Chair 504

Specialties:

Applied informatics (in economics)

Economics and management at engineering enterprises

(specialization Electronic business)

Directions for the preparation of bachelors:

Applied Informatics"

Management"

METHODOLOGICAL MATERIALS AND ASSIGNMENT OPTIONS

by disciplines:

"Information Management", "E-Business Project Management", "Information Systems Management", "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

	page
1. Purpose laboratory work……………………………………………………………….
2. Task for laboratory work……………………………………………………………..
3. Recommended order of procedures for generating a stochastic network model using Microsoft Project…………………………………………………………………
4. The composition of the report on the implementation of laboratory work…………………………………….
Annex 1. Initial data for laboratory work in accordance with the task options.…………………………………………………………………………..
Annex 2. Methodology for calculating some time indicators and forming the main versions of the stochastic network model when conducting an analysis using the PERT method ................................................... ................................................. ................................................. .....

Purpose of the Lab

The purpose of the laboratory work is to gain practical skills in compiling a network model for the implementation of design work (tasks) based on probabilistic estimates of their duration using the problem-oriented Microsoft Project tool. The network formed in this case is characterized as stochastic in terms of the duration of individual works and the project as a whole. A website development project is considered as an example.

main feature laboratory work is that when it is performed, the PERT network technology, within which a stochastic network model of the “arc-work” type (PERT-diagram) is formed, is simulated using the Microsoft Project tool that implements the network model of the “vertex-work” type (precedence diagram). For this purpose, the PERT analysis tools provided in the software product are used.

Assignment for laboratory work

Based on the list of design works for the creation of the website and probabilistic estimates of their duration (Table 1 of Appendix 1 to these teaching 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 form a stochastic network model, including a network version of the Gantt chart (time-oriented network) and a canonical network graph of the "vertex-work" type (precedence diagram). 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 teaching materials.

When performing laboratory work, the formation of the initial network model is provided. If necessary, in agreement with the teacher, procedures for optimizing the network model for resources are performed. Implementation of procedures for tracking the implementation of the network schedule during the performance of this lab is not provided.

For all tasks of the project, the use of the “fixed duration” task type is provided. When setting a specific start date for a website development project, keep in mind that the project cannot start earlier than the current date.

The methodology for calculating some time indicators and the formation of the main versions of the stochastic network model when conducting an analysis using the PERT method is presented in Appendix 2 to these methodological materials.

Rice. 1. PERT analysis toolbar

12) Checking the Microsoft Project settings for calculations mathematical expectation the duration of the task in accordance with the formula adopted in the PERT method (see formula (1) in Appendix 2 to these Methodological Materials). To this end, the toolbar PERT Analysis(Fig. 1) you must press the button Specifying Weights for the PERT Method .

In the form that opens, the value of the weight coefficient in the field Optimistic must be 1, in the field Expected– 4 and in the field Pessimistic– 1. If necessary, you can change the values ​​of the weighting factors, bearing in mind that in all cases the sum of the weighting factors must be equal to 6.

13) Switching to the data entry table for analysis by the PERT method: PERT Entry Sheet(the far right button on the panel for analysis by the PERT method, Fig. 1) and then filling it in.

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) Conducting analytical calculations using the PERT method. To do this, press the button Calculations using the PERT method, located in the middle of the PERT analysis panel (see Figure 1 above). Calculations will be performed after the user clicks the button Yes in the dialog box that appears, confirms the intention to carry out the calculations.

Evidence of the performed calculations is the appearance of the results in the "Duration" column in the data entry table for analysis by the PERT method instead of the initial single duration values ​​entered in it, as well as the total data for each of the local network models. It is possible to immediately view and analyze the results obtained.

15) Initiation of the formation and viewing of structural elements and indicators of the generalized network model formed by Microsoft Project.

15.1) Viewing the Gantt Chart (View Gantt Chart), network diagram (View Network Diagram).

