Network and project scheduling. Network planning and management
Basic elements of network planning and management
Network planning and management is a set of calculation methods, organizational and control measures for planning and managing a set of works using a network diagram (network model).
Under complex of works we will understand any task for which it is necessary to carry out a sufficiently large number of varied works.
In order to draw up a work plan for the implementation of large and complex projects consisting of thousands of individual studies and operations, it is necessary to describe it using some kind of mathematical model. Such a means of describing projects is a network model.
Network model- this is a plan for the implementation of a certain set of interrelated works, specified in the form of a network, the graphical representation of which is called network diagram.
The main elements of the network model are work And events.
The term work in SPU has several meanings. Firstly, this actual work- a time-consuming process that requires resources (for example, assembling a product, testing a device, etc.). Each actual job must be specific, clearly described and have a responsible person.
Secondly, this expectation- a long-term process that does not require labor (for example, the drying process after painting, aging of metal, hardening of concrete, etc.).
Thirdly, this addiction, or fictitious work- a logical connection between two or more works (events) that do not require labor, material resources or time. She points out that the possibility of one job directly depends on the results of another. Naturally, the duration of the fictitious work is assumed to be zero.
An event is the moment of completion of a process, reflecting a separate stage of the project.. An event can be a partial result of a separate work or the total result of several works. An event can only happen when all the work preceding it is completed. Subsequent work can begin only when the event occurs. From here dual nature of the event: for all works immediately preceding it it is final, and for all immediately following it it is initial. It is assumed that the event has no duration and occurs as if instantly. Therefore, each event included in the network model must be fully, accurately and comprehensively defined, its formulation must include the result of all work immediately preceding it.
Figure 1. Basic elements of the network model
When drawing up network diagrams (models), symbols are used. Events on the network diagram (or, as they also say, on the graph) are depicted by circles (vertices of the graph), and works - by arrows (oriented arcs):
Event,
Work (process),
Dummy work - used to simplify network diagrams (duration is always 0).
Among the events of the network model, initial and final events are distinguished. The initial event does not have previous works and events related to the set of works presented in the model. The final event has no subsequent activities or events.
There is another principle for building networks - without events. In such a network, the vertices of the graph represent certain jobs, and the arrows represent dependencies between jobs that determine the order of their execution. The “work-connection” network graph, in contrast to the “event-work” graph, has certain advantages: it does not contain fictitious work, has a simpler construction and restructuring technique, and includes only the concept of work, which is well known to performers, without the less familiar concept of an event.
At the same time, networks without events turn out to be much more cumbersome, since there are usually significantly fewer events than jobs ( network complexity indicator, equal to the ratio of the number of jobs to the number of events, is usually significantly greater than one). Therefore, these networks are less effective from the point of view of complex management. This explains the fact that at present, “event-work” network graphs are most widespread.
If there are no numerical estimates in the network model, then such a network is called structural. However, in practice, networks are most often used in which estimates of the duration of work are specified, as well as estimates of other parameters, such as labor intensity, cost, etc.
The procedure and rules for constructing network graphs
Network diagrams are drawn up at the initial planning stage. First, the planned process is divided into separate works, a list of works and events is compiled, their logical connections and sequence of execution are thought out, and the work is assigned to responsible performers. With their help and with the help of standards, if they exist, the duration of each job is estimated. Then it is compiled ( stitched) network diagram. After streamlining the network schedule, the parameters of events and work are calculated, time reserves are determined and critical path. Finally, the network diagram is analyzed and optimized, which, if necessary, is drawn again with recalculation of the parameters of events and work.
When constructing a network diagram, a number of rules must be followed.
In the network model there should be no “dead-end” events, that is, events from which no work comes out, with the exception of the termination event.
Here either the work is not needed and must be canceled, or the need for certain work following the event in order to accomplish some subsequent event is not noticed. In such cases, a thorough study of the relationships between events and work is necessary to correct the misunderstanding that has arisen. There should be no “tail” events in the network diagram (except for the initial one) that are not preceded by at least one job
. Having discovered such events in the network, it is necessary to determine the performers of the work preceding them and include these works in the network. The network should not have closed circuits and loops, that is, paths connecting certain events to themselves
. When a loop occurs (and in complex networks, that is, in networks with a high complexity index, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the original data and, by revising the scope of work, achieve its elimination. Any two events must be directly connected by at most one arrow job
. Violation of this condition occurs when depicting parallel work. If these works are left as they are, then confusion will occur due to the fact that two different works will have the same designation. However, the content of these works, the composition of the involved performers and the amount of resources spent on the work may differ significantly. In this case, it is recommended to enter fictitious event And, while one of the parallel jobs is closed on this fictitious event. Fictitious jobs are depicted on the graph as dotted lines.
