“Managing change in nature-based tourism: A decision-making model using linear programming”

In conditions of forced isolation, nature-based tourism meets the needs of safe and comfortable recreation and travel combined with the solution of acute issues of medical treatment and rehabilitation during the pandemic and post-pandemic periods. This study aims to develop a model for decision-making on change management in nature tourism based on the approach of linear economic and mathematical program- ming. The paper formalized changes in the variability of objective function parameters of the model and the system of its restrictions, following the structure of assets of nature-based tourism, balanced by the sustainability principle. The algorithm for implementing the model includes four stages: collection and processing of relevant data on nature-based tourism; considering changes in the objective function and the system of its limitations; linear programming with variability tests using the simplex method; defining ranges/limits in which decisions are made. The initial data are summarized and averaged based on the primary data analysis on the functioning of sanato- riums and other tourist and recreational facilities in Ukraine. Short-term nature-based tourism is considered, the services of which are classified according to the criterion of the primary purpose of travel: “wow-effect” tourism, sports tourism, health tourism, traditional recreation, and green tourism. The results make it possible to substantiate decisions on changes in recreational land areas and human resources, on the limits of changes in income due to the dynamics of service prices, as well as determine the price range while maintaining income structure and sustainability limits for natural and human assets of nature-based tourism. experiencing increasing external influences caused by the effects of climate change, the COVID-19 pandemic, and other challenges For example, in Ukraine, the situation is complicated by external geo-political threats and military confrontation with the aggressor in the east, respectively, unstable macroeconomic situation, including delays in the formation of the market of recreational and tourist services, and low solvency of most people. In addition, the place and role of natural tourism in the economy (The Verkhovna Rada of Ukraine, 1995), particularly the state support and promotion of sustainable forms of tourism, remain not fully regulated at the level of national legislation. On the other hand, the spread of nature tourism as an effective economic activity is inextricably linked to the possibility of infrastructure development in recreational areas


INTRODUCTION 1
The results and conclusions that directly concern Ukraine must be rethought, and they should be reviewed against the background of the full-scale aggression of Russia.
As an area that combines social, economic, environmental, cultural, and other factors, nature tourism is experiencing increasing external influences caused by the effects of climate change, the COVID-19 pandemic, and other challenges (UNWTO, 2021). For example, in Ukraine, the situation is complicated by external geopolitical threats and military confrontation with the aggressor in the east, respectively, unstable macroeconomic situation, including delays in the formation of the market of recreational and tourist services, and low solvency of most people. In addition, the place and role of natural tourism in the economy (The Verkhovna Rada of Ukraine, 1995), particularly the state support and promotion of sustainable forms of tourism, remain not fully regulated at the level of national legislation. On the other hand, the spread of nature tourism as an effective economic activity is inextricably linked to the possibility of infrastructure development in recreational areas

