The article considers simulation models of risk analysis for IT projects. An article objective is research of simulation models and their application for risk management of information technology projects. An information system based on simulation models of risk analysis for IT projects is developed. The experimental approbation of the developed system is analyzed. One of the major tasks to address within project management is project risk management or project risk management. This task is not separate from most other project management functions. It projects are characterized by a large number of connected processes. The most expedient method for analyzing and managing IT projects risk, including the risks of observing calendar schedules, is imitation modeling. This method provides both accurate analysis and visual representation of alternatives to management behavior. Considered model allows constructing distributions of probability values for the most important parameters of the progress of the project, which in turn allows you to put and check stochastic hypotheses.
One of the major tasks to address within project management is project risk management or project risk management. This task is not separate from most other project management functions. When determining financial needs, calculating budget and budget, preparing and concluding contracts, the task of protecting project participants from various types of risks arises during the control of the project implementation. Risks arise at all stages of the project activity, so the function of managing them is relevant until the project closure. Project risk management permeates all areas of project management activities without exception. This causes various difficulties (organCopyright © 2020 for this paper by its authors. This volume and its papers are published under the Creative Commons License Attribution 4.0 International (CC BY 4.0). izational, personnel, psychological, etc.) to separate this function into an independent element of the organizational structure of project management.
Within the risk management of IT projects, the following issues are relevant [
Within the theory and practice of project risk management, the most important are, in
particular, methods of risk assessment, monitoring and forecasting, risk management
information support [
The project is always focused on the result, the achievement of the set goals, the
specific subject area. The authorized project management, project manager and project
team working under this management, other project participants who perform specific
activities and processes for the project, carry out the implementation of the project. As
part of the project, usually on a part-time basis, representatives of the linear and
functional divisions of companies responsible for performing their tasks, activities,
functions, including planning, management, control, organization, administration, and
other system-wide functions, may participate. [
The managed parameters of the project are [
The main elements of a system of management in situations of uncertainty are: identifying risk in alternatives and keeping it within acceptable levels; development of specific recommendations aimed at eliminating or minimizing the possible negative effects of risk [28-33]. The challenge of managing IT projects is to reduce the impact of unwanted factors on the project lifecycle to produce the results closest to the desired ones. For complex systems, where the problems of research and prediction of states are mostly solved, depending on the chosen management strategies, such as systems of analysis and management of project risks, there are difficulties in the application of analytical models. They are caused by the following factors: • Large projects have many links between processes; • Real projects fall under the influence of random external and internal factors, the accounting of which is not possible analytically; • The possibility of comparison of the original with the model exists only at the beginning and after the application of the mathematical apparatus, since the intermediate results may have no analogues.
In this regard, it is advisable to use a more flexible method, the simulation method.
The model is presented in the form of an algorithm in which all the most essential elements, connections in the system are determined and initial values of the parameters corresponding to the initial moment of time are given.
All further changes occurring in the system by the cause and effect law are calculated by means of logical processing of data when executing this algorithm.
This method does not require equations and does not require their solution, so it is widely used in many areas of human activity without additional special knowledge.
During the simulation experiment, the computer simulates the functioning of the system, process, or project and calculates the characteristics of the properties manifested by the system. The simulation experiment is similar to a full-scale experiment, but unlike a full-scale experiment, it allows you to experiment with systems that are already missing or to predict the behavior of existing systems in the future, to study their behavior in emergencies. It is cheaper and faster than full-scale experiments.
Simulation modeling in the management of IT projects can be seen as a kind of
"simulator" that allows the manager of any level to predict the execution of the project
under the influence of various controlled and uncontrolled factors of the external and
internal environment [
Simulation modeling is a versatile method that provides both accurate analysis and visual display of alternative management behaviors. In addition, because of its versatility, the ability to conduct numerous experiments and plan for various changes, imitation models of complex systems are the most common. In the process of conducting experiments on the simulation model, it is possible to make the following changes: • In the model structure (add new items and links, remove others) • Behavior models, model parameters; • Parameters and laws of distribution of random factors; • In time of values and external variables.
Simulation models allow us to investigate system-wide properties, system behavior in special situations, to find better values of system parameters that were free before the start of the study, to predict system behavior over time. The algorithmic structure of the simulation models facilitates the implementation of various schemes of hierarchical subordination and coordination between the elements of the model.
We distinguish the following eight stages of simulation. 3.1
The objective is external to the system under consideration, determined by the tactical or strategic interests of the individual or group of persons for whom the study is being conducted. Of particular interest is the situation where the ODA (administrator, manager, and supervisor) solves some practical problem. The purpose of the study (or each set of goals) is specified in the form of a set of tasks, the solution of which is necessary and sufficient to achieve the goal. Usually, many tasks have a hierarchical structure and can conveniently depicted as a tree of goals and tasks.
