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2DETERMINATION OF OPTIMAL STRATEGIES IN UNCERTAINTY CONDITIONS BASED ON A RANDOMIZED MULTI-CRITERIA EVALUATION OF ORGANIZATION'S FOREIGN TRADE ACTIVITY EFFECTIVENESS
Abstract
The article defines optimal strategies in uncertainty conditions based on a randomized multi-criteria evaluation of the foreign trade activity efficiency, which the current situation in international trade requires. This situation forces its participants to look for new methods of the foreign trade efficiency analyzing. The search led to the necessary consideration of randomized criteria that allow to perform multicriteria evaluation of foreign trade optimal strategies. One such criterion is the Hurwitz criterion, the structure its many optimal variants is determined by the optimism level indicator of the decision maker. That makes it possible to choose an effective foreign trade strategy even in cases when the world market is not in the most favorable or, on the contrary, extremely unfavorable condition. The property of leveling the Wald criterion extreme pessimism and the maximax criterion extreme optimism in choosing the optimal strategy from the set of available alternatives allows applying the Hurwitz criterion in the practice of analyzing the efficiency of the organization's foreign trade activity.
Keywords
efficiency, foreign trade activity, Wald criterion, Hurwitz criterion, maximax criterion, uncertainty, Markov chain, analysis system, multicriteria, probabilistic model, economic and mathematical modeling
AUTHOR
Olga Martyanova
PhD, Oryol State University of Economy and Trade, Oryol, 12 Oktyabr'skaya Str., Oryol, 302028, Russia.
E-mail: 1263m@mail.ru
Introduction
In his message to the Federal Assembly President set a task to achieve by 20192020 "... the pace of economic growth above the world indices ...", which means "... improvement of Russia's position in the global economy ..." (Putin, 2016) despite the growth of protectionism, which is one of the main problems of world trade today. According to the President of the Russian Federation, a new level of efficiency for domestic organizations will be ensured by strong international competition, which, in its turn, will improve the Russian economy.
We can not disagree with this opinion, since the new level of organization development, and therefore of the economy as a whole, is determined by the quality of the goods sold, the competence of the staff, its labour productivity, its own developments, which improves the organization's efficiency not only in the home market, but also in the international one. A powerful factor for the accumulation of scientifically based reserve, necessary for the growth of the economic efficiency of organization's foreign trade activity (hereinafter referred to as FTA), should be the
45 Modern European Researches No 3 / 2017 criteria for its analysis. The task is not only to evaluate and forecast future trends in the world market, but also to choose the optimal solution that provides to the organization competitive advantages in a particular segment of foreign trade.
The importance of the criteria for analyzing an economic entity's foreign economic activity efficiency is especially growing in the current situation, when trade barriers are being built, external restrictions are growing, access to financial resources is decreasing due to the rise in domestic borrowing costs, which does not contribute either to maintaining the business activity of the FTA member organization or implementing of foreign trade projects with foreign partners. In situation when Russia faces serious economic challenges, resists the unfavorable market conditions and the imposed sanctions, it is relevant for business what criteria will be chosen by the organizations to evaluate the effectiveness of their functioning in the world market, because the activity of each economic entity creates the foundation of the national economy.
Methodological Framework
The analysis of the theoretical base on the problem under consideration made it possible to reveal only a small number of works devoted to the methodological aspects of determining the values of weight coefficients that directly affect not only the formation of a single optimization model, but also the choice of an appropriate solution as the optimal one. We believe that the existing methods and approaches to the procedure of optimizing solutions within the chosen criterion require adaptation to the changing conditions of the business environment, including the sphere of foreign trade. The inadequate studying and significance of this problem determined the direction of the research.
In the work (Martyanova 2016) the author suggests "... in predicting the effectiveness of the entity's financial strategy ..." in terms of foreign trade sphere uncertainties use Wald, Savage, maximax, Hurwitz, Laplace criteria of the expected value the characteristics of which are summarized in Table 1. The criteria allow you to choose the best solution by analyzing each of the options in terms of the advantages and disadvantages that their implementation can bring.
TABLE 1. CRITERIA FOR MAKING A DECISION UNDER CONDITIONS OF UNCERTAINTY
Criteria name Criteria content Solutions The criterion formula
1 2 3 4
The criterion of the expected value (EV) (Melnik, Berdnikov 2011) The choice of the solution by considering the possible results by the degree of their probability High value of this parameter, if profit or income is analyzed, otherwise - the lowest if costs are estimated N EV = Y^Pt x i = 1 Where pi - the probability of i- outcome, x-- the value of i- outcome.
