Thoughtful, well-organized cooperation of specialists in intersectoral projects has an undoubted synergetic effect. At the same time, the support of such a complex project involves the thorough involvement of business analysts. To model the process of selecting additional functions of the information technology, it is convenient to use Petri nets to visualize both parallel and sequential processes. The use of methods of expert evaluation, decision-making, decision-making under uncertainty to support the work of business analysts will allow taking into account various criteria of such intersectoral cooperation. As a criteria of decision-making under uncertainty, the Laplace, Wald, Bayes, Hermeyer, Savage, Hurwitz, Khodg-Lehmann criteria were analyzed, as well as the criteria of extreme optimism, extreme pessimism, compromise criterion, and product criterion.
anymore. To support the processes in PMP Committee now, it is crucial to involve representatives from different branches [9], that are involved in processes of support of disabled persons` lifelong wellbeing.
Traditionally, designing a health care institution management software, developers are led by state standards and protocols of health care. As input data, such software needs patient ID, screening and diagnosing results, etc. These data are saved, can be looked through, and printed out in a form of a history of a disease. To order such software (an information technology, actually), in Ukraine, the public health care organization should use an open electronic system of public procurement ProZorro (https://prozorro.gov.ua/). This resource is an online platform where state and municipal customers announce tenders for the purchase of goods, works, and services, and business representatives compete in tenders for the opportunity to supply it to the state. From the point of view of the PMP Committee needs, in such a way the state could have ensured the cooperation between the state health care organization and IT company. But such cooperation between these three subjects is rather narrowly focused from the side of the state, at least. Such cooperation is rather limited in its variations: the state health organization gets the IT to automate some processes, and the state pays for it. But this fact can be changed by adding one more facet to such cooperation, i.e. the scientific approach. In fig 1, there’s a concept of such cooperation, enriched with possibilities that enable an application of data science to the cooperation of IT, state, and medicine.
To achieve the synergetic effect from such cooperation, it should be well organized. On the opposite of the traditional order of IT development which ends with the IT implementation, the proposed scheme foresees constant cooperation and constant improvement of the outcome (blackcolored edges). By participating in such cooperation, the IT company/ies should provide the project managers of such complex process, and involve business analyst (or a group of one) to control a lot of business processes. It is worth mentioning that the business process is understood as one that enables some profit, expressed in money or time savings (any other kind of profit can be measured in time or money units, as well). The main goal of this research is to suggest an approach to the management of the projects, which should result in an IT that has two layers of functions, i.e. functions that should be realized unconditionally, and functions that are additional, and the very set of the functions, the sequence of its realization, and their effectiveness may vary. If we go back to the example of PMP Committee example, the must-have function of the IT, developed to automate the processes in the Committee, are those that enable the document flow according to state health care standards. The additional functions are those that can the PMP Committee specialists suggest with their experience of working with disabled children, and, of course, those functions that might suggest the data analysts, according to diagnostics results they would be provided [10], [11]. For example, some data science methods can analyze, which diagnosing procedures can be odd, and the decision on the diagnosis can be made on less number of characteristics of a child. 2
Let us recall that during the intersectoral cooperation, mentioned above, demands that the developed information technology should unconditionally have basic functions, realized according to state standards. The list of additional functions can be formed during a cooperation between all participants. Additional functionality of such information technology might be, for example, the following.
• Availability of methods of data and knowledge analysis extraction based on existing results of psychophysical diagnostics. • Availability of methods of data and knowledge analysis, based on which it is advisable to update the protocol of psychophysical diagnosis. • Automation of the PMP Committee activity. • Development of a national system for consolidating the results of psychophysical diagnosis; • Adaptation of IT to the national system of support for lifelong learning. • Automate compliance with IT requirements used by people with special needs, etc.
Collaborators mentioned in Fig.1, can evaluate the usefulness of each of the proposed functions, and the use of optimization methods will support the decision-making process of the business analyst. The model of such an organized decision-making process in project management is conveniently presented with Petri nets, which will allow visualizing sequential and parallel processes. Petri nets have proved to be a convenient tool for modeling the learning processes of people with special needs, maintenance, flows of an online store, basic cyber-physical attack models [12]-[14], etc.
The Petri net С=(Р, Т, І, О) models the process of decision making in choosing additional functions (Fig. 2), where the set of positions Р={р1, р2, …, р8}, the set of transitions Т={t1, t2, t3}; initial marking μ0 is one chip in position р1.
Transitions in the given Petri net are events and are interpreted as processes (Table 1).
Meaning of position The alternatives of the additional functions The criteria of efficiency evaluation of the additional functions The assessments of the alternatives according to the criteria (by data scientists) The assessments of the alternatives according to the criteria (by IT specialists) The assessments of the alternatives according to the criteria (by state) The assessments of the alternatives according to the criteria (by medics) A set of alternative strategies of the realization of additional functions
A strategy of the realization of additional functions
In the process of expert evaluation of each of the additional functions that can improve basic IT, you can use, for example, the method of analytic hierarchy process (AHP). This method has been used for expert evaluation in various fields. For example, to model the delineation of artificial groundwater recharge potential regions, to model the selection of riparian protected area stretches [15]-[17].