Another factor that leads to the identification of this problem is the ability of the researcher (theoretical, financial, time and others). Theoretical capabilities are those data and research methods that a researcher can apply to solve a problem based on their professional knowledge and experience. Financial capability limits the use of tools, the volume of experiments and observations, the number of specialists and support staff. Any research should done in specific timeframes, which significantly depend on the scale of the problem and the depth of its study.
In general, the purpose of the study can be decomposed as follows: • Description of the functioning of the system (description of the system in the framework of an already formulated problem, i.e. some aspect of the functioning of the system); • Forecast of functioning at different impacts (predicting the state of the system in the future under different variants of internal and external influences (scenarios) on the system); • Search for the best version of the system. 3.2
The formulation of the research problem allows us to outline the boundaries of the object, distinguishing it from the environment. The result of the systematic approach to the problem is a conceptual model that reflects the concept of the study and is determined by its goals and opportunities. The conceptual model contains: • Description of the boundaries of the system; • Set of system elements; • The set of status indicators for each element; • A set of links between elements of the system (if necessary, indicate the intensity of resource and information flows); • A list of processes that take place in the system; • A list of internal and external influences on the system.
The most common are verbal (verbal) descriptions of the conceptual model; various diagrams, graphs, tables and charts are also used to provide the information in a clear and concise manner. The conceptual model may contain formalized elements (flowcharts, flow models, mathematical relations, etc.), which facilitates subsequent steps of formalization. 3.3
The next stage of simulation is the formalization of the conceptual model that is obtained, that is, the construction of a formal model. The general appearance of a formal simulation model can defined by the ratios:
x(t + ∆t) = x(t) + (∆t)ft ( x(t), u(t),ξ (t)), x(0) = x0 , t = 0,, T − ∆t, Where x(t) = ( x1(t),, xn (t)) is vector of state; xi (t), (i = 1,, n) is this is the value of the indicators that characterize the state of the system at time t; components of the state vector can take both quantitative (numeric, symbolic, etc.) and qualitative values on some order scale; u(t) = (u1(t),, um (t)) is vector of controlled effects; ξ (t) = (ξ1(t),,ξ p (t)) is vector of not controlled effects; f1( x(t), u(t),ξ (t)) is vector-function of the same dimension as x (t), which determines the dynamics of the state vector under conditions of external influence; x0 = ( x01,, x0n ) is the initial value of the state vector that is known; T is the period during which the dynamics of the system are simulated; ∆t is modeling step (time difference between two consecutive states of the system).
Each of the vectors x(t), u(t) і ξ (t) can take values from some valid range, which is determined accordingly X (t) , U (t) і Ξ(t) . Area of valid states X (t) is characterizes the range of possible states of the system, the range of acceptable controls, U (t) is characterizes the capabilities of the subject to control the system, and the area Ξ(t) is characterizes the possible values of uncontrollable factors (in the complete absence of information this area coincides with the whole space R p ).
Depending on the purpose of the simulation, a system time is introduced to simulate the course of time in a real system. There are two types of scales of model (system) time: uniform and event (by actions). After setting the system state vector and selecting a time step, the model is decomposed and its block design is determined. The block principle of model building has a number of advantages, especially tangible when creating complex imitation models. 3.4
An integral part of applied systematic research is computer simulation experiments with the model. The constructed formal model should presented in the form of a program that implements the corresponding research algorithm: numerical solution of the system of algebraic and differential equations, optimization problem, and transition of the system from the initial state to the final state. 3.5
Before using a built-in simulation model, the following questions must addressed: • Select the values of structural and numerical parameters of the model; • Make sure that with these parameter values, the model fits well with the modeled system and describes it adequately (verification, verification of certain adequacy). 3.6
In simulation modeling, the computer plays the role of an experimental institution, giving the value of managed variables, uncontrollable factors, and the initial conditions of the system trajectory. Since the number of possible combinations of controlled and unmanaged external factors (even for a finite set of them) per system is large, so is the role of planning simulation experiments. 3.7
Usually, the immediate results of the simulation are not yet suitable for solving the tasks. They should systematized, submitted in a form that is more favorable for later analysis, submitted to the ODA, and analyzed. Negative results can obtained at this stage, which means that you need to correct the model and return to the previous steps. The statistical methods of processing the simulation results include: • Data capture and accumulation of modeling statistics; • Determination of intervals for initial values; • Identifying functional relationships between variables using regression analysis; • Identification of the law of distribution on the histogram.