Maximax criterion (Sadchikov, 2003) Maximizing the maximum income The best option for the situation outcome with respect to each alternative Rkm = max max Эij i J
Criterion of minimax risk (Savage criterion) (Sadchikov, 2003; Brodetsky, 2010) Ensuring minimization of the maximum possible losses The worst results of each alternative among the risk matrix Rks = min max rij i J Where rn - the risk, iJ defined as follows: ru = max Э■■ - Э■■where iJ i iJ iJ max Э.. - the maximum i J possible gain in the i-variant, Э■■- the nominal value of iJ the effect.
The maximin criterion (The Wald criterion) (Sadchikov, 2003; Brodetsky, 2010) Ensuring maximization of the minimum income The worst results of each alternative Rkw = maxmin i J
Criterion of the generalized maximin (Hurwitz criterion) (Sadchikov, 2003) Ensuring balance between optimistic and pessimistic options The averaged value between optimistic and pessimistic options Rkw = maxmin i J + (1 - a)max Э■^ j ] Where 0 <a< 1
The Laplace criterion (Sadchikov, 2003) Ensuring optimal strategy, taking into account the probability of outcome state The best variant of outcome, taking into account the probability state of analyzed alternatives N ycp = max^ x pp j = 1 Where ^ = 1p;. = 1
To substantiate decisions in conditions of uncertainty, the author (Brodetsky, 2010) suggests to apply modifications of traditionally used criteria that will allow the decision maker (hereinafter - DM) to use utilities matrix format more efficiently, adapting it to the specific features of the optimization problem, business peculiarities and preferences of DM. However, modifications require from DM the capability to formalize the task in order to provide, in conditions of uncertainty, the choice of such an alternative solution that would best meet its requirements. Today there exist special modifications of Hurwitz (Brodetsky, 2010), Germeier (Brodetsky, 2010), products (Brodetsky, 2010), ideal point (Brodetsky, 2010) criteria.
Approaches to solving the problem
In our opinion the modified criteria have not found wide application due to their laboriousness and the proximity of the obtained results to the outcome of the classical criteria implementation for decision-making under conditions of uncertainty. Therefore, we believe that in the current conditions the organization considering the system of its foreign trade policy analyzing dictated by its long-term interests and world development
47 Modern European Researches No 3 / 2017 trends, should not only develop new criteria but use the previously uncovered possibilities of known criteria in decision-making under uncertainty conditions, one of which is Hurwitz criterion.
Hurwitz criterion represents a compromise between maximax optimistic rule and extreme pessimistic maximin rule or Wald criterion (Sadchikov, 2003), so the efficiency strategy index according to this criterion is the following:
GprSa) = (Mk ~Vk)X a + Vk' k = 1.....f
(1)
Where G - efficiency strategy index D. according to Hurwitz criterion regarding the
prk K
winnings;
Dk - index of optimism chosen by the DM arbitrarily, based on his subjective ideas about the conditions, purpose and complexity of the problem being solved; Mk - index of strategy effectiveness Dk according to maksimax criterion;
Vk - index of strategy effectiveness Dk according to Wald criterion.
Since the Hurwitz criterion recommends some average solution under uncertainty conditions, its value consists in leveling the extreme optimism of the maximax criterion and the extreme pessimism of the Wald criterion. Leveling property of Hurwitz criterion for fixed optimism index a e (0.1) is the presence of the optimal strategy in a number of pure strategies according to this criterion and which is not optimal either by Wald criterion, nor by maksimax criterion (Labsker 2016).