Figure 2. Examples of introducing fictitious events
Fictitious jobs and events need to be introduced in a number of other cases. One of them is a reflection of the dependence of events not related to real work. For example, work A and B (Figure 2, a) can be performed independently of each other, but according to production conditions, work B cannot begin before work A is completed. This circumstance requires the introduction of fictitious work C.
Another case is incomplete dependency of jobs. For example, work C requires the completion of work A and B to begin, work D is associated only with work B, and does not depend on work A. Then it is necessary to introduce fictitious work Ф and fictitious event 3’, as shown in Figure 2, b.
In addition, fictitious work may be introduced to reflect real delays and waits. Unlike previous cases, here fictitious work is characterized by an extension in time.
If the network has one final goal, then the program is called single-purpose. A network schedule that has several final events is called multi-objective and the calculation is carried out with respect to each final goal. An example could be the construction of a residential neighborhood, where the commissioning of each house is the final result, and the construction schedule for each house defines its own critical path.
Organize your network diagram
Suppose that when drawing up a certain project, 12 events are identified: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 24 works connecting them: (0, 1), (0, 2 ), (0, 3), (1, 2), (1, 4), (1, 5), (2, 3), (2, 5), (2, 7), (3, 6), (3, 7), (3, 10), (4, 8), (5, 8), (5, 7), (6, 10), (7, 6), (7, 8), (7 , 9), (7, 10), (8, 9), (9, 11), (10, 9), (10, 11). Created the initial network diagram 1.
The ordering of the network diagram consists in such an arrangement of events and activities in which for any activity the event preceding it is located to the left and has a lower number compared to the event that completes this activity. In other words, in an ordered network diagram, all arrow jobs are directed from left to right: from events with lower numbers to events with higher numbers.
Let's divide the original network diagram into several vertical layers (circle them with dotted lines and denote them with Roman numerals).
Having placed the initial event 0 in layer I, we mentally delete this event and all the arrow jobs coming out of it from the graph. Then, without incoming arrows, event 1 will remain, forming layer II. Having mentally crossed out event 1 and all the work coming out of it, we will see that events 4 and 2, which form the III layer, remain without incoming arrows. Continuing this process, we obtain network diagram 2.
Network 1. Unordered network
Network 2: Organizing your network using layers
Now we see that the initial numbering of events is not entirely correct: for example, event 6 lies in layer VI and has a number lower than event 7 from the previous layer. The same can be said about events 9 and 10.
Network Diagram 3. Ordered Network Diagram
Let's change the numbering of events in accordance with their location on the graph and get an ordered network diagram 3. It should be noted that the numbering of events located in the same vertical layer is not of fundamental importance, so the numbering of the same network diagram may be ambiguous.
The concept of the path
One of the most important concepts in a network diagram is the concept of path. Path - any sequence of activities in which the final event of each activity coincides with the initial event of the activity following it. Among the various network paths, the most interesting is full path- any path whose beginning coincides with the initial network event, and the end with the final one.
The longest complete path in a network diagram is called critical. Works and events along this path are also called critical.
In network diagram 4, the critical path passes through activities (1;2), (2;5), (5;6), (6;8) and is equal to 16. This means that all activities will be completed in 16 units of time. The critical path is of particular importance in the control system, since the work on this path will determine the overall completion cycle of the entire set of works planned using the network schedule. Knowing the start date of work and the duration of the critical path, you can set the end date of the entire program. Any increase in the duration of activities on the critical path will delay the execution of the program.
Network diagram 4. Critical path
At the stage of management and control over the progress of the program, the main attention is paid to work that is on the critical path or, due to a lag, on the critical path. To reduce the duration of a project, it is necessary to first reduce the duration of activities on the critical path.
Introduction
Chapter I. Concept and essence of network planning and management
1.1. The essence of network planning and management methods
1.2. Elements and types of network models
Chapter II. Practical application of network planning and management models
2.1. Network planning and management methods
2.2. Network diagram
Conclusion
Literature
Introduction
In modern conditions, socio-economic systems are becoming more and more complex. Therefore, decisions made on the problems of rationalizing their development should receive a strict scientific basis based on mathematical and economic modeling.
One of the methods of scientific analysis is network planning.
In Russia, work on network planning began in 1961-1962. and quickly became widespread. The works of Antonavichus K. A., Afanasyev V. A., Rusakov A. A., Leibman L. Ya., Mikhelson V. S., Pankratov Yu. P., Rybalsky V. I., Smirnov T. I. are widely known. , Tsoi T.N. and others.