Analysis of simulation results contains: • Evaluation of the accuracy of the simulation experiment; • Reducing the number of model parameters; • Determination of intervals of change of parameters; • Search for the source of errors; • Removal of sharply rejected values; • Selection of coordinate system for presentation of results, etc. 3.8
The key to simulating systems is to solve practical problems. Therefore, the
simulation process does not end even after receiving, processing and interpreting the results
of the simulation ODA and experts. It is necessary to ensure the practical application
of these results in the management of an appropriate dynamic system. It is necessary
that the results can used not only for a single solution of the task, but also for the
multiple solution of a complex of problems related to this system [
In this way, simulation models allow us to investigate the behavior of large systems, in particular, IT projects, that are not amenable to research by other methods. 4
We present information technology project as a certain sequence of wi ∈W processes.
The process is a set of interrelated or interrelated activities that converts the inputs to
outputs [
Building a network of project is based on the following rules: • Each process is fed to one and only one arc; • Each process is identified by two end nodes (a node of the beginning of the process and its node completion); • To maintain the correct relationship of transposing additional process, you must specify: o Which process is directly preceded by the accompanying process; o What process should be performed after the added process is completed; o What process competes, that is performed in parallel, with added process.
The analysis of the risk of compliance with the deadlines of the project is to determine the probability of which the project will executed at a certain time and vice versa, how much time is required for successfully complete the project with the given probability. It is obvious that the project will be successful, that is, in a predetermined period, completed in case of completion of all the work of the project. The performance of the project can be calculated by summing the longest by chronological dimension of path (the critical way), which determines the maximum duration of the project overall. The process is critical if it has no "allowance" for the time of its start and completion. So that the entire project is completed immediately, it is necessary that all the critical processes are started and end in a strictly defined time. For a noncritical process, some deviations in its start time, but within certain boundaries – means when the time of its start does not affect the duration of the entire project. To perform the necessary calculations we define an event as a point on the timeline axis where one process ends and another begins. We introduce the following designations: • t′j is the earliest possible occurrence of the event j; • t′j′ is the latest possible time of occurrence of the event j; • D jq is process Duration ( j, q) .
Calculation of the critical path occurs in two passages. During the first pass, the earliest times of occurrence of events are evaluated, and for the second – the earliest times of occurrence of the same events.
І-st pass. The calculations start at node 1 and finish at last node n. Let’s assume, that t′j = 0 , means, projects starts at zero time point. Then for each node j we define nodes p,q...,v, which are directly related to node j by processes (p,j) (q,j)..., (v,j), for which we already calculated the earliest time of corresponding events. The earliest time of event j is calculated by formula: t′j = max{t′p + Dpj , tq′ + Dqj , tv′ + Dvj}. Moving forward is finished, when value tn′ is calculated for node n.
ІІ-nd pass. Calculations start at the last node n and end in node 1. Let’s assume, that tn′′ = tn′ , means that earliest and latest time for finishing project are the same. Then for each node j we define nodes p,q...,v, directly connected to node j by processes (p,j) (q,j)..., (v,j), for which we already calculated latest time of corresponding events. The latest time of event j is calculated by formula:
t′j = min{t′p′ − Dpj , tq′′ − Dqj , tv′′ − Dvj}.
Moving backward is finished, when value t1′′ is calculated for node 1.
Process (i,j) will be critical, if following conditions are valid: 1. ti′′ = ti′ ; 2. t′j′ = t′j ;
t′′ − ti′′ = t′j − ti′ = Dij . 3. j Critical processes should form a continuous path across the entire network from the initial event to the end. For the implementation of simulation model of IT Projects Risk analysis is developed about a system that decides to determine the probability of successful completion of the project at the specified dates and the time of completion of the project at a specified probability of successful completion.
The project is in the form of a network. An arc oriented in the direction of project implementation marks each process of the project. Each event is set by a network node and establishes a coding relationship among project processes. Its number, title and duration characterize each process of the project.
The duration of the processes can be deterministic, stochastic or probabilistic. In the first case, the Critical Path Method is used, in the second – PERT (Program Evaluation and Review Technique) method.