It should be noted that with the optimism index a=0, Hurwitz criterion is transformed into Wald criterion, and with a=1 it is transformed into maximax criterion, hence, the leveling effect is absent for these values of the optimism index. Therefore, it is possible to obtain a smooth solution by the Hurwitz criterion only for values of the optimism index in the range a e (0.1). Thus, it can be concluded that the effect of leveling is not always possible. Formalization of all of the above mentioned makes it possible to form the structure of many optimal strategies according to Hurwitz criterion depending on the values of optimism index, which has the following form:
F
opt _
Jpr(a)
K') KT'
K' ) I
W)
M
optypt
v ) M opt
U
rat
with with with with with
a = 0 0 < a < a a = a , a < a <1 a = 1
(2)
where FG°pt - the set optimal strategies by Hurwitz criterion depending on the
pr(a)
optimism index values a;
F°ipt- a set of optimal strategies by Wald criterion;
7opt)°Pt M
strategies by Wald criterion ;
7opt)opt V
strategies by the maximax criterion;
^ - a set of strategies optimal by maximax criterion in a set of optimal ?gies by Wald criterion ;
(FÏ) P - a set of strategies optimal by the Wald criterion in the set of optimal
F0^ - a set of optimal strategies by the maximax criterion;
« =( v pt " ^ï'Vii V pt - V;) + (MF° pt - Vp)) (3)
VFopt = max(Vk) - optimal solution by Wald criterion;
Vk = minfakl:k = l,...,t;l = l,...,r) - an index of the strategy effectiveness Ck according to Wald criterion;
эkl - the effect of k- version alternative strategy with l-state of foreign economic environment;
V^t = max{vk:Ck E F°JPt] - the maximum possible minimum profit by Wald criterion in the set of optimal strategies by maximax criterion;
MF°pt = m ax(M k) - the optimal solution by maximax criterion;
Mk = max^kl:k = l,..., t; l = 1,.,r) - an index of the strategy effectiveness Ckby maximax criterion;
Mp°pt = max{Mk:Ck E F°^pt] - maximum possible maximum profit by maximax criterion in a set of optimal strategies by Wald criterion.
Results
For the analysis of the organization practice using Hurwitz criterion may be applied the statement according to which for each strategy Ck not optimal either by Wald criterion, or by maksimax criterion the following inequality is valid (Labsker 2016):
Vk x (mpopt - MF°pt) + Mk x (VF°pt - Vp°pt) < VF°pt x MF°pt - VF°vt x Mp°pt. (4)
The analysis of inequality (4) shows that it is logically connected with system (2). Thus, if there is a strategy to which (4) becomes an equality, then Hurwitz criterion has the property of leveling only with a value of optimism index a.. And the strategy which
is not optimal neither by Wald, nor by maximax criterion, will be optimal by Hurwitz criterion. A further study (4) allows us to conclude that for a strategy in which the left side of inequality (4) exceeds its right-hand side, Hurwitz criterion preserves the leveling property for undetermined values of the optimism index.
We believe that Hurwitz criterion being by its nature the criterion of optimism-pessimism is expedient for using in analyzing the efficiency of organizations foreign trade activity, since it gives the DM a criterial tool that allows to take a compromise solution in the world market uncertainty conditions, understand deeper a complex foreign trade problem, evaluating each possible way of its solutions from various points of view, and, ultimately, to adopt an adequate solution that ensures the competitive advantage for the organization on the world stage.
At the current stage, the situation in the sphere of foreign trade is such that DM who does not have at his disposal the criterion for organization's corresponding segment of activities evaluation is unable to make an adequate decision that contributes to the efficiency increase in the economic entity's functioning both on domestic and international markets. The importance of Hurwitz criterion in evaluating the organization's FTA is that it enables the DM, who is neither optimist nor pessimist, to take the only optimal decision with the optimism index chosen by him, thereby determining the effectiveness of the foreign trade strategy chosen by the organization for positioning on world market. Therefore, we believe that this criterion should be one of the analysis system elements that the organization uses to evaluate the effectiveness of its FTA.
Discussion
We will present a practical implementation of the procedure for analyzing of the foreign trade strategy effectiveness developed by the organization in order to expand the scope of positioning its beer series with an unusual premium recipe for abroad. The information base for the studies are the data of production organization management reporting that supplies premium beer for export. Due to the change in the overall economic situation, accompanied by temporary reduction in beer business, the organization decided to open beer restaurants in several countries where visitors will be offered premium category beer from the manufacturer's brand portfolio. The organization was inspired by the experience of Spain, where beer sales broke all records thanks to the restoration of restaurant sector. Only in 2016, beer consumption in the country increased by 4% compared to last year and reached 39 million hectoliters (Spain: Beer sales hit record thanks to the restoration of the restaurant business, 2016). That became possible thanks to stabilization of Spanish economy and the increase of tourists' number in the kingdom.
