Modeling Optimal Time Allocation for Work and Personal Life at The National Level ( Case in Lithuania )

The article deals with the acute phenomenon in the 21st century – the distribution of time for work and personal life. Employed people in the modern society are most frequently faced with problems of work-life conflict. For this reason, this article primarily focuses on determination of optimal time allocation for work and personal life. First, this study analyzes the theoretical aspects of time allocation for work and personal life. Subsequently, a model for optimal time allocation for work and personal life is presented and the research methodology is substantiated. The model is realized by solving the multicriterial (target) optimization problem using weighting coefficients and priority methods and performing sensitivity analysis. This model is composed based on the employed population of Lithuania, but it can be adapted to other countries as well. In this case, the original questionnaire and time diary data should be obtained in the country under investigation. The results of the empirical research carried out showed that the population in Lithuania in 2017 begins to devote more time to personal life compared to 2003. Nevertheless, employed populations do not optimally allocate time between work and private life. For this reason, the article provides recommendations for employed people in Lithuania seeking to balance distribution of time for work and personal life, taking into consideration the current and desired monthly net wages. Indexing terms /


Introduction
Time is a limited economic resource. Not only is it important to control it, but also to rationally distribute between work and personal life. The distribution of time to work and personal life reflects the behavior of the participants in the labor market, their social habits, differences between market participants, etc.; all of which are important in the analysis of the 21st century labor market issues. In today's society, it can be difficult to balance contradictory goals: the need for self-realization at work, the desire to obtain sufficient wages and enough time to devote to personal life. In such case, it may often be difficult to optimally allocate time between work and personal life. Therefore, it is pertinent to investigate the distribution of time within the employed population and to find the optimal balance between the above mentioned controversial goals.
It is worth noting that the employed population usually seeks to find balance between work and personal life. Nonetheless, there is often an inefficient allocation of time between work and personal life. This kind of situation encourages scientists to continue to discuss time allocation with specific recommendations.
It goes without saying that differences in time distribution between the employed population may depend on personal preferences for work and for private life. In an attempt to balance work and private life, a conflict between work and personal life can be encountered, which may have negative consequences for personal health, Research aims: to review the theoretical principles of the time division phenomenon between work and personal life; to ground the methodology used in the research and to provide an optimal model for time allocation for work and personal life; to identify the main aspects of the distribution of time between work and personal life among employed Lithuanians, and to present a concrete empirical study of time distribution and its generalized results.
The research was carried out using comparative analysis of scientific literature, a questionnaire, time diary method, multicriteria (target) optimization, applying weighted coefficients and priority methods, and performing sensitivity analysis.
At the beginning of the article, the theoretical aspects of the phenomenon of time distribution between work and personal life and its modeling are presented. Subsequently, a model for optimizing time distribution and personal life is presented and the methodology used in the study is presented. Finally, the results of the empirical research on the distribution of time for work and personal life and the distribution of wages are presented, which are more comprehensively interpreted and summarized.

Theoretical assumptions for modeling time distribution for work and personal life
Labor-leisure (personal life) modeling describes the behavior of labor supply participants in the labor market, when the time of individuals is divided into two main areas: work and leisure (Fortin et al., 2010;Kabukçuoğlu, Martínez-García, 2016, etc.). In order to correctly understand the theoretical prerequisites of modeling, the basic terms used are explained first.

Working time
In scientific literature is often defined as paid work time (Aguiar, Hurst, 2007;Manski, 2014, etc.), which can be regulated accordingly, depending on the particular country and / or its belonging to the respective unions (Lee et al., 2007).

