ANALYSIS OF THE LINEAR MODEL AS A ROADMAP METHOD TO IMPROVE SOCIAL SECURITY FOR INTERNALLY DISPLACED PERSONS Abstract. In the process of counteracting the escalation of the military conflict with the Russian Federation and the escalation of the armed conflict, internal displacement from the borders

ANALYSIS OF THE LINEAR MODEL AS A ROADMAP METHOD TO IMPROVE SOCIAL SECURITY FOR INTERNALLY DISPLACED PERSONS Abstract. In the process of counteracting the escalation of the military conflict with the Russian Federation and the escalation of the armed conflict, internal displacement from the borders of Donetsk and Luhansk oblasts was caused. The relevance of this study is guided by the origin and sustainability of the movement within the borders of Ukraine in 2021. In search of a landmark and sustainable adaptation, since 2014 our country has been able to successfully overcome barriers and obstacles. depressed. This encourages action not only to comply with the Minsk Protocol in the format of the «Quartet of Normandy», but also to address the needs of citizens in displacement, to save entire families with young children, disabled people, the disabled, retirees. The aim of the article is to analyze the map of problems to further improve the mechanism of adaptation and integration of internally displaced persons, as minimizing the occurrence of manifestations of maladaptation, is the basis for targeted intervention of host communities. Thorough acquaintance with the methodological principles of problem map analysis is the optimal component of the study. The article examines some specific phenomena in the economic, social, political spheres of the state to analyze the map of problems of internally displaced persons for the needs of appeals to host communities. The article examines the methodological provisions of the cause-and-effect relationship of difficulties at the stages of economic, social, political integration, which should become a typology of rapid response from the public space. Communication strategy and information support of social services are often missing. Lack of dialogue and communication skills among social workers and other stakeholders leads to the formation of a culture of dialogue for interaction with internally displaced persons. The article considers a map of problems in terms of the largest, general areas of optimization of host communities, a map of problems as a tool for comprehensive diagnosis, helps to build a chain of relationships, reflects situational analysis, and clearly shows the pain points of citizens in the local, regional, and national levels.

Introduction. The process of Ukraine's accession to the EU provides for the implementation of European standards to ensure children's rights and support vulnerable families. The Council of Europe Regulation «on the rights of children and the development of child-and family-friendly social services emphasizes the fundamental principles that governments must respect when developing these services» [1].
The fundamental importance of social identity, both in terms of how people think about others and for personal well-being with the emergence of internally displaced persons (hereinafter IDPs) is the priority development of obtaining quality social services at all levels of the host community.
According to the Internal Displacement Monitoring Center, Ukraine is on the list of countries with the largest number of IDPs in Europe and Central Asia at the end of 2020. The number of IDPs is 734,000. There has been a decrease in violence since the July 27, 2020, supplemental ceasefire reinforcement, but the ceasefire has been disrupted in parallel with a lack of substantive political progress [2].
Frequent ceasefire violations in eastern Ukraine during 2017 continued to result in loss of life, a 6% increase from 2016. In addition, damage to infrastructure and property occurred predominantly along the line of contact, with more than 1,500 homes damaged on the side of government-controlled territories alone. Increased insecurity continued to hamper humanitarian access, especially in non-government-controlled areas where access remained highly unpredictable. Despite the insecurity, some 800,000 people continued to live within 20 kilometers on both sides of the line of contact. Some returns to these areas were made mostly by people who did not have sufficient resources to extend their lives elsewhere in Ukraine. Several factors have contributed to the humanitarian needs of internally displaced and conflict-affected people, despite the assumption that the security environment would gradually improve; the ongoing armed conflict, restrictions on freedom of movement, difficulties accessing documents, and the continued suspension of social payments and pensions to thousands of people.
Positively, at the end of 2017, Ukraine adopted a strategy of long-term solutions to help the UN develop a plan of measures to implement improvements on the key issue was little progress on tasks such as paying pensions and social payments to people living in non-controlled territory, creating a birth registration system that better meets the needs of parents or improving freedom of movement through checkpoints where queues remained long, and conditions remained poor [3].
