Mathematical Modeling of Knowledge-Intensive Products Export

Energy Costs

VERETEKHINA SVETLANA V.

Doctoral program Financial University under the Government of the Russian Federation, Faculty of

Information Technologies Russian State Social University

Wilhelm Pieck street, 4, build.1, Moscow, 129226

RUSSIA

Abstract: This article presents the mathematical modeling of export energy costs. The knowledge-intensive

products export energy costs are a set of financial, material, labor costs and resources consumption. Export

costs are a multilevel system of indicators. The author sets out the order of mathematical modeling. At the first

stage, the main trends in reducing export energy costs are identified. A set of integrated logistics support

measures is modeled. The modeling of knowledge-intensive products export energy costs is a system of

technical and economic indices and a cost value dependance: Maintenance and Repair, Material and Technical

Maintenance, Business Model of After-Sales Service, Formation of the Cost of Insurance and Investment

Management Strategy. Formulas, practical calculation examples and graphs are presented. The Ishikawa

systematic analysis method is used to visualize data and dependence relations. The author's mathematical

modeling of knowledge-intensive products export costs includes the calculation of integrated logistic support

costs. Exporting countries require a high level of technical products efficiency. It has been established that "the

more complex a knowledge-intensive products is, the higher the reliability of systems is". Reliability indices

are basic. The author's scientific study confirms a hypothesis of the knowledge-intensive products export

feasibility only with high reliability and efficiency factors. The author developed a set of integrated logistical

support measures for knowledge-intensive products.

Keywords: mathematical modeling, systematic analysis, export problems, integrated logistics support, technical

and economic indices.

Received: March 2, 2021. Revised: November 15, 2021. Accepted: December 17, 2021. Published: January 5, 2022.

1 Introduction

The knowledge-intensive products export energy

costs are understood as a set of financial, material,

labor costs and resources consumption. Exporting

countries require a high level of technical products

efficiency. To ensure a high level of technical

readiness, it is necessary to calculate the cost of

material and technical support, the cost of repair

spare parts, salaries for technical staff, consumable

resources, electrical energy or alternative power

supplies. The cost of knowledge-intensive products

in the international market does not dominate [1].

The presence of integrated logistics support

dominates, including the optimization of financial,

material, labor costs and resources. In other words,

knowledge-intensive products cost is estimated in

millions of dollars, and integrated logistics support

cost throughout the products life cycle is estimated

in hundreds of millions of dollars [2]. The life cycle

of technical products is from 15 to 70 years. In case

of long life cycles, the integrated logistics support

cost is high. It is necessary to find ways to optimize

it. Therefore, it is necessary to carry out

mathematical modeling to optimize the knowledge-

intensive products export energy costs. In the study

by Boitsov M.S. et al. "Energy Costs as a

Manageable Economic Category" organizational

and economic measures to improve energy

efficiency are described [3]. Cost management is an

ability to save resources. Energy efficiency

management is a resource economy. Integrated

logistics support is a set of measures aimed at

modeling the knowledge-intensive products

aftersales maintenance situation. Information

support for complex technical systems is becoming

topical. This is due to the exports growth. Aftersales

maintenance is a modern international service

market. Such services as export, maintenance,

integrated logistics support are standardized.

Standardization is regulated by country regulatory

and legislative documents. Different countries have

their own individual natural resources: industrial

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water, electrical energy, fuel, transport

infrastructure, roads, logistics warehouses, technical

staff. The use of all resource types and the cost of

their use are modeled during integrated logistics

support measures development. To carry out

mathematical modeling of export energy costs

value, we will determine the main trends of

integrated logistics support.

The advantage of this study is the identification

of problems of knowledge-intensive product

exports (paragraphs 2.1.1; 2.12; 2.1.3; 2.1.4).