, ,
From numerous studies of individual aspects of network planning and management methods, a transition was made to the systematic use of a new planning methodology. In literature and practice, the attitude towards network planning not only as a method of analysis, but also as a developed system of planning and management, adapted for a very wide range of problems, has become more and more widely established.
Over the years of practical use in Russia and abroad, network planning has shown effectiveness in a variety of areas of economic and organizational analysis.
Of particular interest is the network method for the formalized representation of control systems, which boils down to the construction of a network model for solving a complex control problem. The basis of network planning is an information dynamic network model, in which the entire complex is divided into separate, clearly defined operations (works), located in a strict technological sequence of their implementation. When analyzing the network model, a quantitative, time and cost assessment of the work performed is made. Parameters are set for each work included in the network by their performer based on regulatory data or their own production experience.
In dynamic simulation, a model is built that adequately reflects the internal structure of the system being modeled; then the behavior of the model is checked on a computer for an arbitrarily long time in advance. This makes it possible to study the behavior of both the system as a whole and its component parts. Simulation dynamic models use a specific apparatus that allows them to reflect the cause-and-effect relationships between the elements of the system and the dynamics of changes in each element. Models of real systems usually contain a significant number of variables, so they are simulated on a computer.
Thus, the topic of research into network planning methods is relevant, because The graphical representation not only gives an idea of a complex process, but also allows for a comprehensive study of the project management system.
Based on the above arguments of the relevance and topic of the work, we can formulate the goal of the work - to highlight the methods of network planning and management in the study of socio-economic and political processes.
To achieve the goal, the following tasks were set and solved:
1. An analysis of network planning and management was carried out.
2. The essence of network planning and management methods is revealed
3. The types of network planning and management methods are considered, and the scope of their application is studied.
4. The basics of practical application of network planning and management methods are considered.
The subject of my course work is the methodology of network planning and management.
The object of my course work is the scope of application of the methodology of network planning and management.
Chapter I . The concept and essence of network planning and management
1.1. The essence of network planning methods
Network planning is a set of graphical and calculation methods of organizational activities that provide modeling, analysis and dynamic restructuring of the plan for the implementation of complex projects and developments, for example, such as:
· construction and reconstruction of any objects;
· carrying out research and development work;
· preparation of production for product release;
· rearmament of the army.
A characteristic feature of such projects is that they consist of a number of separate, elementary works. They condition each other in such a way that some work cannot be started before some others are completed.
Main target network planning and management - reducing project duration to a minimum.
Task network planning and management is to graphically, visually and systematically display and optimize the sequence and interdependence of works, actions or activities that ensure the timely and systematic achievement of final goals.
To display and algorithmize certain actions or situations, economic and mathematical models are used, which are usually called network models, the simplest of which are network graphs. With the help of a network model, the manager of a work or operation has the opportunity to systematically and on a large scale represent the entire progress of work or operational activities, manage the process of their implementation, and also maneuver resources.
In all network planning systems, the main object of modeling is various sets of upcoming work, for example, socio-economic research, design development, development, production of new goods and other planned activities.
The SPU system allows:
· create a calendar plan for the implementation of a certain set of works;
· identify and mobilize time reserves, labor, material and financial resources;
· manage a set of works according to the “leading link” principle with forecasting and preventing possible disruptions during the work;
· increase the efficiency of management as a whole with a clear distribution of responsibilities between managers at different levels and performers of work;
· clearly display the volume and structure of the problem being solved, identify, with any required degree of detail, the work that forms a single complex of the problem resolution process; identify events that are necessary to achieve specified goals;
· identify and comprehensively analyze the relationship between the works, since the very methodology for constructing a network model contains an accurate reflection of all dependencies determined by the state of the object and the conditions of the external and internal environment;
· widely use computer technology;
· quickly process large amounts of reporting data and provide management with timely and comprehensive information about the actual state of program implementation;
· simplify and unify reporting documentation.
The range of application of SPU is very wide: from tasks relating to the activities of individuals to projects in which hundreds of organizations and tens of thousands of people participate.
The network model is a description of a set of works (set of operations, project). It is understood as any task for which it is necessary to carry out a sufficiently large number of different actions. This can be the creation of any complex object, the development of its project and the process of constructing project implementation plans.
The use of network planning methods helps reduce the time required to create new facilities by 15-20%, ensuring the rational use of labor resources and equipment.
The most effective areas of application of network planning and management methods are the management of large target programs, scientific and technical developments and investment projects, as well as complex complexes of social, economic, organizational and technical activities at the federal and regional levels.