The implementation of the global roadmap, as a sustainable strategy in turbulent times [4] is gaining relevance in the present. The meaning of the implementation of the analysis of the road map method as a strategy [5] is to further improve the theoretical and methodological basis of social work of host communities, achieving the desired quality of service, the provision of services, appropriate assistance for the personalities of internal displacement. Among the internal reasons for the analysis of the problem map we shall name the factor of lack of concept [6] coherence in the planning of integration and adaptation program, insufficient information exchange within the financial and economic services, inconsistency in the work with internally displaced persons. Among the problems of the consequences of internal migration [7] in public existence we shall name the basis of proper provision of employment, the necessary programs of grants for entrepreneurship of IDPs by the degree of its importance.
Analysis of recent studies and problem statement. Under the realities of society with the existence of the map of occupied territories there is a need to study the category of the population of internally displaced persons. Oleksandr Yaremenko Ukrainian Institute of Social Research conducted a survey from September 27 to October 24, 2017, in 24 regions of Ukraine and Kyiv. A total of 2002 respondents were interviewed. Standard deviations with 95% reliability and the ratio of variables from 0.1:0.9 to 0.5:0.5 are 1.34 to 2.24%. The method of obtaining information in practice was the individual «face-to-face» interview. With the support of the UNDP project «Strengthening the Capacity of the Secretariat of the Ukrainian Parliament Commissioner for Human Rights» and the Council of Europe project «Strengthening the Protection of Human Rights of Internally Displaced Persons in Ukraine» the experts of the Public Holding Company «Group of Influence» developed the methodology of monitoring the observance of the rights of internally displaced persons for use by the Secretariat of the Commissioner and public organizations. Based on the data obtained in the framework of the nationwide representative survey with the involvement of specialists from the NGO «Center for Women's Prospects», an appropriate gender analysis was made, which allows to assess the status of observing and ensuring the rights of IDPs in the gender profile. Separate issues of IDPs adaptation as a set of processes in the regions of Ukraine were studied by domestic scientists A. V. Putintsev, Yu. Ie. Pashchenko.
The main international document «International Recommendations on IDPs Statistics» [8] (IRIS), containing standards for IDPs statistical production, was adopted by the UN Statistical Commission (UNSC) in March 2020. This document offers key definitions and a statistical framework for its use at both national and international levels, and also offers recommendations for coordination of state and non-state institutions in the IDPs statistical production process.
Evaluating the methodology of decision-making foreign scientists [9] acts as an important factor in creating a roadmap of IDPs problems.
An empirical study to deploy a methodology to improve the comparison between historical and current maps was carried out by Schlegel, I. [10].
The relevance and whole direction of the roadmap method serves for quality criteria in empirical research in various disciplines [11], including economic disciplines [12].
In service quality management [13], roadmap research for improvement identifies the critical importance of changing mindsets in the design of customer experience improvement programs and the ways in which customers can be directly involved in the design and improvement process. It is important to provide a roadmap that organizations can use as a basis for customer experience improvement. It also suggests that it's helpful to have clear goals in three areas: customer; personnel; and cost-effectiveness, to use them to assess the benefits of customer experience improvement.
The purpose of this article is to develop a theory and methodology for improving social welfare and access to public services through the use of the roadmap method of problems of internally displaced persons. Analysis of the use of the roadmap method as a tool to help and improve the social welfare of internally displaced persons and persons in difficult life circumstances.
To identify individual phenomena in the economic, social, political spheres of the state to carry out the analysis of the problem map of internally displaced persons on the needs of applications to host communities. To investigate the cause-and-effect links of the occurrence of difficulties in the stages of economic, social, political integration on the part of the receiving side according to the problems and the list of tools.
Results of the study. The 2030 Agenda for Sustainable Development [14] was adopted by world leaders at the historic UN summit in September 2015 and officially entered into force on January 1, 2016. Over the next fifteen years, countries have pledged to achieve 17 sustainable development goals. They mobilize efforts to end all forms of poverty, fight inequality, and combat climate change, while ensuring that no one is left behind. The Sustainable Development Goals are grouped around five main themes: people, planet, prosperity, peace, and partnership.
Social responsibility is an integral part of the influence of decisions and activities on society proceeding through transparent and moral behavior that contributes to the sustainable development of society, complies with current legislation, consistent with international norms of behavior. The need for ISO 26000 standard is due to the segments of society that can contribute to sustainable development, so there is a need to develop tools to enable the practical definition and implementation of the goals to achieve sustainable development. ISO 26000 [15] Guidance on Social Responsibility provides guidance on how businesses and organizations can act in a socially responsible manner, which involves the inclusion of the principles of non-discrimination and equal opportunity. Key themes and issues articulated in the standard include human rights, labor practices, the environment, fair operating practices, consumer issues and community involvement, businesses and organizations are influenced by many factors. Their relationship with the community or the external environment in which they operate is critical to effective engagement. This standard is increasingly being used as a measure of performance.
