METHODOLOGICAL APPROACH TO JUSTIFICATION OF THE DISTRIBUTION OF THE ARMED FORCES OF THE STATE IN PEACETIME AND WARTIME MILITARY FOMATIONS TAKING INTO ACCOUNT MILITARY AND ECONOMIC ASPECTS Текст научной статьи по специальности «Экономика и бизнес»

DOI: https://doi.org/10.30525/2256-0742/2021-7-2-170-178

METHODOLOGICAL APPROACH TO JUSTIFICATION OF THE DISTRIBUTION OF THE ARMED FORCES OF THE STATE IN PEACETIME AND WARTIME MILITARY FOMATIONS TAKING INTO ACCOUNT MILITARY

AND ECONOMIC ASPECTS

Volodymyr Mozharovskyi1, Serhii Hodz2

Abstract. The division of the armed forces into peacetime and wartime military formations (MFs) is carried out taking into account a number of aspects, namely military and political, military and strategic, military and economic, physical and geographical, operational (operational and tactical), demographic, regulatory, etc. An important place is given to the military and economic aspects, such as macroeconomic indicators of the condition and development of the national economy, the dynamics of changes in its military budget and the maximum possible degree of military and economic tension (opportunities for the deployment of military organization in a special period); the degree of dispersion, protection and vulnerability of important economic facilities of the country, its transport capabilities (infrastructure); cost indicators for maintaining unions (units) with varying degrees of preparedness for the mission execution for the purpose intended, their mobilization (transition to the wartime table of organization and equipment) and alerting; opportunities for the country's economy to modernize and produce new models of AMH, providing the needs of troops (forces) with the necessary material means (fuel and lubricants, food, property, etc.). Analysis of the problematic issues of organizing the armed forces, in particular their division into peacetime and wartime MFs, reflects the following contradiction: on the one hand, increasing the number of permanent readiness (peacetime) unions (units) involves the growth of the amount of financial costs for their maintenance, but at the same time reduces the time for their alerting; on the other hand, increasing the number of wartime unions (units) that need to be mobilized and alerted, provides a reduction in financial costs for their maintenance, but increases the time to alerting.

According to the authors, the solution to this contradiction requires a comprehensive approach, which provides an in-depth consideration of the experience of troops and the use of theoretical research methods to justify the division of armed forces in the peacetime and wartime MFs. However, there is a lack of methods (methodological approaches) that would allow the in-depth consideration of resource and time limitations on the maintenance and alerting of troops, and on this basis, justification of the optimal division of the armed forces into unions (units) with varying degrees of manpower and equipment organization, security, training and preparedness to execute missions for the purpose intended. In this regard, the authors propose a methodological approach, which, taking into account military and economic aspects, in particular, the average annual financial resources required for the maintenance, mobilization (completion) and alerting unions (units) of a certain type, will allow a more reasonable approach to the division of the armed forces into peacetime and wartime MFs. The methodological approach presented in the article also applies to others formed in accordance with the legislation of MFs, which are entrusted with tasks and functions for the national security, protection of the country's sovereignty, territorial integrity and inviolability.

Key words: alertness and mobilization preparedness, armed forces, military formations, unions (units), military and economic aspects, financial resources, methodological approach, optimization problem.

JEL Classification: F45, H83, C18

Corresponding author:

1 Central Scientific Research Institute of the Armed Forces of Ukraine, Ukraine. E-mail: military.technology@icloud.com

ORCID: https://orcid.org/0000-0003-3S42-S407

2 Central Scientific Research Institute of the .Armed Forces of Ukraine, Ukraine. E-mail: sergiigodz1968@ukr.net

ORCID: https://orcid.org/0000-0002-7860-2330

1. Introduction

The armed forces are responsible for national security, protection of its sovereignty, territorial integrity and inviolability. One of the requirements for the armed forces is the need to keep a certain composition of MFs in permanent preparedness to respond immediately to threats to the military security of the state, the rest of MFs should be kept in preparedness for mobilization (transition to the wartime table of organization and equipment) and preparedness to execute missions on purpose in a special period. To this end, by purpose, tasks, manning level, equipment with armament and military hardware (AMH), logistics support (LS), training and preparedness for executing missions for the purpose intended, MFs (subunits, unions, units) are divided into those, which are kept deployed in peacetime, i.e., MFs of permanent preparedness (peacetime MFs) and those, which are subject to mobilization and alerting in a special period (wartime MFs) (Mozharovskyi, Hodz, 2018; Hodz, Mozharovskyi, Pantiushenko, 2020; Mozharovskyi, Hodz, Sakovskyi, 2019).