Leisure time
In scientific literature is understood as the other remaining time, i.e., unpaid work time, including various forms of leisure (Douglas, Morris, 2006;Aguiar, Hurst, 2007;Manski, 2014, etc.). Therefore, leisure time includes time spent with family, for social needs, traveling, sports, etc. (Douglas, Morris, 2006). In this case, the concept of leisure is identified in the broad sense. According to M. Aguiar, E. Hurst (2007), leisure, as a unison of four categories (entertainment, relaxation, social activity, and active leisure), is defined as leisure in the narrow sense. Leisure time can also be understood as the time left from the total time (e.g., the time of day, that is, 24:00 hrs.), minus the time spent on paid and unpaid work (Cavagnoli, 2008).
Another leisure time breakdown is provided by X. Wei et al. (2009). Scientists divide free time into three groups: leisure for learning; necessary leisure time (for relaxation, house work, etc.); nice leisure (for traveling, for fun, for sports, etc.). Another one by O. Hawrylyshyn (1977) who suggests that daytime should be divided into four main areas: biological needs (sleep, personal care); work (paid labor market); productive activities (house work, caring for children, learning); leisure activities (entertainment, recreation). Although there is a wide range of leisure-time interpretations in scientific literature, this research study considers leisure time phenomenon in the context of the labor-leisure (personal life) model in the broad sense.
Thus, the time of day can be divided into time spent for work and personal life as indicated by E. J. Douglas, R. J. Morris (2006), G. Yaniv (2011), S. E. Forris (2015) and other authors. Such division of the time of day into two main parts: the time spent on work and personal life is chosen for the research to be presented in the article. Thus, time spent on personal life is understood as the time allocated to all activities, except for paid work. In this case, the concept of time spent on personal life is identical to the interpretation of leisure time in the broad sense.
Having reviewed the main concepts, it is expedient to introduce more widely the model of labor-leisure (personal life) and related aspects. It should be emphasized that in the context of this model leisure is understood in the broad sense and the concept of personal life can be used as a synonym.
The basic idea of the labor-leisure (personal life) model relates to the rational individual's desire to maximize the benefits in choosing two products: work and consumption (Sendi, Brouwer, 2004;Myck, Reed, 2006;Dagsvik et al. 2012;Manski, 2014, etc.). In this case, an employed person seeks to choose the best possible time allocation option between work and leisure time (personal life).
The labor-leisure (personal life) model is based on budget, time, and environmental constraints. The budget constraint identifies person's financial capabilities, where two types of income -work and non-work related income can be obtained (Becker, 1965). This condition in the labor-leisure (personal life) model is important because a person, taking into account available and desired income, can make appropriate decisions regarding the allocation of time for work and personal life.
It should be emphasized that not only the budget but also the time is limited. The time constraint defines the aspect of time constraints, where time can be appropriately allocated to two main areas -work and other nonwork-related activities (personal life; Becker, 1965). All of this is important in the labor-leisure (personal life) model, as employed people who do not allocate time between work and private life optimally, experience a conflict of work / personal life. This phenomenon can be named as negative. According to the International Labor Office (2011), the conflict between work and personal life has a negative impact on personal career, work quality, employee health, personal relationships, etc. Additionally, S. H. Laeeque (2014), investigating the case of the Pakistan banking sector, also finds that conflict between work and personal life negatively affects person's productivity and personal career opportunities.
The environmental constraint refers to the production of economical / non-economic goods based on knowledge, skills, physical and mental skills (e.g., housekeeping, childcare, etc.; Staudigel, 2012). In other words, dedicating time to one good, sleeping for example, affects the functioning of the other goods, for example, work. Understandably, sleep time will often depend on personal preferences. Consequently, the need to restrict environmental conditions in the labor-leisure (personal life) model is based on the person's ability to distribute time between work and personal life, taking into account personal, physical, and mental capabilities. Another extreme is those who prefer work (workaholics), who are addicted to work and spend many hours at work, do their best to achieve the best results, yet experiencing the negative consequences of workaholism, namely in personal life: physical and psychological health problems (Yaniv, 2011;Bakker et al., 2013, etc.)   Despite these facts, time use research is meaningful as it provides detailed information about: individuals' behavior at the national and international levels; work-life balance; the influence of time allocation on employed inhabitants' work and personal life; the influence of time allocation on person's health; the influence of time allocation on wages; the influence on time differences between genders; and other valuable information. Therefore, the research analysis of time allocation research is extensive, and scientists can provide useful information for the employed population by developing and further discussing the distribution of time for work and personal life.
In summary, it is possible to claim that the main theoretical aspects of time division between work and personal life are revealed by analyzing labor-leisure (personal life) modeling, its formation assumptions, budget, time, and environmental constraints.
This article follows the notion that the model of labor-leisure (personal life) describes the behavior of a rational subject when time is allocated to work and leisure (for personal life). Differences in time distribution between the employed population may result in personal preference. Individuals who give priority to private life and those who give priority to work (workaholics) are named as extremes. It is considered that one of the most acceptable options in the context of time distribution is individuals who seek to balance work and private life.
Although research on time distribution is relevant and useful, the lack of the theoretical and empirical analysis of time distribution has been identified. This situation encourages further analysis of time allocation, providing new practical insights and recommendations for the employed in the context of time allocation.