1.2. Elements and types of network models
Network models consist of the following three elements:
· Job (or task)
· Event (milestones)
· Communication (addiction)
Job ( A activity)- this is a process that must be performed to obtain a certain (specified) result, which, as a rule, allows one to proceed to subsequent actions. The terms “task” and “work” may be identical, but in some cases tasks are usually called the performance of actions that go beyond the scope of direct production, for example, “Examination of design documentation” or “Negotiations with the customer.” Sometimes the concept of "task" is used to display work at the lowest level of the hierarchy.
The term "work" is used in a broad sense and can have the following meanings:
· actual work, that is, a labor process that requires time and resources;
· expectation– a process that requires time but does not consume resources;
· addiction or “dummy work” - work that does not require time and resources, but indicates that the possibility of starting one task is directly dependent on the results of another.
Managing the planning process and the progress of work is not an easy task. Obviously, the most correct thing in this case would be to use network planning and management methods (NPM).
SPU methods are developed as mathematical methods for constructing operations research models. The development of the method has been brought to working computer programs and we just have to learn how to use them in relation to our work of searching for ideas. You will master the use of SPM methods in practical classes. SPC methods are based on modeling processes using network diagrams and represent a set of calculation methods, organizational and control measures for planning and managing a set of works. The SPU system allows:
formulate a calendar plan for the implementation of a certain set of works;
identify and mobilize time reserves, labor, material and financial resources;
carry out management of a complex of works according to the “leading link” principle with forecasting and prevention of possible disruptions in the course of work;
increase the efficiency of management as a whole with a clear distribution of responsibilities between managers at different levels and performers of work.
A network model is a plan for the implementation of a certain set of interrelated works (operations), specified in a specific form of a network, the graphical representation of which is called a network diagram. The elements of the network model are events and activities.
A network diagram is a model for achieving a goal, and the goal is a model dynamically adapted for analyzing options for achieving the goal, for optimizing planned tasks, for making changes, etc.
The method of working with network graphs - network planning - is based on graph theory. Translated from Greek, a graph (grafpho - I write) represents a system of points, some of them are connected by lines - arcs (or edges). This is a topological (mathematical) model of interacting systems. Using graphs, you can solve not only network planning problems, but also other problems. The network planning method is used when planning a set of interrelated works. It allows you to visualize the organizational and technological sequence of work and establish the relationship between them. In addition, it allows for the coordination of operations of varying degrees of complexity and the identification of operations on which the duration of the entire work (i.e., organizational event) depends, as well as focusing on the timely completion of each operation.
The network method is a system of techniques and methods that, based on the use of a network diagram (network model), make it possible to rationally carry out the entire management process, plan, organize, coordinate and control any set of works, ensuring the efficient use of monetary and material resources. Using this method allows you to improve:
planning, ensuring its complexity, continuity, creating conditions for improving the identification of required resources and the distribution of existing resources;
financing of work, because there are ways to more accurately calculate the cost of work, their labor intensity and the formation of a regulatory and reference base;
the structure of the management system by clearly defining and distributing tasks, rights, and responsibilities;
organizing procedures for coordinating and monitoring the progress of work on the basis of prompt and accurate information, as well as assessing the implementation of the plan.
A network diagram is an information model that displays the process of performing a set of works aimed at achieving a single goal. The purpose of network planning is to influence management, and management is designed to maintain a rational mode of operation, restore the disturbed state of moving equilibrium of dynamic systems, ensuring the coordinated operation of all its links. At the same time, the system is managed according to a number of parameters: time, cost, resources, technical and economic indicators. However, the most common are systems with the “time” parameter.
The management process when representing the managed system in the form of a model is significantly simplified. The basis of network planning and management is a network diagram, reflecting the technological and logical relationship of all operations of the upcoming work. It consists of three components (main concepts), such as “work”, “event” and “path”.
“Work” is any process that requires time and resources, or just time. If no resources are required to complete the work, but only time is spent, then they are called “waiting”. The work on the network diagram is indicated by a solid arrow (graph arc), above which a number indicates the duration of the work. There is fictitious work (waiting, simple dependence) - work that does not require time, labor and money. It is shown as a dotted arrow on the graph.
Works in the form of an arrow (then the graph is called oriented, or digraph) on the graph are not vectors, therefore they are drawn without scale. Each work begins and ends with an “event”, which is indicated by a circle in which the number indicates the name (name) of this event. An event is the result of the execution of one or more activities, which is necessary for the start of subsequent activities. The antecedent event is the starting point for the work (the cause), and the subsequent event is its result.
Events, unlike jobs, take place at certain points in time, without using any resources. The beginning of a set of works is the initial event. The moment of completion of all work is the final event.
Any network diagram has one initial (initial) and one final (final) event. Any work - an arrow - connects only two events.