The division of the armed forces into peacetime and wartime military formations (MFs) is carried out taking into account a number of aspects, namely military and political, military and strategic, military and economic, physical and geographical, operational (operational and tactical), demographic, regulatory, etc. An important place is given to the military and economic aspects, such as macroeconomic indicators of the condition and development of the national economy, the dynamics of changes in its military budget and the maximum possible degree of military and economic tension (opportunities for the deployment of military organization in a special period); the degree of dispersion, protection and vulnerability of important economic facilities of the country, its transport capabilities (infrastructure); cost indicators for maintaining unions (units) with varying degrees of preparedness for the mission execution for the purpose intended, their mobilization (transition to the wartime table of organization and equipment) and alerting; opportunities for the country's economy to modernize and produce new models ofAMH, providing the needs of troops (forces) with the necessary material means (fuel and lubricants, food, property, etc.) (Mozharovskyi, Hodz, 2018; Mozharovskyi, Hodz, 2019).

Analysis of the problematic issues of organizing the armed forces, in particular their division into peacetime and wartime MFs, reflects the following contradiction: on the one hand, increasing the number of permanent preparedness (peacetime) unions (units) involves the growth of the amount of financial costs for their maintenance, but at the same time reduces the time for their alerting; on the other hand, increasing the number of wartime unions (units) that need to be mobilized and alerted, provides a reduction

in financial costs for their maintenance, but increases the time to alerting.

According to the authors, the solution of this contradiction requires a comprehensive approach, which provides an in-depth consideration of the experience of troops and the use of theoretical research methods to justify the division of armed forces in the peacetime and wartime MFs. However, there is a lack of methods (methodological approaches) that would allow the in-depth consideration of resource and time limitations on the maintenance and alerting of troops, and on this basis, justification of the optimal division of the armed forces into unions (units) with varying degrees of manpower and equipment organization, security, training and preparedness to execute missions for the purpose intended. In this regard, the authors propose a methodological approach, which, taking into account military and economic aspects, in particular, the average annual financial resources required for the maintenance, mobilization (completion) and alerting unions (units) of a certain type, will allow a more reasonable approach to the division of the armed forces into peacetime and wartime MFs. Some provisions on this methodological approach have been set out in publications (Hodz, Mozharovskyi, Pantiushenko, 2020).

The purpose of the article is to present the essence and main content of this methodological approach.

2. Main content

of the methodological approach

Methodological approach to substantiation of the division of the armed forces into unions (units) of permanent preparedness (peacetime) (Np) and unions (units) that are subject to mobilization and alerting in a special period (wartime) (Nw) (taking into account economic aspects) includes source data and elements of the calculation process (algorithm).

Output data provide indicators that are necessary to calculate the required number of unions (units) of permanent preparedness and those that are subject to mobilization, as well as financial resources (funds) necessary for their maintenance and alerting.

The initial data should include the following indicators: n = ^N. = N + Nw is a predetermined total

number of unions (units) of the armed forces, taking into account their j-th types to be distributed; tpj, twj is the time (normative) for completion (mobilization) and alerting of one union (unit) of j-th type; Tp j is the time (normative) for completion, Twj is mobilization and alerting of all unions (units) of j-th type; Tp is the total time (normative) of completion and alerting unions (units) of all types of permanent preparedness, Tw is mobilization and alerting unions (units) of all types to be demobilized; Tpjn, Twjn is the time taking into account the limitations required to alerting