THEORETICAL BACKGROUND
Change management as an "inevitable element for tourism businesses to increase their speed of response to market and competitive changes" is considered within the following limits: the use of administrative, economic, and socio-psychological instruments; transformation of business model and/or business processes; comprehensive understanding of management style (Hristova et al., 2019). Change management is seen in conjunction with changes in tourism policy, namely in creating an enabling environment to adapt to market transformations, as well as supporting small businesses to improve human resources (Pechlaner & Tschurtschenthaler, 2003). This symbiosis of or-ganizational change and state regulation is aimed primarily at increasing productivity in tourism. The search for increased chances of survival and development in the market of tourist services is carried out in terms of the organizational theory of change management (By & Dale, 2008). In particular, such factors as adaptability and flexibility, continuous learning and improvement, are considered. In terms of leadership, hospitality, and communication, the human factor is one of the main ones within the management of changes in tourism organizations (Shulga, 2021).
In contrast to a narrower view within organizational change management theory, a comprehensive view of change management involves focusing more on the impact of changes than on the lead-ing role of the human factor in addressing them (Burnes, 2005). Changes are studied from a transdisciplinary perspective, including philosophical, psychological, biological, institutional, political, cultural, and other aspects (Graetz & Smith, 2010). For example, Liu et al. (2019) examined the relationship between climate, biological, and economic changes by using the example of the impact of climate change on the duration of autumn leaf discoloration and its contemplation by tourists in Japan.
In this case, change management is appropriate in maximizing profits due to the increase in the tourist season due to the delay of autumn leaf coloration.
Climate change is one of the main external factors affecting tourism (Dogru et al., 2019). At the same time, the industry is more sensitive and resilient to climate change than other sectors of the economy. However, in countries with weak economies, tourism is significantly affected by climate change and is unstable to these changes; in developed countries, the opposite is true. In transition economies, one of the factors influencing the recreation and eco-tourism industry includes changes in land use (Shevchenko et al., 2016), in particular, the direct reduction of areas intended for the provision of services to vacationers (Nahuelhual et al., 2014).
Climate changes are negatively affecting the health of the population, which is a prerequisite for transforming tourist flows and destinations, especially for creating an alternative recreational environment for people whose health is at risk due to global warming (Patz et al., 2005). When managing changes in tourism caused by climate change and other external factors, it should be borne in mind that tourism also affects other industries, the environment, and living conditions of residents, etc. Tourism can even lead to conflict situations, for example, due to the alternative use of natural resources and the environment: the lake can be a center of tourist destination and, at the same time, a water area for fishing. An increase in the number of tourists will simultaneously complicate the working conditions of anglers, as well as increase the level of pollution of the coast and water in the lake (Lopes et al., 2017). To maintain the level of accessibility to wild and semi-wild areas with a significant increase in tourist flows, it is necessary to plan tourist visits, taking into account the types of demand and behavior of tourists, as well as natural values, including biodiversity (Csagoly et al., 2017).
Tourism is a factor in bringing communities together to develop a common territory (Jenkins & Romanos, 2014). In a situation where several communities manage shared natural resources, including recreational resources, their joint action should be used to combat climate change and promote sustainable tourism development (Bitsura-Meszaros et al., 2019).
Processes directly related to tourism and recreation (Shevchenko et al., 2020), including sports, can influence social changes (Ladda, 2014). Welfare growth, as well as positive political changes in the country, increase the demand for tourism services and, consequently, stimulate the tourism industry to develop its competitiveness (Henderson, 2015 Using the integer linear programming approach makes it possible to optimize tourist routes (Nadizadeh, 2021; Zhu, 2020), particularly in smart cities (Mangini et al., 2021). In addition, Barrena et al. (2016) use integer linear programming to determine the prospects for the development of eco-tourism taking into account the interests of rural communities using the example of national parks in Spain.
Economic and mathematical programming is used to study cross-sectoral relationships in the field of tourism, such as the "tourism-energy" relationship, including integer linear programming in the study of energy consumption in hotels using the example of the Canary Islands (Meschede, 2020). Belliggiano et al. (2020) examined the sustainability of agritourism, particularly in aspects of its programming, in the transition from a linear to a circular economy. Bukša et al. (2019) apply a linear economic-mathematical model of finding compromises between the port management and, accordingly, the center of maritime tourism and consumers of yachting services, taking into account environmental costs. Finally, Lekić et al. (2018) investigated the model of non-parametric linear programming to determine the potential of the wine industry in order to diversify economic and tourism activities at the regional level using the example of Serbia.
Fedorchenko et al. (2020) investigate regional tourism logistics using the methods of linear and integer programming. Tourism is considered in the sense of integration at the interstate level. Hodžić and Alibegović (2019) use a linear programming approach to evaluate decisions on tourism devel-opment at the regional level using the example of Croatia. Shahraki et al. (2015) used this approach to identify the links between tourism and other sectors of the national economy, such as Iran, to identify the tourism industry's potential to promote macroeconomic development. The combination of linear programming and input-output analysis models makes it possible to explore economic issues related to energy, environmental and social factors and find multifaceted compromise solutions ( Given the above, this study aims to develop a model for decision-making on change management in the field of nature tourism using the example of Ukraine based on the approach of linear economic and mathematical programming. This was done by formalizing the studied changes in the variability of parameters of the model's objective function and the system of its constraints in accordance with the structure of nature tourism assets balanced by the principle of sustainability. The linearization of change management in the field of nature tourism in the context of the need to take into account socio-environmental factors of sustainable development of the transition economy in terms of natural asset management (Boyce, 2001; Martinez-Harms et al., 2018), when the market mechanism is inefficient to direct economic relations in the right direction (Menshikov, 2006), is appropriate and possible given the features of the classical model of economic and mathematical programming (Kantorovich, 1965), as well as its modifications (Danzig & Thapa, 2003), which are summarized as: • linear economic and mathematical programming in the context of descriptive modeling of restrictions on nature tourism management corresponds to the aspects of sustainable development, namely, formalizing restrictions on the use of financial, human, and natural assets, as well as their balance in the application of appropriate mathematical procedures; • target function that maximizes revenues from nature tourism (dual minimization function is not detailed in this paper, as the aim of the study is to determine the variability of the main target function and the corresponding constraints), corresponds to the economic and mathematical content of the above assets, the effective use of which depends on their productivity and the management of relevant changes in the tourism sector; • in the context of developing decision-making mechanisms, in particular within the frame-work of change management in the field of nature-based tourism, the proposed linearization has the following three advantages: "simplicity: arguments based on linear programming are both elementary and transparent; unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design; reach: it provides the ability to solve problems that appear to be beyond the reach of traditional methods "(Vohra, 2011, p. 4).