Presentation of the optimal time allocation for work and personal life model and the methodology of empirical research carried out
The purpose of the empirical study is to review time distribution of the employed population in Lithuania in 2017, determining the optimal distribution of time for work and personal life among employed Lithuanians.
The logic of the research is based on R. Kumar (2011), an eight-step model. The questionnaires and time diary method (the questionnaire and the time diary were compiled on the basis of Eurostat (2009) methodological recommendations for the implementation of the HETUS survey) were used for collecting the primary data: 1) the purpose for using an individual questionnaire -is to find out the respondent's type, the main needs, the current and desired wages, general information about the respondent; 2) the purpose of using time diary -is to find out how long the respondent (employed person) devotes to eight time allocation areas. The time diary was being completed for two days: during one work day and one free from work day. The diary of time has been structured so that respondents should indicate the time allocated to eight time distribution areas: sleep; other physiological needs; work; study; house work and childcare; leisure time (in the narrow sense); travel; and other activities. This time distribution model has been selected based on the public data available from the HETUS (2007)  The research sample -is 406 respondents, with a sample error of 4.9 percent. The research sample was conducted according to the following four criteria: gender, age, type of person, place of residence. The distribution of respondents by personal type is related to the size of the salary, and this is related to the employee's productivity. In order to objectively determine this distribution, based on the data of the Statistics Lithuania (2016b) of the Republic of Lithuania (more recent statistical data were not available at the time of the survey), three adjusted salary intervals were established. These wage ranges are based on the following assumptions: (1) individuals who give priority to their personal lives receive relatively low incomes (Cuff, 2000); (2) persons seeking to balance work and private life, earn an average wage; (3) those who give priority to work receive the highest wages (Hammermesh, Slemrod, 2005).
The distribution of the survey sample in relation to gender, age and place of residence (county) was established taking into account the data of the Department of Statistics of the Republic of Lithuania (2016b; more recent statistical data were not available at the time of the study). Criterion, quota, random, "snowball" sampling methods were used for respondents in the primary data collection process.
It is assumed that the population of the employed population is fully described by the three types of employed population (the ranking of individual types is presented at random): The first type -individuals who prioritize personal life. These individuals are defined as employed people who relatively more time per day spend on seven activities that are not related to work: sleep, other physiological needs, house work and childcare, leisure activities (in the narrow sense), study, travel, or other activities.
The second type -individuals who seek to balance work and private life. These employed people coordinate time devoted to eight areas of time allocation to avoid work-life conflict.
The third type -individuals who prioritize work (workaholics). These individuals are understood as employed people who relatively allocate the most of the time to work, compared with other areas of life.
The primary data collection process was carried out in Lithuania from January 3 to March 5 in 2017. 10 counties of Lithuania, 15 cities, and 5 villages participated in this research.