unions (units) of j-th types; cpj, cwj are the average annual financial resources (funds) (excluding the cost of AMH), which are necessary for the maintenance, completion (mobilization) and alerting one union (unit) of j-th type; CP j = cpj ■ Np j, cWj = cw j ■ NWj - are the average annual financial resources (funds) required for maintenance, completion (mobilization) and alerting

ji

are

unions (units) of j-th type; Q j = Cpj + Cwj < Q the average annual financial resources (funds) that are needed to maintain and alert Nj = Npj + Nwj < NJn

all unions (units) of j-th type; Cp cpj ■ Npj

are the average annual financial resources (funds) required for maintenance, replenishment and alerting Np = ^ Npj, unions (units) of all j-th types;

are the average annual financial

resources (funds) that are needed to maintain, mobilize

and alert, Nw Nwj unions (units) of all j-th types;

j

c = c + c = V C . = V (C . + C .) =

^p ^w ^ J pj wj'

= Vcp. • Np. J

• NwJ

are the total average annual financial resources (funds), which are necessary (depending on the level of development of the country and the military and political situation) for the maintenance and alerting unions (units) of all j-th types; C; l C; jl

are the total financial resources (funds) (subject to limitations), which are allocated by the state for one year for maintenance and alerting N unions (units) of all types (value Q is determined not only on the basis of economic capabilities of the state but also taking into account the values , ,„; values

c

jl

pJ n ? w J n>

Npj, NwJ are interconnected,

they cannot be appointed independently of each other). It is assumed that the total number of

N = X Nj = Np + Nw = ^ (Npj + Nwj) unions (units),

to be distributed are determined in advance. Financial resources (funds) is necessary to maintain and alert them. It should be noted that Q " Ql.

Taking into account the indicators of the initial data, we formulate in more detail the contradiction mentioned above:

- on the one hand, there is considered an attempt or expediency to keep most or all of N = Np unions (units) deployed in peacetime, which minimizes the total time T to bring them ready to execute missions for the purpose intended. However, in this case, taking into account the average annual financial costs cpj (excluding the cost of AMH) for the maintenance, completion and alerting one union (unit) significantly increases the total financial costs Cp j = cpj ■ Np j. These costs may exceed the allocated (subject to

limitations) average annual financial resources

Ci i = ^Ci ji;

- on the other hand, the other extreme is considered when in the special period the majority or even all N = Ne unions (units) will be subject to demobilization and alertness. This version of their maintenance, taking into account the average annual financial costs cp j > cwj (excluding the cost of AMH) to mobilize and alert one union (unit) minimizes the necessary total financial costs Cwj = cwj ■ Nwj (for example, holding mobilization meetings, classes, etc.). However, in this case, the time T to alert these unions (units) increases significantly and complicates the process of their combat coordination (for example, due to the possible lack of personnel trained in full in peacetime).

As a result of such a contradiction, in fact, there is a problem of finding a compromise solution, i.e., the most acceptable option for the division of the total number of MFs N into peacetime unions (units) Np (those deployed in peacetime) and wartime unions (units) Nw (those that are subject to mobilization and alerting in a special period with reduced staff). This takes into account the limitations on the allocated average annual financial resources Q t and time TMn,, Te n, required for maintenance and alerting of Np, Nw unions (units).

3. Stages of the calculation process (algorithm)

The algorithm for substantiating the division of the armed forces into unions (units) of permanent preparedness and those to be mobilized and alerted in a special period includes two successive and interrelated stages.

At the first stage the calculation of the following indicators is performed: the required value of human, material and financial resources, subgect to limitations C! on the average annual financial resources allocated for completion (mobilization) and alerting of Npj , Nwj number of unions (units) of j-th types; required (maximum allowable) number Npj and Nwj. of unions (units) of j-th types taking into account time limitations Tpjn, Twjn for alerting.