The event from which the arrow comes out is called prior to this work, and the event into which the arrow enters is called subsequent. The same event, in addition to the initial and final one, is antecedent in relation to one work, and subsequent to another. Such an event is called an intermediate event. Events can be simple or complex. Simple events have only one input and one output operation.
Complex events have multiple inputs or multiple outputs. Dividing events into simple and complex is of great importance when calculating network graphs. The event is considered completed when the longest duration of all the works included in it is completed.
A continuous technological sequence of work (chain) from the first event to the last is called a path. This path is the complete path. There can be several complete paths. The length of the path is determined by the sum of the duration of the work lying on it. Using the graphing method, each of the paths can be determined. This is achieved by sequentially identifying the elements of each path.
As a result of comparing different paths, the path on which the duration of all contained activities is the longest is selected. This path is called the “critical path”. It determines the time required to complete the entire plan for which the schedule is drawn up. The final deadline for completing the plan depends on the activities located on the critical path and their duration.
The critical path is the basis for plan optimization. In order to reduce the duration of the entire plan, it is necessary to reduce the duration of those activities that are on the critical path.
All complete paths whose duration is less than the critical one are called non-critical. They have time reserves. Time reserves are understood as permissible shifts in the timing of events and completion of work that do not change the timing of the final event.
Time reserves can be full or free. Full time slack is the period by which the start of work can be postponed or its duration can be increased while the length of the critical path remains unchanged. Total slack is defined as the difference between the late and early start of work or between the late and early finish of work.
Activities on the critical path do not have a full time reserve, because their early parameters are equal to their late ones. Using the full slack time on other non-critical paths causes the path to which the slack belonged to to become critical.
Free time reserve is the period by which the start of work can be postponed or its duration can be increased, provided that the early starts of subsequent work do not change. This time reserve is used when one event includes two or more jobs. Free time reserve is defined as the difference between the early start of the subsequent work and the early finish of the work in question.
The time reserve allows you to increase the duration of work or start it a little later, and also makes it possible to maneuver internal financial, material and labor resources (money, amount of equipment, number of employees, start time of work).
Analyzing network graphs, you can see that they differ not only in the number of events, but also in the number of relationships between them. The complexity of the network diagram is assessed by the complexity coefficient. The complexity coefficient is the ratio of the number of works on the network schedule to the number of events and is determined by the formula:
K = R / C, (3)
where K is the complexity coefficient of the network diagram;
P and C - number of works and events, units.
Network diagrams with a complexity coefficient from 1.0 to 1.5 are simple, from 1.51 to 2.0 - medium complexity, more than 2.1 - complex.
When starting to build a network diagram, you should establish:
What work must be completed before this work begins;
What work can be started after completion of this work;
3. What work can be performed simultaneously with this work. In addition, you must adhere to the general provisions and rules:
the network is drawn from left to right (the work arrows also have the same direction);
each event with a large serial number is depicted to the right of the previous one;
the schedule should be simple, without unnecessary intersections;
all events except the final one must have subsequent work (there should be no event in the network, except the initial one, which would not include any work);
the same event number cannot be used twice;
in the network diagram, no path should pass through the same event twice (if such paths are detected, this indicates an error);
if the beginning of any work depends on the end of two previous works coming from one event, then a fictitious work (dependency) is introduced between the events - the endings of these two works.
The use of network models can provide significant assistance in planning and implementing activities within the framework of innovation management, so they cannot be neglected.
Network planning is one of the most important management tools that is used in the process of developing, making and implementing complex decisions.
The German industrial standard DIN 69900 defines network planning as all techniques for the analysis, description, planning and control of processes based on graph theory, in which time, costs, resources and other influencing parameters can be taken into account.
The network plan can be considered the most accurate planning tool, especially useful for large and complex projects. It has the following main advantages: 1.
Drawing up a network plan forces all project participants to carefully consider its progress, carry out the necessary approvals in advance and make appropriate decisions. This plays a big role especially in cases where different companies or different divisions of the same company are involved in the project.
2.
Due to the graphical representation of the work, the network plan provides an excellent overview of the project and allows you to clearly record its planned progress.
3.
The above advantages make it easier to control the completeness of planning.
Each network plan is a graphical representation of the progress of the project, containing a certain number of nodes and lines connecting them.
An effective tool in project management are the so-called network matrices, which represent a higher level of scientific development of traditional network graphs. The network matrix is a graphical representation of the project implementation process, where all work (managerial and production) is shown in a certain technological sequence and the necessary relationships and dependencies. The network matrix is combined with a calendar-scale time grid. The rows of the matrix indicate the management level, structural unit or official performing this or that work; columns - stage and individual operations of the project management process occurring over time. For example in Fig. Figure 6.7 shows a fragment of the network matrix for dividing administrative tasks
An “event” is understood as the result of completing all the work included in this event, allowing subsequent work to begin. On a network matrix, an event is usually depicted as a circle.