In AHP, the evaluated alternatives are additional functions (mentioned before), and the evaluation criteria are the usefulness according to the assessments of experts (the representatives of the intersectoral cooperation process from Fig. 1). As a result of the application of the basic stages of AHP we will receive estimations of the usefulness of alternatives (at Fig. 3 there is an example of such estimations, where three alternatives are estimated by four experts). To obtain such estimations, the eigenvectors of each of the pairwise comparison matrices are multiplied by 10 and rounded to the integers.
To decide which of the alternatives should be realized, we propose to apply optimization methods, namely methods of game theory. Such a decision is made under conditions of uncertainty because even the most experienced experts do not always rationally estimate the magnitude of expected benefits or losses. Therefore, the problem presented by the matrix in Fig. 3 we propose to understand as a problem of game theory, namely games with nature, where decisions are made in conditions of uncertainty [18]. Several criteria have been developed for decision-making in conditions of uncertainty, which we will consider below. 3
In decision-making under uncertainty, the information required for decision-making is presented in the form of a matrix Q = qij , i = 1,..., n, j = 1,..., m with rows S = {Si},i =1,...,n and columnsV = {Vj}, j =1,...,m . According to the analyzed example (Fig. 3), the rows Si of such a matrix are the strategies of implementation of additional functions in information technology. The columns V j of the matrix correspond to the conditions under which the corresponding additional functions will be implemented. Thus, the elements qij of the matrix are the numerical values of the usefulness of the corresponding strategy implementation (Fig. 4). We will consider the best strategy as one that is the most useful. The choice of such a strategy is complicated by a large number of alternatives and the need to take into account many conditions, which affect the usefulness of additional IT functions. Such conditions can be, for example, to promote the development of each particular industry, represented by the participant of the intersectoral cooperation process.
V V2=<promotion of IT
development>
We will choose one of the alternatives according to different criteria C: the criteria of Laplace, Wald, Bayes, Hermeyer, Savage, Hurwitz, Khodg-Lehmann, as well as the criteria of extreme optimism, extreme pessimism, compromise criterion, and product criterion [19]-[24]. Each of the criteria has certain features and characteristics. 3.1
The criterion is considered a pessimistic criterion, because it focuses on the worst result, thus
reducing the risks of decision-making. For each of the alternatives find the values of least usefulness,
and choose the maximum of the values found. Wald criterion is formalized by formula (
i j
(
Finding the best alternative by Wald's criterion for the task in Fig. 4, calculations are given in Fig. 5.
V1
V2
V3
V4
mijn qij
According to the Wald criterion, it is advisable to choose alternatives S1 or S2. 3.2
The criterion involves the choice of the alternative with the highest efficiency, the criterion does
not take into account possible risks. To find the best alternative by this criterion, choose the maximum
of the found maximum efficiency values for each alternative. The criterion of extreme optimism is
formalized by formula (
CХ = max max qij , i = 1,...,n, j = 1,...,m .
i j
(
Finding the best alternative by the criterion of extreme optimism for the task in Fig. 4, calculations are given in Fig. 6.
V1
V2
V3
V4 max qij
j
According to the criterion of extreme optimism, it is advisable to choose an alternative S1.
The criterion involves choosing the alternative with the most pessimistic result. Only the worst
possible result is taken into account. To do this, choose the minimum value among the smallest for
each strategy, which is formalized by formula (
CР = min min qij , i = 1,...,n, j = 1,...,m .
i j
(
Finding the best alternative by criterion of extreme pessimism for the task in Fig. 4, calculations are given in Fig. 7. According to the criterion of extreme pessimism, it is advisable to choose an alternative S3.
V1
V2
V3
V4
mijn qij
It is believed that the criterion makes it possible to choose a compromise strategy between
optimistic and pessimistic. According to this criterion, the strategy with the highest value of the
average between the maximum and minimum value of utility is selected. The criterion is formalized
by formula (
max qij + min qij CК = max j j , i = 1,...,n, j = 1,...,m .
i 2
(
Finding the best alternative by the criterion of compromise for the task in Fig. 4, calculations are given in Fig. 9. According to the criterion of compromise, it is advisable to choose an alternative S1.
V1
V2
V3
V4 max qij + min qij j j
The criterion makes it possible to indicate how close to the optimistic or pessimistic development
the decision-maker is inclined. To do this, we use a coefficient λ called the coefficient of pessimism
(realism), which is given within [0, 1]. In the case of λ = 1, the decision maker is prone to pessimism,
and when λ = 1 to optimism. The difficulty of applying this criterion is in the need to determine the
coefficient λ. The criterion is formalized by formula (
i j j
j
(
Finding the best alternative by Hurwitz criterion for the task in Fig. 4, calculations are given in Fig. 10. According to the criterion of Hurwitz criterion, it is advisable to choose an alternative S1.