The development of its own beer restaurants network will allow the organization to improve its position in the international market. That plays an important role in negotiations with other restaurateurs and gives an advantage in the dialogue with foreign suppliers. In our opinion, beer consumption in pubs and bars is a barometer not only of the restaurant business state, but of the economy as a whole, because beer is the first item on which consumers start to save and it is from it that the return of life to its normal course begins.
Since at the initial stage the organization decided to use the leased space, it was offered premises of 100, 150, 200, 250, 300 square meters. Under the terms of the premises lease, the organization will bear the costs listed in table 2. The income of the organization from beer restaurant should be 601 euros per day.
The organization needs to decide on the area of the premises, which it is advisable to lease for the implementation of its foreign trade project.
TABLE 2. SUMMARY OF COSTS FOR RENTING PREMISES
Parameter Amount
Expenses, including:
- not dependent on the choice of the city 12 000,00
A) licensing 1 000,00
B) the maintenance of the adjacent territory 150.00
C) routine maintenance of premises 10 000.00
D) security post 850.00
D) advertising 1 150.00
- determined by the area of the leased premises 11 180,00
A) insurance of restaurant property, liability to third parties 2 300,00
B) furniture for visitors 5 400,00
C) equipment for a beer bar in the hall 2 500,00
D) the maintenance of one hall (communal, operational costs) 360.00
E) one waiter 270.00
E) one barman 350.00
- depending on the number of visitors 53.00
A) laundry 7.00
B) cleaning 6.00
C) dry cleaning of furniture 40.00
In our opinion, it should be considered that in order to find the optimal solution it is expedient to use the Hurwitz criterion. Then, in the framework of the set task formalization the area of the premises which the organization plans to lease (sk), will be
as follows:
Sk = 50 x (k + 1), k = 1,2,3,4,5. (5)
Expression (5) assumes that the size of the leased area can only be an integer not exceeding 300. The period under investigation is a statistical month equal to 30 days.
The organization's month expenses for the foreign trade project may be expedient to calculate by the formula
Rkl = 11180 x Sk + 53 x 30 x zkl + 12000 =
= 559000 x k + 1590 x zkl + 12050, (6)
where zkl = min[Sk, n} I = 1,2,3,4,5,6,7,8,
zkl = min[Sk, nj, I = 1,2,3,4,5,6,7,8,
n{ - the area of the beer restaurant, occupied by visitors per month, the values of which are presented in Table 3.
TABLE 3. AREA OF THE BEER RESTAURANT OCCUPIED BY VISITORS PER MONTH
Parameter Number of visitors Area Value
Beer restaurant area occupied by visitors per month(nl), at People Sq. meters
I = 1 13 50
I = 2 18 70
I = 3 20 80
I = 4 25 100
I = 5 38 150
I = 6 50 200
I = 7 63 250
I = 8 75 300
Income of the organization per month (Pkl) is determined by the formula
Pkl = 601 x 30 x zkl = 18030,00 x zkl (7)
In the uncertain situation on the international market analysis of the organization's foreign trade activities efficiency may be appropriate to examine from the viewpoint of this business segment profitability. This is due to the fact that "the efficiency of the enterprise is characterized, above all, by the presence of profit. The more profit per
51 Modern European Researches No 3 / 2017 unit of used resources it has, the more efficiently the company operates" (2009). Therefore, the organization views as winning the received profits from foreign trade project in the analyzed period ^kl) which can be defined as
эkt = Pkt - Rkl = 16440,00 x zkt - 559000,00 x k- 12050. (8)
Using formula (8), we calculate winnings ^kl). On the basis of which we form the billing matrix (Table 4), where Bk is the foreign project option when rentable area is B1
= 100, B 2 = 150, B 3 = 200, B4 = 250, B 5 = 300 square meters.
We choose the optimal solution on the basis of Wald and maximax criteria and form the table 5.