It is assumed that the strength of the armed forces to perform missions of national defence, as well as the total number N of unions (units) of the armed forces to be distributed, are the predetermined values. For example, the number of armed forces is determined in accordance with the forecast of the military and political (military and strategic) situation, intentions and capabilities of a potential aggressor, military and economic (resource) capabilities of the state, and so on. The set limits on financial resources (funds) Cjt allocated and time Tpjn, TwJn, required for alerting the unions (units) of j-th type. It is these

indicators that largely determine the possible number Nj = Npj + Nwj of all unions (units) of j-th types. It is also taken into account that depending on the availability of trained personnel and the necessary means, troops (forces) can be alerted in successive and parallel ways. In a successive way, each subsequent union (unit) is alerted after alerting the previous union (unit), i.e., in the absence of parallel sections for alerting this or that union (unit). In a parallel way, the unions (units) are alerted almost simultane ou sly; this on average takes the time t of alerting one union (unit). To perform calculations, a value is entered that will characterize one or another way of alerting unions (units) in the presence of the necessary resources. This value is called a coefficient of simultaneity (parallelism) P of the start of alerting (this coefficient can also be called the coefficient of simultaneity (parallelism) of works on alerting unions nits)). When (5 = 0 there is a successive way, when p = 1 there is a parallel way, when 0 < P < 1 there is a combined way of alerting unions (units). Accordingly, for unions (units) of permanent preparedness, given their staffing (crews), there can be taken on average P pj = 0,7 - 0,9; for unions (units) to be mobilized, given the uneven supply of these unions (units) with mobilization resources, the lack of the required number of services (crews) prior to their alerting, there can be accepted, according to the experience of troops, on average p . = 0,2 - 0,6 .

Given the timeliness (Tpj " Tpjn , Twj" Twjn) of alerting unions (units) of j-th type, we have:

T . = N . ■ t .

pi pi pi at 0 < ß < 1

a-ßi+tpip <T

Twj = Nwj ■ twj ■ a -ßwj ) + Kj-Kj ± Twjn at 0 < ß < 1

(1)

(2)

These time indicators are interrelated. Each of them depends on the number of peacetime and wartime unions (units) NpJ , Nwj of j-th type, as well as from the allocated financial resources. Taking into account (1), (2) we obtain:

N, < TpJ" - 'p{ 'Ppj, 0 <p„. < 1, (3)

PJ tpj • C1 -Kj)

Nwj <—^^, o <p <i. twj ■ (1 -Pwy) '

Taking into account the average annual costs c

(4)

which are necessary for the maintenance, completion and alerting of one union (unit) ofj-th type Np j, as well as average annual costs cwj, which are necessary for the maintenance, mobilization and alerting of one union (unit) of j-th type Nwj, this can be written:

Tp]n tpj -$pj "P] *'p]--p]' tpj■(1 -ßpj)

■ NP] < cP

(5)

• Nw ; < Cw

Twjn - twj

■ (6)

twj ■ (1 -Pwj )

Adding the right and left parts of these inequalities we obtain:

T . ot ,.p .

" • Nplncr N , < c sin s' Vp> ■

p j p j

Twjn - twj

ßw

tpj ■ C1 -ßpj)

Vj twj • a-ßwj)

(7)

This takes into account that values NMj and NeJ should fulfil not only conditions (3) - (6) but also the condition of correspondence between the necessary C j and average annual funds Q jo6M :

C;, = + C^ = • NMj + cej • Nej <Cm

r -1 -ß

m j nomp m j r m j

T -1 -ß

e j nomp e j re j tMi -(1 -ßM,) TCej - tei -(1 -ß,.)

< C;

j OÔM

(8)

From (8), the relationship between the maximum values NpJ and NwJ can be obtained taking into account the allocated financial resources Q j t:

Cf - Cwj • Nwj

C j,

■ N,

Cpj > Cwj

(9)

The same equation, expressed with NeJ, can be written:

Nwi < 1J

Ci-cPj • NPJ

C j,

J' PJ-. N

CPJ > Cwj

(10)

