1
Composition of the project team
Option 22.
Table 1
Composition of the project team
APPENDIX 2
PERT analysis
In the PERT method it is accepted beta distribution probabilities of duration of work with mode at a point t nv(i - j) and ends at points t min (i - j) And t max (i - j), Where:
t min (i - j)- minimum (optimistic) estimate of work duration;
t nv(i - j)– assessment of the most probable duration of work (mode);
t max (i - j)– maximum (pessimistic) estimate of the duration of the work.
These estimates of the duration of the work are set by experts, and the experts, as a rule, are the future performers of the work.
To calculate the expected duration (mathematical expectation of duration) of work when using the PERT method, the following formula is used:
t cool (i - j) = (t min(i - j) + 4 t cool (i - j) + t max(i - j)) / 6 , where (1)
It is important to emphasize that the calculation according to formula (1) is performed by the Microsoft Project tool based on expert data entered by users of the software product. When performing laboratory work, these calculations should not be duplicated: computer technology allows you to obtain more accurate results, in addition, a comprehensive system of various time indicators of the network model is formed, expressed both in working (duration of tasks and project, time reserves) and in calendar (deadlines occurrence of events, project completion) days.
Based on four estimated work duration indicators ( t min (i - j), t nv(i - j), t max (i - j) And t cool(i - j)) four main versions of the network model are formed with critical paths of different durations, and, consequently, different estimates of the duration of the project as a whole - minimum (optimistic), most probable, maximum (pessimistic) and expected ( Tmin, Tnv, Tmax And T cool) and the timing of its implementation.
The network model, formed on the basis of the results of calculating the expected duration of the project tasks, can be considered as a generalizing one, and the remaining models can be considered as local ones complementing it.
For a stochastic network of this type, additional time indicators are calculated, aimed at assessing the possible spread in the duration and timing of individual works and the project as a whole due to the influence of the uncertainty factor. An adequate beta probability distribution is expert review duration (and timing) of work and the project as a whole. The spread of duration in this case is defined as the difference between its pessimistic (maximum) and optimistic (minimum) value:
a) for the project:
Δ t (i - j) = t max(i - j) - t min(i - j)(2)
a) for the project as a whole:
Δ T = T max - T min(3)
A relative disadvantage of the expert assessment of the dispersion is that the dispersion of the project duration due to the effect of the uncertainty factor may directly exceed the value of its expected duration or, at least, be commensurate with it. This makes the assessment of the spread of the duration of the project and the timing of its implementation insufficiently correct. At the same time, it can be argued that the probability of the project duration falling within the “scatter interval” practically equal to 1 (if force majeure circumstances are not taken into account).
If the mode and mathematical expectation are close in value, then you can use statistical estimates spread of durations and terms of project implementation, accepted for normal probability distribution, – standard deviation and variance of the duration of the work, as well as the project as a whole. It is assumed that the range of fluctuations (spread) of the duration of work under the influence of uncertainty is equal to six standard deviations, i.e. standard deviation can be determined by the formula:
σ (i - j) =(t max (i - j) - t min (i - j)) / 6 (4)
The variance of the work duration in this case is equal to:
σ (i - j) 2 =[(t max(i - j) - t min(i - j)) / 6] 2 (5)
The variance of the project duration as a whole is defined as the sum of the variances of the critical activities. The standard deviation of the duration of the project is determined by extracting square root from the project variance value. Based on this, according to what is known in mathematical statistics The “three sigma” rule can determine the possible variation in the duration (and timing) of the project as a whole.
The statistical estimate of the spread of project duration is noticeably less than the expert estimate due to the fact that the project duration falls within the “scatter interval” in the absence of force majeure guaranteed with probability 0.997 (which is less than 1, but seems quite sufficient) . It is easy to see that for project work the expert and statistical spread of duration coincide, therefore the smaller value of the statistical spread of the duration of the project as a whole can also be interpreted on the basis of the hypothesis of paying off the delay of some critical works by completing others ahead of schedule.
The calculation of the standard deviation and variance of the work and the project as a whole is carried out outside of Microsoft Project, for example, using the Microsoft Excel spreadsheet processor.
For Microsoft Project 2007 and older.
The technical editors of the Russified version of Microsoft Project used the expected rating to mean the most probable rating (mode).
Mathematical expectation of duration.
It is more precise to talk about the mathematical expectation of the duration and completion dates of the project.
If there is a significant discrepancy between the mode and the mathematical expectation of the project duration, replacing the beta probability distribution with a normal one can lead to a significant error in estimating the spread.
The Greek letter sigma in statistics usually denotes standard deviation.
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