By “path” we mean a continuous sequence of work, starting from the initial event and ending with the final one. The path that has the longest duration is called critical and is indicated in the matrix by a thickened or double arrow.
Since 1956, many network planning options have been developed, which are usually grouped into three groups: the critical path method, the PERT method and the Metra-potential method.
Critical path method
The arrow usually displays the name of the job, and below the arrow is the corresponding time of its completion. The first node is called
The method was developed in the USA and was called the “critical path method” - Critical Path Method (CPM). In this method, work is depicted as an arrow, and the dependencies between them are represented as nodes (Fig. 6.8).
the initial event, the second - the final event. Nodes are assigned serial numbers.
Node 1, which is not approached by arrows, is called the start node or start event. If no arrow departs from node 4, then it is called a target event. These two nodes limit the start and completion of the project.
Job D can only begin after both Job A and Job C have been completed. This is symbolized by node 3, whose condition is the completion of Jobs A and C. Thus, the dependencies represented in a node can be thought of as states that must be achieved so that subsequent work can begin.
These events may also have a corresponding time frame. There are two cells for this purpose. The first number shows the earliest possible date by which the event can occur (early end of the RC), the second - the latest permissible date by which the event must necessarily occur (late end of the PC). The start event has an early end RK=0.
When drawing up a network plan, first, the early end of each event is determined sequentially. Late endings of events are determined by counting down. If two jobs run in parallel, i.e. begin and end with the same events, then for their unambiguous representation the so-called fictitious work is introduced (work 5 in Fig. 6.9).
Rice. 6.9. Displaying parallel jobs
Fictitious jobs always have zero duration. They are introduced for clarity of presentation of work and in the case when many works are completed (or started) by one event, even if not all works that begin require the completion of all previous works. In the example in Fig. 6.10, the introduction of fictitious work 5 allows us to demonstrate that the condition for starting work B is the completion of work A and C, and the condition for starting work D is only the completion of work C.
Rice. 6.10. Fictitious work in the network plan
In Fig. 6.11, the first column presents typical mistakes when drawing up network plans, and the second column presents the correct solutions.
It should be remembered that when calculating time, and accordingly in the network plan, waiting times must also be taken into account, for example for drying, curing concrete, etc. To do this, activities with appropriate durations must be entered in the network plan.
Metra-potential method
In the MPM method (Metra-Potenzial-Methode) developed in France, works are displayed as nodes, and their relationships as arrows (Fig. 6.12). The node contains all the information related to the work, and the arrows show only the dependencies, i.e. previous and subsequent work.
The rectangle displaying the work contains its serial number, title and duration. In addition, short texts can be placed, for example, indicating the performers A FA B FA SA SA of the work. Further, along with the duration of work, free time reserves are indicated, as well as Fig. 612 The principle of the Metra-potential method in earlier and later times
start and end of work.
PERT method
Another version of the network plan is the PERT (Program Evaluation and Review Technique) method developed in the early 1960s by the US Navy. It has been successfully used in ballistic missile project management. This project involved a number of activities that required research and development, the duration of which could not be estimated with reasonable accuracy. The PERT method implements a probabilistic approach to determining the duration of work using the average value of the ^-distribution:
fX (x) = ~r~-\ x“ 1 (1_ X)(1, xX ’ B(“, ()
where a, b > 0 are arbitrary fixed parameters, and
B(“, () - ) x“-1 (1 - x)(-1 dx -
For each work package, three estimates of its execution time are given: optimistic (a), most likely (t) and pessimistic (b), and the average value T and standard deviation 5 are calculated using the formulas
a + 4t + b _b - a T - , ^ -
Note that the β-distribution gives the greatest weight to the most probable value.
Next, the network plan is calculated in the same way as in the CPM method. The expected completion time for the project as a whole will be equal to the sum of the average completion times for activities on the critical path. The standard deviation of project completion time can be defined as the square root of the sum of the squares of the standard deviations of all activities lying on the critical path.
If the duration of the work is specified (for example, by the customer), then the probability of meeting this deadline should be assessed. It is obvious that the calculated average project completion time will be achieved in 50% of cases. To calculate the probability of meeting a deadline, you need to calculate the difference between this deadline and the calculated average. By dividing this value by the standard deviation, we can use statistical tables to determine the required probability that the project will be completed on time.