V1
V2
V3
V4 min qij + (1 − ) max qij j j
It is used in case of insufficient information about the event to be decided, and the probability of
occurrence of each condition Vi will be considered the same. Then the optimal alternative is
determined by the maximum average efficiency values (
CL = max i 1 m
qij , i = 1,...,n .
m j=1
(
Finding the best alternative by Laplace criterion for the task in Fig. 4, calculations are given in Fig. 11. According to the Laplace criterion, it is advisable to choose alternatives S1 or S2.
In contrast to the Laplace test, where the probabilities of conditions Vi are equal, the Bayesian
criterion is based on the assumption that such probabilities are different. This fact often indicates that
the conditions under which decisions are made are sufficiently studied, and it is possible to indicate
т
the corresponding probabilities рі of occurrence of each of the conditions, and j=1p j = 1 . According
to the Bayesian criterion, the alternative for which the mathematical expectation is higher is also
considered optimal. The criterion is formalized by formula (
m т
CB = maix j=1p jqij , i = 1,..., n , p j [0,1] , j=1p j = 1 .
(
Finding the best alternative by Wald's criterion for the task in Fig. 4, calculations are given in Fig. 12. Here, the vector of probabilities of occurrence of each of the conditions is Р=(0.2, 0.3, 0.1, 0.4).
V1
V2
V3
V4 m p j qij j =1
According to the criterion of extreme optimism, it is advisable to choose an alternative S2. 3.9
As in the Bayesian criterion, the Hermeyer criterion takes into account the different probabilities of occurrence of each condition, however, the optimal alternative is chosen for which the minimum product of utility values on the probability of occurrence of the corresponding condition is the largest. The criterion is formalized by formula (9): т CG = max min p j qij , i = 1,..., n , p j [0,1] , j=1p j = 1 .
i j (9)
Finding the best alternative by Hermeyer criterion for the task in Fig. 4, calculations are given in Fig. 13. Here, the vector of probabilities of occurrence of each of the conditions is Р=(0.2, 0.3, 0.1, 0.4). According to Hermeyer criterion, it is advisable to choose alternatives S1 or S2.
V1
V2
V3
V4
As in the Bayesian criterion, the Hodge-Lehmann criterion takes into account the different probabilities of occurrence of each condition. Also, as in the Hurwitz criterion, you need to set the value of the subjective variable z, which expresses the degree of confidence in the information about the conditions under which the decision is made, z is set within [0, 1]. The criterion is formalized by formula (10):
CHL = max z n qij pi + (1 − z) min qij , i = 1,...,n, j = 1,...,m .
i i=1 j (10)
It should be mentioned that in the case of z=0 (extreme distrust of the received information about the state of the system), the Hodge-Lehmann criterion becomes the Hermeyer criterion, and at z=1 (the information about the state of the system is reliable), the Hodge-Lehmann criterion becomes the Bayesian criterion.
Finding the best alternative by Hodge-Lehmann criterion for the task in Fig. 4, calculations are given in Fig. 14. Here, the vector of probabilities of occurrence of each of the conditions is Р=(0.2, 0.3, 0.1, 0.4), z=0.3.
V1
V2
V3
V4 n i=1qij pi
The criterion should be used to protect the decision-maker from excessive losses. To make a decision, a risk matrix R is constructed on the basis of the initial condition matrix: the differences between the found maximum values in columns and the values of the initial matrix ( rij = max qkj − qkj ) are put into the risk matrix. The criterion is formalized by formula (11): k
CS = min max rij , i = 1,...,n, j = 1,...,m .
i j (11)
Finding the best alternative by Savage's criterion for the task in Fig. 4, calculations are given in Fig. 15. According to Savage's criterion, it is advisable to choose an alternative S1.
V1
V2
V3
V4
According to the results of calculations based on decision-making criteria, alternative S1 was the most useful according to four criteria (it is more than 36% of all criteria), according to three criteria alternative S2 (over 27% of criteria), according to one criterion – alternative S3 (over 9% of criteria), according to three criteria – alternatives S1 or S2 are equally useful (more than 27% of the criteria). Let's summarize the results of calculations graphically.
To manage complex projects involving specialists from different fields, it is advisable to have a
tool that will allow you to take into account the needs of such specialists. The proposed approach
should be used by business analysts in the case of project management, which has some alternative
scenarios, each of which is more or less useful in different conditions. In this case, the combination of
AHP and decision-making under the uncertainty method will allow choosing the best alternative. The
decision can be made from a pessimistic or optimistic point of view, and the ability to adjust certain
parameters of the criteria (for example, in Hurwitz and Hodge-Lehmann criteria) will allow taking
into account the views of experts involved in intersectoral cooperation.
6
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