The time Tp for completion and alerting all Np Npj peacetime unions (units) of peacetime

will be determined by the maximum value of the time of alerting unions (units) of j-th type, which should not exceed the required (maximum allowable) time subject to value restrictions Tpjn . Similarly, the time Tw for mobilization and alerting all Nw Nwj

unions (units) to be mobilized will be determined by the maximum value of the time of alerting unions (units) of j-th type, which should not exceed the required (maximum allowable) time subject to value restrictions Twjn. The acceptable time limits Tpjn , Twjn for alerting troops are prior; on their basis, there are determined the number Np j, Nwj and the necessary funds for this C; j. Increasing the financial resources Qjt allocated in the interests of the troops will change the value Nj = Npj + NwJ and the overall value N = ^(Npj + Nwj) subject to the condition Tpj < TpjJ or Twj < Twjn for alerting unions (units) at the expense of the measures connected with reduction of time tpj, twj for alerting one union (unit) of j-th type.

c

c

In the case of limitations, the distribution problem Nj = Npj + NwJ of unions (units) of j-th type on the peacetime unions (units) NpJ and wartime unions (units) Nwj, depending on the selected condition of the source and other data, taking into account the time twj, necessary for mobilization and alerting one union (unit) of j-th type Nwj., as well as time tpj, necessary

for completion and alerting one union (unit) of j-th type NPj.

In terms of finding the right solutions, there can be used three main options (regarding priority selection): the first option supposes that the priority is the predetermined total number of unions (units) to be distributed according to the order of their maintenance and the time spent for alerting them, as well as the required number of unions (units) of permanent preparedness; the second option means that the priority is the average annual financial resources (funds), which are allocated in the interests of unions (units) of j-th type of the total amount of funds allocated per year in the interests of unions (units) of all types, as well as the required number of unions (units) of permanent preparedness; the third option means that the priority is the time required (maximum allowable) taking into account the limitations for alerting unions (units) of the relevant types of permanent preparedness and those to be mobilized in a special period.

The first option: a predetermined number N = ^ Nj = Np + Nw = ^ (Npj + Nwj) ofunions (units)

to be distributed according to the order of their content and time spent for alerting them, as well as the required value X N . of unions (units) of permanent

J p

preparedness for combat duty and other tasks in peacetime are priority (set). In this case, the maximum

allowable number X N ■ of unions (units) to be

j w

mobilized will be calculated:

ZNwj = N NPJ ,

(12)

After this, for the known values twj, p . the time is calculated

Twjn = Nwj • tw] • a -Kj ) + twj ■ßwj

(13)

Required for alerting Nwj unions (units) of j-th type. According to the known values cpj > cwj the necessary financial resources (funds) C1 are determined for maintenance and timely (Tpj < Tpjn, Twj < Twjn) nalerting of the mentioned number

N = ZNpj + ZNwj of unions (units).

jj

The second option: the allocated amount of financial resources (funds) Q jl , as well as the required value Npj , consequently, Tpjn ., are priority (set). In this case, the maximum allowable number Nwj , according to the known values cp j > cwj, will be calculated:

Nwj =

Cjl -cpj • Npj

C ji

• Npi , (14)

Then the time, calculates the time required to mobilize and alert this number of unions (units) of j-th type calculates according to the known values twj, Pwj:

Twjn = Nwj ■ twj ■ (1 -Pwj ) + twj -Pwj . (15)

The total number Nj of unions (units) of j-th type in accordance with the average annual financial resources (funds) allocated for their maintenance C; jt will be:

•PPi . cji -cp

T - t r

N _ pjn pj rpj

J~ tpi • C1 -ß pj )

^pj- • Npj

(16)

The third option: the time Tpjn , Twjn , is priority (set), then according to the known values tpj , ppj , twj , Pwj the values are clearly determined under the accepted conditions:

T . -t .-p .

N _ p i" p. p.

tpj ■ C1 -ßpj)

(17)

(18)

" twj • C1 -Pwj )

According to the known values cpj > cwj the financial resources C;j " C;jt (8) necessary to maintain and alert the number Npj, Nwj found are determined. Then, the certain funds Q j can be used to maintain and subsequently alert N j of unions (units) of j-th type:

T . -t .-p .