TABLE 4. BILLING MATRIX
B k\ ni n2 n3 n4 ns n6 n7 n8
B1 250950 579750 744150 1072950 1072950 1072950 1072950 1072950
B2 (308050) 20750 185150 513950 1335950 1335950 1335950 1335950
B3 (867050) (538250) (373850) (45050) 776950 1598950 1598950 1598950
B4 (1426050) (1097250) (932850) (604050) 217950 039950 1861950 1861950
B5 (1985050) (1656250) (1491850) (1163050) (341050) 480950 1302950 2124950
TABLE 5. SELECTION OF EFFECTIVE SOLUTIONS USING OPTIMIZATION CRITERIA
^^^^ Bk B1 B2 B3 B4 B5
ni ^^^^
ni 250 950 (308 050) (867 050) (1 426 050) (1 985 050)
n2 579 750 20 750 (538 250) (1 097 250) (1 656 250)
n3 744 150 185 150 (373 850) (932 850) (1 491 850)
U4 1 072 950 513 950 (45 050) (604 050) (1 163 050)
n5 1 072 950 1 335 950 776 950 217 950 (341 050)
n6 1 072 950 1 335 950 1 598 950 1 039 950 480 950
n7 1 072 950 1 335 950 1 598 950 1 861 950 1 302 950
n8 1 072 950 1 335 950 1 598 950 1 861 950 2 124 950
Indexes of the foreign trade strategy efficiency by the criteria:
Wald:
Vk 250 950 (308 050) (867,050) (1,426,050) (1 985 050)
VFopt 250 950
VFM0pt (1 985 050)
maksimax:
Mk 1 072 950 1 335 950 1 598 950 1 861 950 2 124 950
MF0Pt 2 124 950
MFVopt 1 072 950
According to our calculations, the results of which are shown in Table 5, the optimal by Wald criterion is the foreign trade strategy version Bi, while by maximax criterion the greatest possible profit organization can receive by selecting the foreign trade strategy version B5. Since foreign trade strategy versions B2, B3, B4 do not belong
52 Modern European Researches No 3 / 2017
to the set of optimal strategies either by maximax criterion F0^ or by Wald criterion
F°,pt, then the validity of inequality (4) should be checked only for them. Using the data
of Table 5 we calculate values of the left and right sides of the inequality (4) for foreign strategy versions B2, B3, B4 presenting obtained results in Table 6.
Analysis of the calculation, the results of which are summarized in Table 6, show that for foreign trade strategy versions B2, B3, B4 inequality (4) is not satisfied, because
it becomes an equality for them. Then Hurwitz criterion has leveling property only with the index a = a which value according to expression (3) will be
' 250950 - ( - 1985050)
a = (250950 - ( - 1985050)) + (2124950 - 1072950) = 0,68
Thus, with optimism index equal to 0.68, foreign strategy versions B2, B3,B4 are optimal by Hurwitz criterion.
TABLE 6. EVALUATION OF FOREIGN TRADE STRATEGY VERSIONS B2, ByB4
Strategy Bk Calculation The result of the calculation
The right side of inequality(4) V ropt X M rOpt — V ropt X M rOpt h h h M h V -
B2,83,84 250950 X 2124950 — ( — 1985050) X 1072950 2663115600000
The left side of inequality (4) Vk X (MFopt — MFopt) + Mk X (vFopt — Vpoppt) -
B2 ( — 308050)X (2124950 — 1072950) + + 1335950 X (250950 — ( — 1985050)) 2663115600000
B3 ( — 867050)X (2124950 — 1072950) + + 1598950 X(250950 — ( — 1985050)) 2663115600000
B4 ( — 1426050)X (2124950 — 1072950) + + 1861950 X(250950 — ( — 1985050)) 2663115600000
Taking into consideration conducted calculations and equation (2) we form the structure of optimal strategies set by Hurwitz criterion for the problem which will have the following form:
F
opt _
Jpr(a)
(Bj
with 0 <a < 0,68 wit^M a = 0,68 with 0,68 < a< 1
(9)
The analysis of system (9) indicates that the DM is more optimistic since optimism index a exceeds 0.5. If a = 1 the DM acts as an extreme optimist. In this case, the optimal decision by Hurwitz criterion is to hire a beer restaurant with an area of 300 square meters. This option is the optimal decision by maximax criterion also, which is extremely optimistic, since it convince the DM that when he chooses strategy version B5, external economic environment will be the most favourable for the organization, that is, its profits will be maximized under the given state of foreign trade conditions. In this
53 Modern European Researches No 3 / 2017 case, the weighted profit of organization from the foreign trade project depending on DM's index of optimism a will be
Gpr(a) = (M5 - V5)xa + V5 = 4110000 x a- 1985050 при a e (0,68;1]. (10)
If the decision maker is at the optimism level a = a = 0,68, then he is more optimistic than pessimistic. Then, according to Hurwitz criterion, the optimal solution is to rent premises area
300 100
150 - 250
square meters square meters square meters
as an extremely optimistic scenario choice
as a pessimistic choice variant
as a levelled choice of restaurants rentable area
In this case, the weighted profit for any option of chosen solution will remain unchanged and amounts to 809,950 euros because if
Vfe(°'68) = (Mfc- ^>x°,68 + Vk,
then