Mathematical model
A mathematical model is developed to determine time distribution optimization of employed population in Lithuania based on the data collected by individuals seeking to balance work and private life. Persons who give priority to their personal lives and those who give priority to work (workaholics) are defined as exceptions in the research population.
The mathematical model consists of eight variables indicating how the time is allocated to the appropriate time distribution domain (per day, in minutes): x1-is the time for sleep; x2 -is time for other physiological needs; x3 -is time for work; x4 -is time for study; x5 -is time for house work and childcare; x6 -is time for leisure (in the narrow sense); x7 -is time for travel; x8 -is time for other activities.
The used model is realized in two cases depending on the person's current / desired monthly net wage. In this research presented in the paper, the current net monthly wage is understood as the net monthly wage earned at that moment. The desired net monthly wage is defined as the net monthly wage, which would fully satisfy the basic needs of the individual in relation to the primary eight time allocation areas. Primary statistics were obtained from a survey questionnaire.
Eight goals and limitations are formulated based on the analysis of scientific literature, economics, mathematical logic, and social experience. In the multicriterion optimization task, individuals who seek to balance work and private life have the following goals: to maximize sleep, work, house work and childcare, and leisure time (in the narrow sense), and to minimize time allocated for other physiological needs, study, travel, and other activities. Restrictions on all time allocation areas, except time spent on work, are associated with the minimum and maximum time allocation, data derived from time diaries. Work target limitation is defined as the minimum / maximum value (in euros) of the current / desired monthly net wage for the most commonly chosen range. The limitation of the work target is expressed mathematically in such a way that the inequalities are aligned with the logical, economic, and mathematical meanings.
In the mathematical model, the target weights are determined according to the order of satisfaction indicated by respondents of the person's type concerned (indicated in the questionnaire survey). Also, based on mathematical logic and social experience, it is assumed that each of the above priorities is twice as important as before.
The order of priority satisfaction in the mathematical model is determined on the basis of the questionnaire results. In all cases, it is assumed that the target related to time devoted to other activities is the lowest priority. Only if the target(s) of the above priority has been implemented can the following objective(s) be realized. when 3 ≤ 720, 2 + 4 + 5 + 6 + 7 + 8 = 480, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 1440, ≥ 0, = 1,8 ̅̅̅̅ , Here: Z -function of minimization of deviations from the corresponding targets; -target weights when = 1, ̅̅̅̅̅ ; −a deviation that measures how much is missing towards the goal, − ≥ 0; +deviation, which measures how far the target is exceeding, + ≥ 0; Twenty four hours time constraints -the total time of all allocation areas in a day can not exceed 1440 minutes per twenty four hours (see formula 7). Also, the time spent per day must be non-negative for the appropriate time allocation (see formula 8).
Deviations -a deviation measuring how much a target is exceeded must not be greater than the difference between the maximum and the minimum value for the time domain in question (see formula 9). The deviation measuring how much is missing to the target must be non-negative (see formula 10).
Thus, in this article, based on the eight goals set forth, a time-optimization model is presented estimating the current / desired monthly net wage. This model is suitable for individuals who seek to balance work and private life.

Summary of the empirical study results of optimal time allocation for work and personal life
In this part of the article, the results of general distribution of work time and personal life of employed Lithuanians are presented first. It is followed by an overview of the distribution of the current and desired wages of employed Lithuanians among different types of persons. Finally, a mathematical model is implemented and the optimal time allocation between work and personal life among employed Lithuanians is identified, taking into account the size of the current / desired salary. Based on the results of the research, recommendations are made for the employed Lithuanians seeking to balance work and private life.
Actual data on the time distribution of employed population. Reviewing time allocation data of the employed Lithuanians in 2017, it was found that on average 75.3 percent of employed persons spend time on private life, and 24.7 percent of time to work (see Figure 1).

Distribution of the current and desired wages of the employed population.
In 2017, employed people in total (29.6 percent) and by gender (30.2 percent for men, 29.0 percent for women), had the current net monthly wage fall usually in the range of [419; 519] euros (see Table 1). Note: the first type persons -individuals who prioritize personal life; the second type persons -individuals who seek to balance work and private life; the third type persons -individuals who give priority to work (workaholics). There may be minimum error in column sum due to action of rounding.
The difference between men and women in the most commonly received monthly net wage is relatively small, i.e., 0.8 percentage points (see Table 1). Thus, it can be argued that there is no discrimination in this case.
Considering the distribution of the current net monthly wage, rational differences are observed. It can be assumed that the existing differences in the net wages of the current month between employed persons in Lithuania by type of person may be based on differences between the time spent on work and the productivity of work. However, in order to obtain more precise conclusions, a more detailed study should be conducted.
The prevailing desired net monthly wage among employed people in Lithuania is observed in all cases (in general, by gender, by type of person), which falls into the interval of [875; 2090] euros (see Table 1). It should be emphasized that in all cases (in general, by gender, by type of person) the current net monthly wage is lower than the desired net monthly wage. Relatively smallest gap between the current net monthly earnings and the desired net monthly earnings is between workaholics, and the biggest gap among the persons who prioritize personal life. It may be assumed that there should be a rational difference between the current and the desired net monthly wage, so that there is a possibility for a person to receive the corresponding desirable wage in the labor market. One of the further directions of research could be related to the identification of the rational difference between the current monthly net wage and the desirable monthly net wage.
Consequently, taking into account the existing difference between the current and the desired net monthly wages of the employed population, it became clear that the current net monthly wage does not meet the needs. It shows one of the existing problems in the Lithuanian labor market, with the possible consequences such as: increased emigration of the working-age population; involvement in the shadow market; increased social problems; dissatisfaction with political decisions, etc. Another possible further research direction could be related to the identification of needs that can not be met by employed people occupants due to the existing