15.2) Initiating the formation and viewing the schedule for loading resources ( View Resource Graph), the Project Statistics tab ( Project Project details Statistics).

15.3) Initiating the formation and viewing of the table Calendar plan : Right-click in the upper left corner of the Gantt chart in the menu that opens, select the "Calendar plan" option.

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 in the menu that opens, select the option "Summary data".

16) Initiating the formation and viewing the lists of critical and non-critical tasks: Set the "Critical tasks" option in the Grouping menu(originally looks like ) Right-click in the upper left corner of the Gantt chart in the menu that opens, select the option "Calendar plan".

17) Ensuring the printing of structural elements and indicators of the generalized network model formed by Microsoft Project. For this you need to use standard "Print" button , standard "Preview" button , dialog box Page settings, its tabs (for example, tab Page), as well as 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. Printing of the Project Statistics tab is carried out using the Print Screen procedure.

18) Implementation of 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 to be pressed Gantt chart - optimistic estimate , Gantt Chart - Expected Score or Gantt chart - pessimistic assessment .

The printing of the relevant data must be carried out in accordance with the recommendations set out in paragraph 17 above.

19) Determining the spread of the duration and timing of project completion due to the action of the uncertainty factor statistical method based on the calculation of the standard deviation of the duration of the work and the variance of the work and the project as a whole (if applicable) outside of Microsoft Project, for example, based on the use of a Microsoft Excel spreadsheet.

20) In agreement with the teacher, the initial network model is optimized for resources.

4. The composition of the report on the performance of laboratory work:

1) Time-oriented network (network version of the Gantt chart) for a generalized network model.

2) The canonical network graph of the "vertex - work" type (precedence diagram).

3) Schedules for loading labor resources (selectively for two or three resources; presentation of schedules for overloaded resources is mandatory).

4) List of resources after the calculations.

5) Table "Summary data".

6) Table "Calendar plan".

7) List of critical and non-critical tasks.

8) Time-oriented 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: indicated in p.p. 8 and 9, diagrams and tables for each version of the network model can be combined into one form.

10) Data entry table for PERT analysis 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:

● the 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 –

● salary costs for the project in rubles –

11.2) Expert assessment of the variation in the duration and timing of the project:

● optimistic duration in business days –

● pessimistic duration in working days –

● most likely duration in business days –

● expected duration in business days –

● expert spread of duration in working days and percentage of the duration of the project -

● 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 (difference between the most probable and expected project completion dates) –

● conclusion about the correctness of the statistical assessment of the spread of the duration and timing of the project.

11.3) Statistical assessment of the spread of the duration and timing of the project:

● duration dispersion 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 the project duration, working days -

● Statistical estimation of the optimistic duration of the project in working days –

● statistical assessment of the pessimistic duration of the project in working days -

● statistical dispersion of the project duration in working days and percentage of the project duration –

● optimistic project completion date based on statistical evaluation –

● pessimistic project completion date based on statistical evaluation –

● statistical spread of project duration in calendar days –

● conclusions on the procedure for comparing expert and statistical estimates of the spread in the duration and timing of project completion.

The composition of additional final forms in the case of network optimization by resources is agreed with the teacher.

ATTACHMENT 1

Initial data for laboratory work

in accordance with the task options

Option 1.

Table 1

The composition of the design team

Option 2.

Table 1

The composition of the design team

Option 3.

Table 1

The composition of the design team

Option 4.

Table 1

The composition of the design team

Option 5.

Table 1

The composition of the design team

Option 6.

Table 1

The composition of the design team

Option 7.

Table 1

The composition of the design team

Option 8.

Table 1

The composition of the design team

Option 9.

Table 1

The composition of the design team

Option 10.

Table 1

The composition of the design team

Option 11.

Table 1

The composition of the design team

Option 12.

Table 1

The composition of the design team

Option 13.

Table 1

The composition of the design team

Option 14.

Table 1

The composition of the design team

Option 15.

Table 1

The composition of the design team

Option 16.