N = N + N =- "Jn p

Tw.n -twj-ßwj

: (19)

■ ■■ - tpj ■ d-Ppj) tw] .(1-P„j) ( )

Using one of the selected priority options, the total number N of unions (units) is calculated, which can be distributed according to the order of their maintenance, taking into account the time spent and allocated funds for alerting N of unions (units). The problem is considered solved if the condition N" Nn is fulfilled, with T " Tn of alerting all unions (units) of j-th types. In this case, it is considered that the average annual financial resources (funds) Q jt, allocated for unions (units) of j-th type from the total amount of funds C; t, allocated for unions (units) of all types, are enough for Npj, Nwj of unions (units) of j-th types out of the total number N" Nn of unions (units). If the condition is not fulfilled, it is necessary to increase the allocation of average annual financial resources (funds) C; t or shorten the time tpj, twj for alerting one union (unit) of j-th type.

The second stage. It is known that for the same allocated (subject to limitations) average annual financial resources Q l C; jt. different values of

indicators can be obtained regarding the number of unions (units) of permanent preparedness (Np j) and unions (units) to be mobilized (Nwj). So, taking into

c

c

account the previously stated contradiction, the problem of distribution of unions (units) of j-th type in relation to the order of their content provides an optimization option for its solution, i.e., finding the optimal values Nop j, Now j, given their integrity, subj ect to conditions-limitations regarding the allocated average annual financial resources (funds) Q jl and time Tpjn, Twjn required for alerting these unions (units). The criterion for solving this problem may be the desire to achieve the maximum relative to the total number Nj of unions (units) of j-th type.

It is assumed that the unions (units) can be alerted in a sequential, parallel or combined way depending on the degree of their staffing, equipment and training; therefore, the coefficient of simultaneity (parallelism) P - of the start of alerting unions (units) of j-th type is calculated. To record the optimization problem, the following indicators are taken into account: Qj 1. is the average annual financial resources (funds) allocated for unions (units) of j-th type of the total amount of funds C l = ^ C jl, allocated for unions (units) of all types;

C j is the is the required amount of financial resources (funds) to alert all the unions (units) of j-th type; the time Tpj " Tpjn, Twj " Twjn. for alerting unions (units) of j-th type. It should be noted that cpj > cwj, tpj < twJ. The proposed optimization problem belongs

Ci. = Cpj + ^j = Cpj • NPJ + • Nwj = cpJ

to the class of problems of linear integer mathematical programming. The essence of this problem is the need to find the values of variables Npj and Nwj of unions (units) of a certain j-th type, which deliver the extremum - the maximum of a given scalar function, taking into account the accepted system of conditions-limitations on financial resources (funds) Q jt and sometimes Tpjn, TwJn. With regard to the system of limitations, it is assumed that limitations, like variables, are non-negative values, and the number of limitations-equations is less than the number of variables. Given the above, the objective function of the linear integer programming problem will be written as:

max Nj = Npj + Nwj. (20)

With limitations: values Npj and Nwj should fulfil the condition regarding the timeliness of alerting unions (units) of j-th type:

TPj = Npj • <p; • a-P pj) + tpjp pj ± TPjn ,

Twj = Nwj ■ twj ■ a-ßwj ) + twj-Kj ± Twjn

(21)

values NpJ and Nwj should fulfil the condition of balance between the required average annual financial resources (funds) C; j and financial resources (funds) Cj j i. allocated per year for unions (units) of j-th type of the total amount of funds Q,:

Tpjn - tpj -ß PJ + c

■ (1 -ß pj ) wJ

twj ■ (1 -ßwj ) 11

(22)

Where variables Npj, NwJ are non-negative integers, with cPj > ; tpj < twj; Vpj >pWj.