In the case of probabilistic lifetime’s processes, for each of them it is necessary to obtain probabilistic distributions of time of execution of this process. To obtain the kind of law probabilistic distribution and its parameters, you can use several methods. The First is to obtain the type and parameters of the distribution law by questioning experts (subjective probabilities). The second is based on the plural of analogues projects (objective probability). To determine the analogues projects must first classify the simulated project. To do this, we use the database of already executed projects and with the help of fuzzy classification; we divide the projects into classes by certain signs. Later after conducting cluster analysis of a simulated project determine the class to which it belongs and choose the rationing procedure for calculating the parameters of the project. 5
For example, the developed system is to take the project given by the network in Fig. 1. Input the data in this system to enter the project's network model is the characteristics of the project processes: process numbers and their names, the longest and shortest duration. In order to establish relationships, project processes as input parameter for each process are set numbers of processes without which the process is impossible to start. This data is entered in the dialog box (Fig 2) in the table (Fig 3). For all project processes the probabilistic distribution law is specified, which will be used with a random values generator and the distribution parameters are necessary if necessary. The number of settlement iterations is given separately (Fig. 4). To provide random values by the selected distribution law, the generators of random quantities are used. In particular, the system provides random value generators to provide random values after we have the law of distribution: Uniform distribution; Normal distribution (D); β- distribution (parameters α and β); Exponential distribution; γ-distribution (parameter α). The system works as follows. After specifying input data is generation of random duration of work with a specified user. Generation occurs according to the selected law distribution. Later passes the process of finding the critical path of the project, in accordance with the given order of following works and their generated lifetimes. The number of such transitions depends on the number of the settlement iterations.
For the project, the table (Fig. 3) and the distribution parameters (Fig. 4) critical path be the following (Fig. 5). Then the system forms probabilistic distributions for the found critical ways, analyzes them and depicts graphically (Fig. 6). The source data of the system are the formed probabilistic distributions in both separate found critical ways and for the project in general (Fig. 7).
As a result of the system work, we can get an answer to the question: • How long will the project is performed in advance of the given likelihood? • What is the probability that the project may executed in a specified period? For example: For a period of 72 time units, a project that is specified in Fig. 1 will be finalized with a probability of 0.80373, and the completion of this project with the probability of 0.9 is possible in the period not later than 73 time units (Fig. 8).
The received information can used to develop specific recommendations for reducing the impact of undesirable factors on the life cycle of the IT project in order to obtain the results closest to the desired ones. 7
It projects are characterized by a large number of connected processes. The most expedient method for analyzing and managing IT projects risk, including the risks of observing calendar schedules, is imitation modeling. This method provides both accurate analysis and visual representation of alternatives to management behavior. Considered model allows constructing distributions of probability values for the most important parameters of the progress of the project, which in turn allows you to put and check stochastic hypotheses. The project is in the form of a network. An arc oriented in the direction of project implementation marks each process of the project. Each event is set by a network node and establishes a coding relationship among project processes. Its number, title and duration characterize each process of the project. The duration of the processes can be deterministic, stochastic or probabilistic. In the first case, the Critical Path Method is used, in the second – PERT (Program Evaluation and Review Technique) method. In the case of probabilistic lifetime’s processes, for each of them it is necessary to obtain probabilistic distributions of time of execution of this process. To obtain the kind of law probabilistic distribution and its parameters, you can use several methods. The First is to obtain the type and parameters of the distribution law by questioning experts (subjective probabilities). The second is based on the plural of analogues projects (objective probability). To determine the analogues projects must first classify the simulated project. To do this, we use the database of already executed projects and with the help of fuzzy classification; we divide the projects into classes by certain signs. Later after conducting cluster analysis of a simulated project determine the class to which it belongs and choose the rationing procedure for calculating the parameters of the project. Further work in this direction will focus on the research of situations in which every particular IT project process may have a different kind of probabilistic runtime distribution. 28. Babichev, S.: An Evaluation of the Information Technology of Gene Expression Profiles Processing Stability for Different Levels of Noise Components. In: Data, 3 (4), art. no. 48. (2018). DOI: 10.3390/data3040048 29. Babichev, S., Durnyak, B., Pikh, I., Senkivskyy, V.: An Evaluation of the Objective Clustering Inductive Technology Effectiveness Implemented Using Density-Based and Agglomerative Hierarchical Clustering Algorithms. In: Advances in Intelligent Systems and Computing, 1020, 532-553. (2020). DOI: 10.1007/978-3-030-26474-1_37 30. Shpak, N., Sorochak, O., Hvozd, M., Sroka, W.: Risk evaluation of the reengineering projects: A case study analysis. In: Scientific Annals of Economics and Business, Volume 65, Issue 2, 215-226. (2018) 31. Shpak, N., Dvulit, Z., Luchnikova, T., Sroka, W.: Strategic development of cargo transit services: A case study analysis. In: Engineering Management in Production and Services, Volume 10, Issue 4, 76-84. (2018). DOI: 10.2478/emj-2018-0024 32. Shpak, N., Kyrylych, T., Greblikaite, J.:Diversification models of sales activity for steady development of an enterprise. In: Sustainability (Switzerland) Volume 8, Issue 4, 393. (2016). DOI: doi.org/10.3390/su8040393 33. Shpak, N., Seliuchenko, N., Kharchuk, V., Kosar, N., Sroka, W.: Evaluation of product competitiveness: A case study analysis. In: Organizacija, Volume 52, Issue 2, 107-126. (2019). DOI: 10.2478/orga-2019-0008