A special feature of the PERT method is that it does not display the work itself, but the occurrence of certain events during the project. These events are represented by nodes, and the relationships between them are represented by arrows. Such a network plan contains less detailed information than the previous two and is not suitable for directly obtaining work instructions for individual processes from it. Its use is advisable in cases where either sufficient information does not yet exist, or a concentrated presentation of the plan is desired to provide better visibility. For example, if the plan is used to inform other parts of the enterprise about the progress of the project or its current status, then it may make sense to neglect the details and focus on significant events. Such significant events are called milestones.
Elements of the three considered network plan options can be combined with each other. So, for example, in the Metra-potential method, significant milestones can be additionally introduced, which, unlike works, are depicted in circles. Then these milestones mark certain events at which the status of the project is monitored, or report to the management of the enterprise or to the customer.
Along with the three considered network plans CPM, MPM and PERT, the following variants and combinations have also become widespread in the world:
LESS - Least Cost Estimating and Scheduling;
CPS - Critical Path Scheduling;
CPPS - Critical Path Planning and Scheduling;
RAMPS - Resource Allocation and Multi-Project Scheduling;
PCS - Project Control System.
Time planning
Given the known duration of the project and a given start date, a sequential calculation can be used to determine the time of its completion. This approach is called progressive time planning. Similarly, given a project completion date, a backward calculation can be used to determine the latest date when it is necessary to begin the project. This approach is called regressive time planning. If the calculation shows that it is not possible to meet the specified deadlines for the project, then it is necessary to either agree with the customer to postpone the project completion date, or find alternative solutions that would allow the work to be completed in a shorter time.
Project time planning is complicated by the fact that many activities involve other activities. The German industrial standard DIN 69900 defines work as an action with a fixed start and a fixed end, which is further characterized by the fact that once it has started, it is carried out without interruption until the end.
Dependencies between individual jobs can be caused by a variety of reasons, for example:
technical necessity,
technological requirements,
limited resources,
legislative regulation,
requirements of the authorities,
organizational considerations,
the need to equip the construction site,
decision of the enterprise management,
employer's requirements,
financial considerations.
Some of these reasons are almost uncontrollable, while others, within certain limits, can be changed either through negotiations or through additional costs.
This problem may be relevant from the very beginning of the project, when as a result of planning it turns out that the deadlines obtained as a result of the calculation are unacceptable. It may become relevant as the project progresses, when it is necessary to compensate for the accumulated backlog from planned deadlines. A common mistake when planning time is to plan the number of workers based on 100% of the working time budget, although it is known that a significant part of the time they may be busy with activities not related to the project.
Some jobs can be carried out in parallel, but some can be started and completed only after other jobs have been completed or partially completed. Therefore, before direct time planning, a project execution process plan is developed based on the project structure plan, which reflects the mentioned interdependencies. This plan, which can be presented in the form of a graph or table, contains information about what activities are related to each other and how they should be arranged in time, taking into account such dependencies. To do this, first, based on the project structure plan (PPS), all works (work packages) are entered into the work table. Each job is then analyzed for its dependencies on other jobs, and those jobs are marked in the table as “predecessors” or “successors.”
The scope of activities or operations that are termed "work" is usually weighed against the risk associated with it (both in terms of time and cost). Because the risk of a large job is difficult to estimate and even more difficult to manage, every project manager should strive to break down the work to a certain level. This level is determined by the degree of visibility of the work. In this case, the risk turns out to be quite well calculated. Further, those responsible for performing the work must take care of these risks with appropriate preventive measures.
It is possible to determine all relationships in large and complex projects only with a systematic approach to their identification. In practice, two main methods are used. The most common method is to start at the end of the project and go step by step to its beginning. For each specific work, all previous actions (works) that must be completed before the work can begin are determined. Another, less common way is to start with the first work from the start of the project and determine all subsequent works that can be started.
The next task is to estimate the duration of each job. To do this, first select a unit of time that is practical for a given project (days, hours, weeks, etc.). Reliability of time estimates is extremely important for future time planning. Therefore, this matter must be taken seriously and, if necessary, for insurance purposes, experts or those persons who will subsequently be responsible for meeting these deadlines must be involved in the assessment. There are different opinions regarding whether to define optimistic, pessimistic or average terms. This depends primarily on the specific project.
As a next step, for each job, its early start time (ER) and early finish time (EC) are determined. This is done directly, starting from the start of the project. If a number of jobs can start simultaneously without previous jobs, then they start with one of these jobs. Activities that require the completion of one or more preceding activities may not start until the completion of the latest one.
After determining the earliest start and finish times for each job, you need to calculate the latest times when the job should start or finish, respectively. The determination of these times - late start (LO) and late finish (LC) - is made by reverse counting either from the time of early completion of the project determined by direct counting, or from the permissible deadline for completing the work specified in the contract.