In our opinion, it is important to reveal the factors of difficulties at the stages of economic, social, political integration, which should become a reference point for laying the theoretical and methodological provisions of the roadmap of IDPs problems.
«Mission of the International Organization for Migration in Ukraine comprehensively supports innovative projects on social cohesion. To assess the needs of IDPs in entrepreneurship and employment, a case study of 25 IDPs in five regions of Ukraine was conducted, including 11 women and 14 men in the age category from 25 to 45 years, 14 entrepreneurs / self-employed and 11 wage workers» [16] .
«The majority of the IDP entrepreneurs (10 out of 14) were not able to transport business assets -equipment and property -to the place of relocation or host communities. Only one was able to relocate the assets in full. Accordingly, support in access to resources for the reproduction of entrepreneurial activity is most relevant. Entrepreneurs need more credit resources and fixed assets (equipment, vehicles) to resume and succeed in business. To a lesser extent they need information about business environment, local markets, and new business partners. Less, according to the respondents, IDPs need office premises and hired workers» [16].
The authors conducted an analysis of the mathematical model of linear programming. The review of the mathematical model of linear programming [17] applied to solve the problem of business management of entrepreneurs IDPs includes two studies of mathematical programming, the essential and important elements are duality theorems [18].
The duality theory in linear programming is based on two main theorems. Theorem 1. One and only one of the following statements is valid for both direct and dual problems. If one of linear programming problems has a finite optimum, then the dual problem also has a finite optimum, and the optimal values of linear forms of both problems coincide, i. e. � ��� � � ��� or � ��� � � ��� .
(1) If the linear form of one of the dual problems is unconstrained, then the conditions of the other problem are inconsistent. Both problems have no solution since the constraint systems are contradictory.
Theorem 2. The components of the optimal solution of one of the problems are equal to the absolute values of the coefficients at corresponding variables in the expression of the objective function (linear form) of the other problem (dual or direct) when it reaches its optimum and under the condition that the obtained optimal solution is not congenital.
It follows from the theorems given: to solve one of the mutually dual problems of linear programming, i.e., to find its optimal solution and the optimum of the objective function, we can write the optimal solution and the optimum of the objective function of the other problem. To illustrate the theory, a numerical example of economic interpretation of the dual linear programming problem is presented -the direct linear programming problem and the dual problem below.
Direct task is to maximize the function The double problem is to minimize the function � � � � � � + ⋯ + � � � � , when limited � �� � � + ⋯ + � �� � � ≥ � � ; � �� � � + … + � �� � � ≥ � � ; … � �� � � + … + � �� � � ≥ � � , * � � ≥ 0 �� � �, �, . . ., ��. In these problems a is the cost of raw materials of a certain kind of production of one kind of product, b is the stock of raw materials of a certain kind, c is the profit from a unit of production of a certain kind. In the direct problem x is the number of units of production of a certain kind. In the dual problem b -the price of raw materials of the corresponding kind. The target function Z is the total cost of purchasing raw materials which should be minimized. The maximum profit determines the solution of the direct problem. By solving the dual problem of linear programming, we find the prices y, more precisely, objectively determined estimates, at what prices it is necessary to sell each type of product, they are the components of the optimal solution of the dual problem of linear programming.
The factors of rapid industrial decline were annexation of Crimea by Russia, military confrontation in the east of the country, undermining of Ukrainian sovereignty and territorial integrity over a part of Donbass territory, also unfavorable price environment for main Ukrainian export goods, technical barriers, and low level of cooperation of Ukrainian industry with EU industry, falling domestic demand and economy openness to imports of industrial products. Autonomous preferences, the functioning of a free trade zone between Ukraine and the EU did not lead to growth in Ukrainian industry. In 2014-2015, the industrial production index collapsed by 10.1% and 12.3%, respectively. After that, in 2016-2018, the index of industrial production showed minimal recovery growth in the range of 1.1-4%, which in the context of the collapse of previous years can be considered stagnation [19].