Interval of wage
The current net monthly wage The desired net monthly wage Employed persons difference between the current and the desired monthly net wages. Upon identification of the main unsatisfactory needs, a project / plan could be developed to enable the Government of the Republic of Lithuania to contribute to improving the satisfaction of relevant needs (e.g., subsidizing relevant areas, promoting various campaigns, etc.).
Summing up the distribution of wages of the employed population in Lithuania, one can conclude that there is a rational differentiation between types of persons. Persons who prioritize private life receive relatively the smallest net monthly salary, and those who give priority to work receive the highest net monthly earnings. Furthermore, it became clear that there is a difference between the current and the desired monthly net wages in general, by gender and by type of person. It is likely that the search to find a solution(s) to this problem, and ultimately seeking to reduce the manifestation of this problem, would contribute to the increase in the welfare of the employed population, households and the state, improving the situation in the Lithuanian labor market.
The optimal time allocation to work and personal life by employed Lithuanians. This part of the article presents a mathematical model based on primary data, which is realized in two cases, taking into account the current / desired net monthly wage. Later the identified optimal time allocation for work and personal life is compared to actual data, a sensitivity analysis is performed and recommendations of a corresponding nature are presented.
Using the Microsoft Excel Solver tool, a mathematical model is implemented and the optimal solution is determined = (540; 47; 420; 0; 363; 63; 7; 0). In this case, 17:00 hours a day should be devoted to personal life and 07:00 hours for work, and the person should earn € 529.20 a month (see Figure 2). ). These differences may be affected by differences in hourly wage rates, non-compliance with the recommendations (or lack of information) due to the time available for sleep, the traditional work-rest cycle, etc.

Optimization model for time allocation for work and personal life, taking into account the person's desired monthly net wage
The mathematical model constraints are the same as in the first case (see formulas 12-13, 15- It should be emphasized that in this case there is no optimal solution (the sleep goal is not fulfilled). This suggests that employed Lithuanians are likely to want excessive monthly net wages. In this regard, a model is implemented where the desired net monthly wage falls within the range [617; 874] euros (second option based on frequency, see Table 1). Consequently, 25-27 restrictions are abandoned and, in addition, the following working time constraints are included in the model (see formulas [28][29]: 3 + ≤ 203,97. In this case, the optimal solution = (470; 47; 489,68; 0; 363; 63; 7; 0). Compared to the first case, the results of this study change the ratio of work to personal life: the work should be given at 08:10 hours, personal life -15:50 hours, and the person should earn 617 euros per month (see Figure 3). Therefore, sleep should be given (daily) at 07:50 hours, for other physiological needs -at 00:47 hours, for work -at 08:10 hours, house work and childcare -06:03 hours, for leisure time (in the narrow sense) -01:03 hours, travel -00:07 hours (see Figure 3). There would be no time for study and other activities.
When comparing the results of the second realized model with the first time optimization, the main difference is between work and sleep time (see Fig. 2   2. An overview of the time distribution research, it has been identified that research on this topic is important and relevant in the 21st century. On the other hand, the limitations of the theoretical and empirical nature of the analysis of time distribution is emphasized, especially in the case of Lithuania. This justifies the importance of the paper presented in the study because it provides theoretical insights and the results of the empirical study that complement the research insights and encourage further discussions in the field of time allocation. 3. The methodological part of the article presents a model for optimal time allocation for work and personal life and a research methodology. The population of the survey is employed persons in Lithuania. Primary data were collected using questionnaire and time diary techniques. The model for optimal time allocation for work and personal life has been compiled through multicriteria (targeted) optimization, using weighted coefficients and priority methods and performing sensitivity analysis. ). The second implementation of the mathematical model, which took into account the desired net monthly wage of the employed population, suggests that the employed people in Lithuania want a too high monthly net wage. On the other hand, it has been established that for employed persons in Lithuania seeking optimal distribution of time between work and private life and obtaining the desired net monthly salary, falling into the interval [617; 874] euro, more time is needed for work and less for sleep than within the first realized mathematical model. 6. The study could be continued by improving or using the same research methodology at other national levels.
The main aspects of research continuity could be related to the implementation of a similar study using statistics from another country. The study could also be continued on a Lithuanian scale. In this way, the most recent data of identifiable behavior of employed Lithuanians could be obtained and changes traced.