The optimization problem mentioned (20-22) is provided for unions (units) of j-th type. However, such a problem can be written in a more general form, as the linear integer programming problem in a standard (symmetric) form:

max N = Np +NW =^NfJ =1 (fJ + N*j). (23)

pi i—i wi ¿—¡^ pi i 1 1

The limitations set: values N = E N and

p j pj

C = (cp ■ Np) + (c~w ■ NJ =XCj = Z(Cp

where variables Np , Nw are non-negadve integers, with Cpj > cWj ; tpj < twj ; Ppj >pWj ; (cp ■ Np ) and (cw ■ Nw ) are the scalar product of vectors given in the coordinate form: cp {c ,,cp,,cp3,...,cp!\ isthe vector

P \ P1 p 2 p 3 p J )

of average annual costs (excluding the cost of AMH) for the maintenance, completion and alerting of each of the unions (units) of j-th type deployed in peacetime; cw \cwj,cw2,cw3,...,cwJ} is the vector of average annual costs (excluding the cost of

N = EN- should fulfil the condition of timeliness

wj

of alerting unions (units):

TP =Z Npj ■ tpj ■ C1 -Ppj)+tpj-Ppj < TPn,

Tw = Z Nwj ■ twj ■ (1 - Pw j ) + twj • Pwj < Twn ;

i

values Np and Nw should fulfil the condition of balance between the required total average annual financial resources (funds) Q and total financial resources (funds) C; l., allocated for a year for unions (units) of all types:

- tpi-P p

tPi ■ (1 -ß)

Twjn - twj -Pw

tw: ■ a-Pw,)

-) = Cp + Cw < C11

AMH) for maintenance, mobilization and alerting of each union (unit) of j-th type, with cpj > cwj; Np {{ppNp2'Np3,...,Npj) is the vector of unions (units) of j-th type, deployed in peacetime; Nw {Nw 1,Nw2,Nw3,...,NwJ) is the vector of unions (units) of j-th type to be mobilized in a special period.

4. Example of calculations

An example of solving the linear integer mathe-matical programming problem according to the third option of

Baltic Journal of Economic Studies . „ „.,,, --- Vol. 7 No. 2, 2021

Table 1

The results of solving the linear integer mathematical programming problem on the third option of priorities (option)

Indicators Calculation max N j Np j + Nw j

j-th type of unions (units)

j-1 j-2 j-3 j-4 j-5 j-6 j-7 j-8 j-9

cpj (mln UAH) 85.8 97.9 231 264 42.9 13.1 40 80 50

tpj (hours) 38 22 44 26 36 28 12 24 17

ß „ 0.8 0.7 0.71 0.8 0.7 0.71 0.83 0,8 0,71

tP; • C1 -ßPj) 7.6 6.6 12.76 5.2 10.8 8.12 2.04 4,8 4,93

hi ■ßPj 30.4 15.4 31.24 20.8 25.2 19.88 9.96 19,2 12,07

T pjn (hours) 48 24 48 28 40 30 24 48 34

T . -t .ß . N s pJn p. p. pi" tP] • a-ßp.) 2.32 1.30 1.31 1.38 1.37 1.25 6.88 6,00 4,45

Tpj = NPj ■ tpj ■ C1 -ßpj) + tpjßpj 48.0 23.98 47.95 27.98 39.99 30.0 23,99 48,0 34,0

Cond. fulfilled: Tp j " Tp j n yes yes yes yes yes yes yes yes yes

CPj = cPj ■ NPj x (mln UAH) 199.06 127.27 302.61 364.32 58.77 16.38 275,2 480,0 222,5

cwj (mln UAH) 25.4 29.0 68.25 78.0 12.65 3.7 10 16 10

Cond. fulfilled: Cp j > CwJ- yes yes yes yes yes yes yes yes yes

t-wj (hours) 107.28 136.75 89.89 186.11 180.38 124.86 93,64 133,33 82,66

Cond. fulfilled: tpj < twj yes yes yes yes yes yes yes yes yes

ßwj 0.6 0.5 0.5 0.6 0.5 0.6 0,6 0,6 0,6

Cond.fulfilled: ßpj >ßwj yes yes yes yes yes yes yes yes yes

twj • C1 -ßwj ) 42.913 68.374 44.896 74.445 90.188 40.946 37,456 53,333 33,064

twj -ßwj 64.369 68.374 44.896 111.67 90.188 74.916 56,184 80,0 49,596

wjn (hours) 326 194 242 240 314 194 218 288 192

TwJn -^-Kj WJ twj • C1 -hj ) 5.96 1.81 4.35 1.72 2.46 2.86 4,27 3,90 4,30

TWJ = Nwj • tWJ • a-ßwj) + twj-ßwj 320.13 192.13 240.19 239.72 312.05 192.02 216,12 287,99 191,77