RESULTS
Based on the above, the rationale for decision-making on change management in nature tourism requires the use of linear economic and mathematical programming as an alternative to the aggregation of many individual environmental, social, financial, and other indicators of this sphere (algorithm in Figure 1). Do the results ensure the dentification of changes in decisionmaking?
Is linearization of change anagement in the field of NBT appropriate?
According to this algorithm, after proving the feasibility of using linear programming as opposed to other approaches and instruments, the first stage of change management begins. The initial data (Table  A1) are summarized and averaged based on primary data analysis on the functioning of sanatoriums and other tourist and recreational facilities in Ukraine and abroad. The conditional example considers short-term tourism (during the weekend), which is in demand in conditions of forced isolation of the population during the COVID-19 pandemic (services are provided at the regional level in Ukraine). Given certain transformations in the recreational needs of the population during the pandemic, it is proposed to generalize the types of nature tourism services into 5 specialized groups (classified by the main goals of tourism), namely: "wow-effect" tourism, sports tourism, health tourism, traditional recreation, and green tourism. Furthermore, to simplify complex iterative calculations, nature tourism destinations are also classified by a limited number of types, namely: "wow-effect" tourism, green tourism and health tourism (depending primarily on the specifics of natural recreational resources within the location of these objects).
During the following stages, in accordance with the formalization of linear economic and mathematical programming, change management (in the context of analysis of the objective function coefficientsformula 1, as well as asset restrictions -formula 2) in the field of nature tourism (within one type of destination) is formulated as: where r(s) -the result of economic activity of the nature-based tourism enterprise, thousand UAH; m i (m e , m m , m s , m t , m g ) -market price of nature tourism services of the first type (thousand UAH/10 people): m e -"wow-effect" tourism (based primarily on the tourist's unique experience related to the environment, such as glamping), m m -health tourism (for example, sanatorium treatment), m s -sports tourism (primarily in sports and training bases located in natural areas), m t -traditional rec-reation (for example, stay in recreation centers in recreational areas in combination with gastro-tourism), m g -green tourism (organized visits to ecosystems: rural, forest, protected wildlife tourism, etc.); ∆m i (∆m e , ∆m m , ∆m s , ∆m t , ∆m g ) -the magnitude of change in prices for nature tourism services of the i-th type, thousand UAH/10 people; s i (s e , s m , s s , s t , s g ) -the number of services of the i-th type provided by an enterprise in the field of nature tourism, units; (S i -the total volume of i-th services, thousand units.); A k -the total value of assets (A N -natural, A H -human, A F -financial) of nature tourism; A N -total area of recreational land suitable for nature tourism services, Ар. a iN (a eN , a mN , a sN , a tN , a gN ) -area of recreational land based on the number of nature tourism services, taking into account the ecological capacity of these lands, according to the source (The Verkhovna Rada of Ukraine, 2003), Ар/10 services; A H -the total number of qualified human resources that can be involved in nature tourism, persons; a iH (a eH , a mH , a sH , a tH , a gH ) -number of qualified human resources, by type of nature tourism, persons/10 services; A F -the total amount of financial investments that can be attracted to the field of nature tourism within one type of tourist destination, thousand UAH. a iF (a eF , a mF , a sF , a tF , a gF ) -financial investments by the i-th type of nature tourism, thousand UAH/10 services. To simplify the calculations and increase the weight of human and natural assets in nature tourism costs, it is assumed that the share of financial investments does not exceed half of the price of service; ∆A k (∆A N , ∆A H , ∆A F ) -the total value of change in the k-th type of assets of nature tourism, respectively: natural, human and financial. Since this example is an approximation for the further development of local small-scale projects in nature tourism, it is assumed that the total financial investment is not a constraint.
The calculations according to the above formulas assume compliance with the rules of filling in the standard table and iterative procedures (Table A2) given by Kantorovich (1965) and Danzig and Thapa (2003).
Changes that occur in the external economic and other environments and have an impact on the field of nature tourism are the object of management through their formalized internalization in the proposed model (formulas 1 and 2), which from an economic and mathematical standpoint (primarily by controlling the change in parameters (∆m i and ∆A k ) to create a basis for making relevant decisions.
Depending on whether the problem of complex accounting of changes (step 2.1) or the problem of model analysis due to changes in a specific parameter (step 2.2) is solved, all possible options for changing model parameters (step 3) are explored. Finally, ranges of change are determined (step 4), within which decisions should be made to optimize the management of nature tourism in a changing environment.
At the beginning of stage 3, according to formulas 1 and 2, the results of basic calculations are obtained (Table 1), which is the basis for testing the variability model. An example of such calculations is given in Table A2:  Table  A2), which means the achievement of the opti-mal value of function r(s * ) and the corresponding set of parameters in the column of basic variables (optimal program for the development of nature tourism).
Therefore, changes in model parameters are analyzed according to the following options: • variability of prices for nature tourism services included/not included in the optimal program of its development; • changes in restrictions on assets for which there is/no reserve within the optimal program of nature tourism development.
This analysis is carried out in more detail on the example of a destination that specializes in "wow-effect" tourism.
2.1. Analysis of the variability of prices for nature tourism services (∆m i ) included in the optimal program of its development The optimal program for the development of nature tourism includes "wow-effect" services and traditional vacationing services (basic variables at Then in Table А2: m m = 6,000 → 6,000 + ∆m m .
The result of iterative analysis (  The variability and limits of price sustainability for traditional recreation services are determined similarly - Table A3. 2.2. Analysis of price variability for nature tourism services (∆mi), which are not included in the optimal program of its development Health, sports, and green tourism services were not included in the optimal program of nature tourism development (free variables at the top of  Table 1 are S m , S s , and S g , respectively). Within the analysis of changes in the coefficients m m = 3,500 UAH, m s = 3,000 UAH, and m g = 1,000 UAH (according to formula 1) relative to the economically permissible limits of these changes, in particular, for the coefficient m m the increase of the objective function is ( The transition m m = 3,500 → 3,500 + ∆m m causes only a change in the coefficient in the row of the objective function in column S m , which is an additional double estimate V m. That is, for 3500+∆m m and the corresponding optimal value V m * = 4.408, there is a change V m ** = 4.408 -∆m m. An additional double estimate explains the disadvantages of providing services: V m * = 4.408 means that the marginal cost of production of health tourism services exceeds its price by 4.408/100 = 440.8 UAH. The optimality of the value of the objective function meets the condition: Similarly, the variability and limits of price stability for sports tourism services are (0 ≤ ∆m s ≤ 3,264.5) and for green tourism (0 ≤ ∆m g ≤ 1,429.4).

