Mathematical balancing of capabilities in Zara forest park for allocating space and capital to tourism development

Introduction:
In recent decades, mathematical planning methods have been widely applied for optimization of decision-making processes under resource constraint conditions (Filip, 2017). The application of these methods has been emphasized in studies such as the allocation of land to various types of utilization in forest areas (Diaz & Romero, 2002), planning agricultural-forestry plans (de Sousa Xavier, 2015) and assessment of tourism development investment options (Carrillo et al., 2017). The present study applied a multi-objective programming method to optimize the level of investment and land allocation for the development of various types of tourism activities, considering three goals of increasing profit, decreasing erosion rate and increasing employment in Zara Park with an area of 73 hectares in Mazandaran Province.
Materials and methods:
The required information was collected from area maps, relevant organizations and completed questionnaires from 120 visitors.  The scale of erosion for each activity in a special area was determined with the use of affecting criteria from the FAO erosion assessment method and expert opinions for each activity in a special site. Limitations related to the physiological features of the area were considered through the creation of six homogeneous areas for the allocation of sports site, children's park, picnic, forest seeing and conservation. Other information was entered into the model as input data of objective function and constraint. By solving the model in Lingo11 mathematical programming software, a pay-off matrix was first created from separate optimization of goals, in order to assess the degree of conflict between them (Romero et al., 1987). Then, with the use of the weighting method, a series of efficient solutions were obtained. Finally, using the compromise programming method and creating a balance between the goals, the best answer among them was chosen. Agreed solutions were determined based on the preference of the decision makers in the weight of the goals. 
Results and discussion:
According to the results, on the condition of maximizing profits, annual revenue was estimated as 5.6 billion rails, the number of employees is 239 and the erosion rate was approximately 28. With a separate optimization minimizing erosion, the erosion was expected to decrease by 14 units, due to the modification in the area and the state of site assigned to each activity. In this case, a significant reduction of 3.1 billion rails in annual revenue and 19 people in employment can be envisaged. By maximizing the employment rate individually, the annual income was reduced to 3.4 billion. By simultaneously optimizing three goals in a multi-objective optimization approach, an efficient set of solutions was obtained in which the exchange between the goals could be observed. According to the results the change in the level of optimization of an objective affects the extent to which the other goals are achieved. From this set, optimal investment patterns were obtained with the use of a compromise programming method taking into consideration a different combination of objective weighting from the perspective of the three groups of park managers, tourism organizations and environmentalists. Based on these results, changing the weight of the goals significantly changed the amount of area and location allocated to each activity and the level of profitability. In the state of increasing the weight of the goal Profit, based on the preferences of park managers, the annual revenue will become nearer to the park estimation which is equal to 4.6 billion rails per year according to the comprehensive park studies and the sites allocated to each activity is approximately similar to the site expected by tourist’s point of view, as evaluated in the questionnaires. On an equal weighting, based on the preferences of the tourism authorities, although the level of income is lower than the estimated revenue, the other goals in this condition can come closer to their optimal level; ultimately, by considering environmentalist’s preferences, the percentage allocated to each land use changes in favour of the activities which are more compatible with the natural heritage, such as conservation and forest seeing. 
Conclusion:
We face various and often conflicting goals in managing tourism resources, so multi-objective optimization methods integrated with compromise programming approaches which provide the possibility of exchange between the various preferences of managers and stakeholders can be used as an effective tool in facilitating the decision-making process.