Cond.fulfilled: Twj " Twjn yes yes yes yes yes yes yes yes yes

Cwj = cwj • Nwj (mln UAH) 151.38 52.49 296.89 134.16 31.12 10.58 42,7 62,4 43,0

Ci' ji (mln UAH) 355.0 200.1 610.0 510.0 100.1 28.5 320,0 548,0 270,00

C11 (mln UAH) 2941.7

1 = Cpj + Cwj mln UAH 350.44 179.76 599.5 498.48 89.89 26.96 317,9 542,4 265,5

C =Z c;, j mln UAH 2870.83

Cond.fulfilled: C j " C{ yes yes yes yes yes yes yes yes yes

Cond.fulfilled: C[ " Cj' i yes

(End of Table 1)

Optimal values obtained

No j = Nop j + Nowj 7 2 5 2 3 3 10 9 8

Nop =Z Nopj j 23 (46.9 % of No)

Now =Z Nowj j 26 (53.1 % of No)

No = Now + Nop 49

priorities is given in Table 1. Here, j-th type of unions (units) means unions (units) of the corresponding types of troops such as mechanized, tank, artillery, antiaircraft missile brigades (regiments), etc.

5. Conclusion

The main content of the methodological approach to justify the division of armed forces, as the basic component of forces of national security, on peacetime and wartime MFs taking into account military and economic aspects, in particular the average annual financial resources required for the maintenance, mobilization (completion) and alerting unions (units) of a certain type. The authors believe that the originality of this methodological approach is as follows: - the proposed algorithm of calculations (l) - (19) allows to solve the problem of distribution of armed forces by several options, depending on the chosen condition of initial data (options of priority) It provides for the use of three priority options: the first option supposes that the priority is the predetermined total number of unions (units) to be distributed according to the order of their maintenance and the time spent for alerting them, as well as the required number of unions (units) of permanent preparedness; the second option means that the priority is the average annual financial resources (funds), which are allocated in the interests of unions (units) of j-th type of the total amount of funds allocated per year in the interests of unions (units) of all types, as well as the required number of unions (units) of permanent preparedness; the third option means that the priority is the time required (maximum allowable) taking into account the limitations for alerting unions (units) of the relevant types of permanent preparedness and those to be mobilized in a special period. According to the selected priority, the total number of unions (units) is calculated, which can be distributed according to the order of their maintenance. The

References:

problem is considered solved if the condition N" Nn is fulfiled, with T " Tn alerting of all types of unions (units). In this case, it is considered that the allocated average annual financial resources (funds) are enough to form the required number of peacetime and wartime unions (units). If this condition is not fulfilled, it is necessary to increase the allocation of average annual financial resources (funds) or shorten the time for alerting one union (unit) of j-th type. The advantage of this methodological approach, compared to the known ones, is that depending on the selected priority and a predetermined number of unions (units), it allows you to easily determine the number of unions (units) of permanent preparedness and unions (units) to be mobilized, taking into account the time for alerting them, which does not exceed the allowable values for the time of alerting, as well as the allocated average annual financial resources (funds); - the optimization problem offered (20) - (22) allows you to determine the maximum number of unions (units) in relation to the order of their maintenance, taking into account the limitations on the time required to alert unions (units), as well as allocated financial resources. The advantage of this optimization problem, compared with the known problems of this area of research, is that due to the developed equations of the relationship between the main indicators of the distribution, it is confined to the known linear integer programming problem taking into account the most important restrictions on the time of alerting unions (units) and allocated financial resources.

It is believed that the methodological approach outlined in the article (the main content) allows a more reasoned approach to the division of the armed forces into peacetime and wartime unions (units), taking into account military and economic aspects, in particular, average annual financial resources required for the maintenance, mobilization (completion) and alerting unions (units) of a certain type.

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