Gvr (0,68)= (M1 - V1) x 0,68 + V1 = (1072950 - 250950) x 0,68 + 250950 = (м2 - v2) x 0,68 + v2 = (1335950 + 308050) x 0,68 - 308050 = (M3 - V3) x 0,68 + V3 = (1598950 + 867050) x 0,68 - 867050 = (M4 - V4) x 0,68 + V4 = (1861950 + 1426050) x 0,68 - 1426050 = (M5 - V5) x 0,68 + V5 = (2124950 + 1985050) x 0,68 - 1985050 =
prx
Gw 2(0,68) = Gw 3(0,68) =
V 4(0,68) =
Gw 5(0,68) =
(11)
809950 809950 809950 809950 809950
If the DM optimism index is in the range a e [0;0,68), then with = 0 DM is an extreme pessimist,
e (0;0,5) DM is a pessimist,
a = 0,5 DM is neutral,
a e (0,5;0,68) DM acts as an optimist.
In this case, the optimal decision by Hurwitz criterion will be a choice of rentable area under a beer restaurant of 100 square meters. And this decision is optimal by extremely pessimistic Wald criterion orienting DM to the fact that with his chosen strategy external economic environment will be extremely unfavorable for the organization, decreasing its profits to the lowest possible value at the present state of foreign trade. Weighted profit serving as selected foreign trade strategy indicator will be
Gpr ( a) = (M1 - V1)xa + V1 = 822000 x a + 250950 при a e [0;0,68). (12)
Conducted calculations allow us to conclude that Hurwitz criterion is appropriate to apply in the uncertainty conditions by the organization, which in making predictions about its activities in the foreign market, due to any circumstances, does not adhere to any position of extreme pessimism, or extreme optimism. In this case, the economic entity is recommended to use Hurwitz criterion that provides a balanced approach to effective foreign policies, and allows to choose from them the optimal strategy.
Conclusion
High economic uncertainty in the international market requires the development of the foreign trade activity effectiveness analysis system appropriate to modern conditions that allows to justify decisions on a new methodological basis. Multicriteriality and complexity of problems solved by FTA participants in the new global models, require not only a correct account of the multidimensional export-import operations but also changes in the theoretical and methodological approaches to their analysis. We believe that Markov chains are the modern method of information-analytical FTA study, which will justify the decision making on a fundamentally new methodological basis, providing accurate results with the use of probabilistic models in the analysis of various foreign trade situations. We represent the economic and mathematical modeling procedure based on Markov chains for the above-mentioned example.
Organization management conducted an analysis of commercial real estate rented properties in the country, where the manufacturer is going to open a chain of beer restaurants. The study revealed the following trends: the contracts which specify the high rents, are replaced by contracts with lower rates for the rental of one square meter. It is also possible the time comes when changes in rental rates are so low that they can be neglected. Conditional probabilities reflecting the underlying state of the commercial real estate market are listed in the matrix of transition probabilities P :
/0,3 0,2 (0,3
0,6 0,3 0,6
0,1\
0,5
0,1/
(13)
After receiving this information, the Department of Finance, according to the assignment of business owner, must analyze the short- term state of the foreign real estate market.
To solve this problem, it is necessary to find final probabilities that characterize homogeneous Markov chain. Final probabilities are the system state probabilities in the final steady-state mode in which the probabilities of the system states do not depend either on time or on their initial distribution (Labsker 2014).
We choose as system S the market of commercial real estate rented properties in a foreign country, where the organization intends to open a chain of beer restaurants. The marked graph of system S states is shown in Figure 1.
1 p22=0,5 1 1
s2 J3
w
ÍJal=0,3
p.. =0,3
FIGURE 1. MARKED GRAPH OF COMMERCIAL REAL ESTATE MARKET STATE, RENTED PROPERTIES, IN A FOREIGN COUNTRY
Since the system can be in one of three states, based on primary data: s1 - number of proposals for the rented premises does not change;
as =
s2 - number of proposals for rented premises is growing; s3 - number of proposals for rented premises is reduced,
then the process taking place therein can be qualified as discrete. Besides, the periods of time t1,t2,t3 between the states are so small that the system S does not change its
state between them, that allows us to treat the analyzed process as a process with discrete time.