In 2019, Ukraine's industrial production index fell by 0.5%, was only 85% of the 2013 level, 80.7% of the 2011 level. It was this year that was the last peak of industrial growth, as some restrictive measures against Ukrainian goods were started by the Russian Federation back in 2012-2013 -on the threshold of Ukraine's preparation for signing the Association Agreement with the EU, which at that time was actively pursued by the Ukrainian authorities. In 2020, Ukrainian industry acquired a state of crisis, as the industrial production index fell 5.1% in January and 1.5% in February. In March it received a crushing blow in the form of the COVID-19 pandemic and the global economic crisis. The consequence was an 8.3% decline in the industrial production index in the first half of 2020. The industrial production index in the first half of 2020 was 80.6% of the first half of 2013 and 77.7% of the first half of 2013, as shown in Table 1.   Table 2. The data are given without taking into account the temporarily occupied territory of the Autonomous Republic of Crimea and Sevastopol, for Q4 2014 also without taking into account the part of the temporarily occupied territories in Donetsk and Luhansk regions. So, if the production data for the reporting and previous months are updated synchronously, it may not affect the chain rate calculated on these data (the reporting month by the previous month) or have a weak effect» [19]. Source: concluded by the authors on the basis of statistical reporting data [20].
The prospects of Ukraine's industrial development are based on reindustrialization as part of the policy of accelerated economic growth, the prerequisite for reindustrialization as part of the policy of accelerated economic growth should be: implementation of changes by the National Bank of Ukraine in monetary policy, introduction of state support for exports of goods and services, restructuring of the banking sector in restoring their credit activity and strengthening the confidence of borrowers, popularization of Ukraine as an attraction for The main risks for economic growth and macroeconomic stability will remain: possible aggravation of pandemic crises processes; volatility on the global capital markets, in particular due to significant inflation surge in the world, uncertainty of timing of monetary policy normalization in the leading countries and probable growth of risk premium; sharp deterioration of trade conditions in general, including with main trading partners of Ukraine; military conflict escalation with Russian Federation; decline in yields of the main crops of Ukraine. Ukraine's economy is expected to gradually recover thanks to consolidation of all branches of power and the National Bank at the stage of structural reforms and coordinated state economic policy aimed at maintaining economic growth, as well as successful vaccination programs in the world and strengthening of global demand. The return of the economy to the trajectory of sustainable growth will also be facilitated by the positive results of the stimulating monetary policy and fiscal stimulus in 2020-2021.
Consumer demand will be fueled by a gradual decline in unemployment, remittances, and wage increases [21]. A significant responsibility and additional burden on the host societies is to deal with local affairs with private sector involvement at the center of gravity. The armed conflict initiated by Russian detachments has changed the lives of local communities on the «line of demarcation». Host communities have a need for contact with the coordinating group, humanitarian and logistics centers for security and social cohesion, and the latest methods and resources to restore sovereignty to the territories, but the relevance of a policy of marketing partnerships with the private sector is the key to the success of most communities. Private companies invest in the community resources of capital investment, the introduction of digital technology.
Majority privatization increases multifactor productivity by 4-10%, and the impact over time increases to about 16-18% 6 years after privatization. Privatization tends to increase firm survival and reinforces the redistribution of aggregate productivity through a stronger link between survival and productivity. Relatively few foreign takeovers are associated with a much larger impact, 17-33% compared to domestic private ownership, but the gap is much smaller when the foreign source country is «offshore» -an indirect channel for Ukrainian citizens-and it is also lower when the source is Russia [22].
The state of private sector involvement in the development of certain communities (Bolshaya Novoselka, Severodonetsk, Novhorodske, Druzhkivka, Schastie, Belovodsk) was investigated in October 2019, the analysis of available information from open sources, interviews with representatives of businesses, local authorities was conducted. By the Law of Ukraine «On temporary measures for the period of the antiterrorist operation» the country created conditions for economic encouragement of business entities in the ATO operation zone. A list of the main preferences should be given: exemption from payment for the use of land plots of state and municipal property; cancellation of rent for the use of state and municipal property and concession payment for the right to create (construction) and/or management (operation) of state and municipal property; prohibition of charging penalties and/or fines on the principal amount of debt on obligations under loan agreements and loans; measures to preserve property that is in mortgage; self-extension of licenses and documents of authorization.
Regarding the political sphere, forced passportization is currently an element of the aggressor state's repressive policy toward Ukrainian citizens forced to live under occupation; it is also an element of systemic pressure by the Russian occupation administration on Ukrainian citizens, planned in advance and cynically implemented, the Ukrainian Ministry of Foreign Affairs stated.