Analysis of changes in asset
constraints for which there is a reserve within the optimal program of nature-based tourism development The reserve is for financial assets ( Provided that the initial conditions of investment are preserved (Table 4), that is A F ≤ 1,000, ∆A F ≥ 0: Therefore, the change in financial assets within certain limits does not affect the model's parameters, including the structure of nature-based tourism services. At the same time, the ability to change the size of the financial assets reserve is vital for decision-making.

Analysis of changes in assets'
constraints for which there is no reserve within the optimal program of nature-based tourism development Within the determined limits, the change in the area of recreational lands (as a unified basis of natural tourism assets) does not violate the structure of nature-based tourism services ("wow-effect" tourism destination), but affects the amount of income and number of services by types S e and S t ( Similarly, Table A4 presents variability and limits of sustainability for human resource constraints ("wow-effect" tourism destination), determined by qualification requirements for the provision of quality tourism services, including the level of special education, experience, and hospitality.
The results of economic and mathematical substantiation according to the above algorithm are given in Tables A5-A8 (green tourism destination) and Tables A9-A10 (destination of health and medical tourism). The generalized results of testing the variability of the developed model's parameters presented in Table A11 are an integral completion in forming the basis for change management in the field of nature tourism based on linear programming. Given the approximate nature of the model and the specifics of the field of change management, more important are not absolute, but relative values of indicators and the format of ranges in the resulting table.

CONCLUSION
The study develops a model for decision-making on change management in nature-based tourism using economic and mathematical programming approximated to a linear form to simplify iterative calculations. Using the example of destinations in Ukraine, the model considers short-term tourism services classified according to the criterion of the main goal of travel by type: "wow-effect" tourism, sports tourism, health tourism, traditional recreation, and green tourism. The substance of the changes formalized in the model is determined by the factors of tourist risks and safety, quality of services, and recreational environment, in their socio-economic and natural-ecological context. In particular, the negative value of changes in the parameter of natural assets may reflect an anthropogenic decline in the capacity of the recreational area. Both market and other institutional factors explain the dynamics of restrictions on natural and other assets. When formulating restrictions for the assets of natural tourism destinations two cases are considered: assets for which there are reserves, in particulars, financial ones, and assets for which there are no reserves. The iterative analysis revealed that for all destinations where services are included in the optimal program of nature-based tourism development at the regional level in Ukraine, the limits on human assets have no reserves, which affects the number of services and the income of tourism companies. A change in the amount of financial assets for which there is a reserve does not affect the amount of income. The results of assessing the variability of the model parameters make it possible to analyze and make appropriate decisions on changes in recreational areas and human resources, on the limits of changes in income due to the dynamics of service prices and to determine sustainability limits for restrictions on natural and human assets of nature-based tourist destinations. These results also substantiate adjustments to the relevant legislation, particularly the methodology for calculating the volumes of tourism activities in Ukraine.