Table 1

The composition of the design team

Option 17.

Table 1

The composition of the design team

Option 18.

Table 1

The composition of the design team

Option 19.

Table 1

The composition of the design team

Option 20.

Table 1

The composition of the design team

Option 21.

Table 1

The composition of the design team

Option 22.

Table 1

The composition of the design team

APPENDIX 2

PERT analysis

The PERT method accepts beta distribution probabilities of job duration 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 the duration of work;

t nv (i - j)– estimation of the most probable duration of work (mode);

t max (i - j) is the maximum (pessimistic) estimate of the duration of work.

These estimates of the duration of the work are given expertly, and the experts, as a rule, are the future performers of the work.

To calculate the expected duration (expectation of duration) of work using the PERT method, the following formula is used:

t cool (i - j) \u003d (t min (i - j) + 4 t nv (i - j) + t max (i - j)) / 6, where (1)

It is important to emphasize that the calculation by 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 get more accurate results, in addition, a system of various temporal indicators of the network model is complexly formed, expressed both in work (task and project duration, time reserves) and in calendar (terms occurrence of events, project implementation) days.

Based on four estimates of the duration of work ( t min (i - j), t nv (i - j), t max (i - j) and t exp(i - j)) four main versions of the network model are formed with critical paths of different duration, and, consequently, different estimates of the duration of the project as a whole - the minimum (optimistic), most probable, maximum (pessimistic) and expected ( Tmin, T nv, T max 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 general one, and the other models as complementary local ones.

For a stochastic network of this type, additional time indicators are calculated, aimed at assessing the possible spread in the duration and timing of the implementation of individual works and the project as a whole due to the action of the uncertainty factor. Adequate to the beta probability distribution is expert review the duration (and timing) of the 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 work of the project:

Δ t (i - j) \u003d t max (i - j) - t min (i - j)(2)

a) for the project as a whole:

ΔT = Tmax - Tmin(3)

A relative disadvantage of the expert assessment of the scatter is that the scatter of the duration of the project due to the action of the uncertainty factor can directly exceed the value of its expected duration, or at least be commensurate with it. This makes the estimate 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 into the "scatter interval" almost equal to 1 (unless force majeure circumstances are taken into account).

If the mode and the mathematical expectation are close in their value, then you can use statistical estimates scatter of durations and terms of the project implementation, taken for the normal distribution of probabilities, - 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 (scatter) of the duration of work under the influence of uncertainty is equal to six standard deviations, i.e. the standard deviation can be determined by the formula:

σ (i - j) =(t max (i - j) - t min (i - j)) / 6 (4)

The dispersion of the duration of work 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 critical activities. The standard deviation of the duration of the project is determined by extracting square root from the project variance. Based on this, according to the well-known mathematical statistics the rule of "three sigma" can be determined by the possible variation in the duration (and timing) of the project as a whole.

The statistical estimate of the spread of the project duration is noticeably less than the expert one as a result of the fact that the project duration falls into the "scatter interval" in the absence of force majeure guaranteed with a probability of 0.997 (which is less than 1, but seems to be quite sufficient) . It is easy to see that the expert and statistical scatter of duration for the project work coincide, therefore, the lower value of the statistical scatter of the duration of the project as a whole can also be interpreted based on the hypothesis of repaying the delay of some critical work by early completion of others.

The calculation of the standard deviation and variance of work and the project as a whole is carried out outside of Microsoft Project, for example, using a Microsoft Excel spreadsheet.

For Microsoft Project 2007 and later.

The technical editors of the Russified version of Microsoft Project meant the most probable assessment (mode) under the expected assessment.

Mathematical expectation of duration.

It is more accurate to talk about the mathematical expectation of the duration and timing of the completion of the project.

With a significant discrepancy between the mode and the mathematical expectation of the duration of the project, replacing the beta probability distribution with a normal one can lead to a significant error in scatter estimation.

The Greek letter sigma in statistics usually denotes the standard deviation.

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