Important given the Russian -Ukrainian war unleashed by the Kremlin in 2014 is the prevalence of PTSD, the level of PTSD by symptom clusters, and the association of sociodemographic factors with positive PTSD indicators among internally displaced citizens in Ukraine during the long conflict in Donbas [23]. It has also long been known that women in the ATO zone without identity and/or special status documents face particularly harsh working conditions, and the lack of documentation prevents access to key social benefits (e. g., state health insurance, paid maternity leave, child benefit and subsidized care), women's work situations are crucial to their well-being during pregnancy and in terms of potential risks to the fetus, attention to undocumented labor [24]. «There has been a mutual affirmation since 1997 that good-neighborliness and cooperation between these countries are important factors in enhancing stability and security in Europe and the world, and the states will cooperate closely to strengthen international peace and security. Furthermore, Moscow and Kyiv claimed that they were taking the necessary measures to facilitate the process of general disarmament, the creation and strengthening of a collective security system in Europe, as well as the strengthening of the UN peacekeeping role and the effectiveness of regional security mechanisms In 2010, with Yanukovych and the pro-Russian Party of Regions coming to power, the interdependence in Ukrainian -Russian relations on energy, trade and economic contacts, military-strategic cooperation became apparent and more unconcealed March 17, 2014. The Supreme Council of the Autonomous Republic of Crimea proclaimed Crimea's independence at gunpoint of Russian guns, and the very next day in Moscow the so-called Contract on the Admission of Crimea to the Russian Federation was signed. On April 1, Russia denounced all treaties and agreements with Ukraine regarding the Black Sea Fleet. On March 24, 2014, Acting President of Ukraine A. Turchinov signed a decree on withdrawal of Ukrainian troops from Crimea and Sevastopol. The Ukrainian Crimean peninsula was temporarily surrendered to the Russian occupiers. The decisive role in this was played by the Black Sea Fleet of the Russian Federation, but the political (and not only) responsibility for its stay on the territory of Ukraine (contrary to its Constitution), conditions of functioning and status, etc., as well as the quarter-century destruction of the Ukrainian Armed Forces is borne by all major Ukrainian state officials and its power and political top brass» [25, p. 112 [28] of social service of natural assistance was approved. «The listed standards define the content, scope, conditions and procedure of social service provision, monitoring the quality of social service provision of social support to families (people) in difficult life circumstances -constant or periodic review of the subject providing social service aims to assess the current results, identify difficulties, identify problems, provide recommendations for their elimination, improvement and/or improvement of social service provision.
Global justice is a broad concept consisting of multilevel and multidimensional aspects relating to both normative and empirical realities. Therefore, in order to address some of the major and important issues being studied, a coherent integrated theoretical framework encompassing normative frameworks and various empirical dimensions is needed. The Global Equity Index report is a multi-year research project conducted to conceptualize and measure each country's contribution to achieving greater global equity» [29].
The authors compiled a list of tools guided by the components of the 17 Sustainable Development Goals, forming one whole, relating to the political, social, and economic dimensions. The roadmap of changes in the sphere of social security of IDPs and residents of the ATO zone in Fig. So, the article develops the hypothesis that the increase in the level of adaptation and integration ability of IDPs is due to the method of developing a roadmap of problems. For the first time the economic interpretation of the dual problem of linear programming is presented and confirmed. The key advantage of using this model is that it allows to cover the solution of the problem of business management of IDPs entrepreneurs, because there are objectively stipulated estimates at what prices should be sold for each type of product.
The authors have developed a generalized form of a strategic road map that can be used in practice.
The roadmap of problems inside displaced persons can be an effective preventive factor of the mechanism to improve the quality of life of IDPs through the improvement of social security and access to public services. This roadmap was developed by taking existing successful roadmaps from the literature and then adapting them to implement a specific company perspective on internal displacement. This study complements the current roadmap literature.
The proposed roadmap can be replicated and/or adapted for companies seeking to support IDPs. The theoretical and methodological analysis of the sources according to which the roadmap of this study was developed can be used as a guide for the development of further roadmaps.

List of tools for minimizing the risks of UPE integration О Problem
Industrial development [20] Changes in monetary policy

Economic sector
Reindustrialization in fiscal and customs policy Development of the secondary market for government directed loans in four areas

Consolidation of market infrastructure
Industrial parks as a tool for creating a production site with infrastructure Technoparks as a tool for industry research and production clusters Mathematical model of linear programming for IDPs entrepreneurs [27] A quality system of social service delivery, taking into account the involvement of the private sector [22] Social sector