The upcoming state of the system S to which it goes, depends only on the state, in which it currently exists, but does not depend on the previous state so this process is Markov chain (Martyanova, 2016).
It has been proved (Labsker 2014) that if homogeneous Markov chain with a finite number of states is regular, there are the final probabilities p1,_,pn.Considering the fact
that all the elements of matrix Pa3 are positive, the system S is regular and so there are
limiting probabilities 1, 2, 3 of states 1, 2, 3, respectively.
In his work (Labsker 2014) the author proved, that if there are final probabilities the final vector(p1,_,p n) can be found from the following equation:
(?1.....P n) = (P1.....P n)p, (14)
wherein P - the transition probability matrix.
Then with = 3 from the equation (14) and using matrix (13), we obtain
/0,3 0,6 0,1\
( 1, 2, 3) = ( 1, 2, 3) x
0,2 0,3
0,3 0,6
0,5 0,1
(15)
Making multiplication of row vector by the matrix of the right side of the equality, the expression (15) takes the form
(P\>P 2>P 3) = (0,3p1 + 0,2p 2 + 0,3p 3; 0,6p1 + 0,3p 2 + 0,6p 3; 0,1p1 + 0,5p 2 + 0,1p 3).
Whence it appears
,p1 = 0,3p1 + 0,2p 2 + 0,3p 3; , p 2 = 0,6p1 + 0,3p 2 + 0,6p 3; p 3 = 0,1p1 + 0,5p2 + 0,1p 3,
(0,7p1 - 0,2p2 - 0,3p3 = 0; 0,6p1 - 0,7p2 + 0,6p 3 = 0; 0,1p1 + 0,5p2 - 0,9p3 = 0.
Performing transformations, we obtain
,0,7p1 - 0,2p 2 - 0,3p 3 = 0; - 3,7p 2 + 6p 3 = 0;
P1 =- 5p 2 + 9P 3.
whence
'0,7p1 - 0,2p2 - 0,3p 3 = 0; , p2 = 1,622p3; p1 = 0,890p 3.
The general solution of equation (15) depending from one arbitrary parameter p3 is vector(°'890p3; t62^; p3). Replacing in (16) the first equation by normalization
(Pl + P2 + P3= 1
condition we obtain the system
p2 = 1,622p3; p1 = 0,890p3,
having solved which, we find the final probability vector of system S having the following form (Pi P2< Ps) = (0,253; 0,462; 0,285).
Thus, the short- term forecast for commercial real estate in a foreign country is following: the number of proposals in the segment of rented premises is likely to grow (p2 = 0,462 > p1,p3). However, they do not depend on the initial state of the market.
Therefore, if an organization has time reserve for its foreign trade project implementation, it can be advised not to hurry with contract signing for the rent of beer restaurant with area of 100 square meters.
Recommendations
Systematization of the research results leads to the following conclusions:
1. In the conditions of foreign trade uncertainty it is appropriate to apply Hurwitz criterion, since it allows you to find the best solution when the decision maker (DM) can be considered neither as extreme optimist nor as extreme pessimist in the analysis of the organization effectiveness in the international market. Solutions, optimal by Hurwitz criterion match the DM optimism index determined not subjectively but on the basis of expression, including both winning value by Wald criterion in the set optimal strategies by maximax criterion and winning value by maximax criterion in a set of optimal strategies by Wald criterion, so and winnings by Wald and maximax criteria.
2. Hurwitz criterion does not exclude the optimal solution being such by extremely optimistic maximax criterion or as such recommended by Wald criterion so being extremely pessimistic. The property of Hurwitz criterion to level extreme pessimism of Wald criterion and extreme optimism of maximax criterion allows us to analyze the uncertainty and risk influence on the effectiveness of economic entity FTA with different decision-making models.
3. Conducted calculations have shown that Markov chains instrument does not disprove but rather confirms the validity of the decision maker desires, having a certain value of optimism index, to use Hurwitz criterion in selecting the optimal solutions. It allows to create a system of analysis that offers a balanced approach in predicting the organization's foreign trade strategies effectiveness.
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