The late end of work (PC) is at the same time the late start date of the subsequent work, in other words, the work must end no later than the work that follows it must begin, and for many subsequent works no later than the earliest of them must begin.
By comparing the timing of early start and early completion of work with the timing of late start and late completion of work, it is possible to determine the work reserve times, which are very important for subsequent maneuver. In this case, a distinction is made between the total work reserve (OR) and the free work reserve (SR). Their determination also occurs in two steps. The total operating time reserve is defined as
OR = PN - RN = PC - RK, i.e. The total reserve is the difference between the deadline no later than which the work must be completed and the earliest possible completion date.
Some jobs have zero free time. If the duration of the work is estimated correctly and the interdependencies of the work are established correctly, this means that any delay will simultaneously lead to a shift in subsequent work, and, accordingly, to a shift in the completion date of the project as a whole. Due to the importance of work with zero slack, they are also called critical.
The presence of a general reserve of work time does not mean that it can be freely used for this particular work, otherwise some subsequent jobs may end up without any reserve. In this regard, the still free reserve of work time is calculated, which is defined as the length of time for which work can be delayed, with the condition that subsequent work can still be started at its earlier start.
Determining slack time gives project management a useful tool. Free time reserves provide a certain freedom of action. But even when the free slack time is zero, but the total slack time is greater than zero, the delay within these limits can still be made up if the project management manages to refuse the free slack time for subsequent work.
Jobs for which free and total slack time are equal to zero lie on the so-called critical path. Any delays along this path lead to a delay in the completion of the entire project, unless, of course, the project management at subsequent stages through special measures manages to reduce the completion time. This, as a rule, is only possible by attracting additional resources and, accordingly, brings additional costs. If the early completion date of the project according to the calculation goes beyond the contractual deadlines, then one should look for opportunities to reduce the time for completing work, especially those that lie on the critical path.
The next step is to link the work to the calendar, which should take into account weekends and holidays, and sometimes even the vacation period.
For a more visual representation of time planning, a Gantt chart is used. Individual jobs are entered in lines, and their duration is noted in the calendar part of the diagram, starting from the start day. A particular advantage of this technique is its clarity, thanks to which at any point in time you can figure out what work should already be started or completed. If you subsequently mark in the diagram the actual moments of the beginning and end of work in a different color, you can clearly see the correspondence (or discrepancy) between the actual and planned progress of work. In addition, it is clearly visible what work is being performed simultaneously.
This diagram is quickly and easily understood by non-planning workers and is therefore very popular. Each worker himself is able to draw up such a diagram without training or special instructions. However, this circumstance sometimes leads to a lightweight approach to work planning. When quickly drawing up a diagram, essential details are often missed, which results in the appearance of illusory work plans. Unrealistic time planning, in turn, leads to unrealistic cost planning.
Practical experience in using network planning, as E. Wisniewski rightly emphasizes^. Wishnewski), very controversial. On the one hand, it is generally accepted that drawing up and maintaining network plans is the alpha and omega of project management. Network plans have the undeniable advantage that they clearly represent the interdependencies of work. In addition, they include timing calculations as well as critical path calculations. This is certainly a valuable aid in project planning and management.
The time spent on drawing up a network plan, regardless of the level of knowledge of the compilers, is always very significant. A network plan is only useful if it is drawn up well. Since its compilation requires detailed information about all works, a lot of preparation is necessary for its compilation. After the first pass, when the usually calculated project completion date exceeds the contractual time frame, the need arises to optimize the network plan. Often the estimated completion date of a project goes so far beyond the contractual deadlines that various reserves have to be intensively sought.
Practice has shown that in many implemented projects, even if it was possible to carefully develop network plans for them, down to the details, their further tracking required a colossal amount of time. If, for the sake of simplicity, only a rough network plan is drawn up, the whole “exercise” serves only to satisfy the client who wants to see it.
In connection with the above, usually a network plan drawn up once during the course of a project is no longer (voluntarily) updated. For example, when the High Voltage Research Institute at TPU created the nuclear explosion simulator “Reper R/T”, a network diagram was drawn up at the insistence of the Representative Office of the Ministry of Defense. A lot of time was spent studying network planning techniques and drawing up the network schedule itself. In reality, it was not used to manage the project. Therefore, although the network plan contains information that is very important for project management, its preparation and maintenance is not always an appropriate tool for project management. A definite way out of this impasse is the use of modern software, of which the most common is Microsoft Project, which runs under the Windows shell, is fully compatible with MS-Office and, accordingly, can use MS-EXEL, MS-Access databases and the Word text editor . 6.4.