Mathematical tools for calculating technical and

economic indicators are proposed in order to

solve the identified problems. The main

indicator for the export of knowledge-intensive

products is the reliability indicator. The more

reliable the product is, the more efficiently all

functions are performed. Therefore, the

proposed formulas (1)-(8), allows to calculate

the performance of the product on a long life

cycle. Mathematical modeling of a large

number of indicators was carried out by the

method of system analysis. The advantage of

this research is the functional and system

analysis of interdependent indicators. The

simulation method chose such an interval of the

normative duration of the intended use of the

product that the probability values are low (see

Table 2). This indicates that the tactical and

technical characteristics of a knowledge-intensive

product were chosen correctly when designing the

product. The author has developed a set of actions

for integrated logistics support for knowledge-

intensive products, taking into account the

calculated coefficients showing high accuracy.

2 Problems and Trends of Export

Energy Costs

The main trends in reducing export energy costs

include:

1. reducing the excess quantity of spare parts

for technical repair, determining the

minimum required and sufficient quantity of

stock elements;

2. using the existing repair and mechanical

shops of exporting countries;

3. dividing the after-sale maintenance stages

into several parts: operation, warranty and

post-warranty maintenance, repair; each

stage is paid under a separate international

contract;

4. outsourcing the Maintenance and Repair

and Material and Technical Support

procedures;

5. optimizing the export costs through

mathematical modeling.

Export energy costs are limited by budget.

The development of integrated logistics support

measures for exports is based on modeling the

optimal stock maintenance processes in an

exporting country by and at the cost of a

manufacturing country, an exporting country

and friendly countries. Foreign export

customers insure orders (purchases) against

losses. Insurance is applicable to the following

types of losses: transportation; stock

maintenance; downtime and unserviceability of

knowledge-intensive products; low level of

maintenance and repair; low level of technical

staff human potential. In the field of exports,

there is a proverb "If you need one

supercomplex and unique thing, then contact

the Russians, if you need 10 identical things,

never contact them"

http://exportcenter.rbc.ru/article-5-ideas.html.

Russia is a country with its own knowledge-

intensive products engineering and strong

engineering and design thought. Russia exports

devices and equipment, power plants, detection

stations, aircrafts, ships and other products. All

these products are knowledge-intensive.

We will analyze the knowledge-intensive

products exporting problems.

Export problems are those related to the

Russian foreign trade at the modern level. In the

study by Ruzhinskaya T.I "Problems of the

Russian foreign trade at the present stage" the

main problems of exports are specified [4].

2.1 Problems of Knowledge-Intensive

Products Export

Export problems are those related to the

Russian foreign trade at the modern level. In the

study by Ruzhinskaya T.I "Problems of the

Russian foreign trade at the present stage" the

export earnings status is analyzed and new

service export areas are specified [4]. As can be

seen from the main trends in reducing energy

export costs, the sale of after-sale maintenance

services (operation, warranty and post-warranty

maintenance, repair) is paid under a separate

international contract. The cost of after-sale

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maintenance services for knowledge-intensive

products in an exporting country is estimated in

hundreds of millions of dollars with a long

product life cycle. Power plants, early-warning

stations, ships and aircrafts serve in an

exporting country for decades. Knowledge-

intensive products ensure the stability of

development in an exporting country. Foreign

trade in knowledge-intensive products is

intended for China, Indonesia, Malaysia, India,

Syria, France and the Near East.

2.1.1 Formation of the Maintenance and Repair

Cost

The first problem of exporting knowledge-

intensive products is a customer's ability to

choose the cost of Maintenance and Repair

(M&R). Maintenance and repair services can

be performed by product developers,

manufacturers or third-party international

enterprises. The application of the Maintenance

and Repair service requires the interactive

electronic technical manuals development

(IETM), electronic catalogs of spare parts and

accessories. The availability of technical

documents allows technical staff to carry out

such activities as operation, maintenance and

repair. Modern interactive electronic manuals

are made in 5 complexity classes:

1. scanned pages of paper documents;

2. a set of texts in the SGML format;

3. data as objects within an information

storage that has a hierarchical structure;

4. direct interface interaction with electronic

modules for product diagnostics;

5. 5. integration with expert systems. An

international standard for interactive

electronic technical manuals is the

S1000D Specification.

The development of classes 4 and 5

interactive electronic technical manuals is

provided for export products. The main

advantage of interactive electronic technical

manuals is an automated translation of technical

documents into such languages as Arabic,

English, Spanish, Sino-Malaysian in real time.

The automated system visualizes the location of

texts and symbols according to the documents

linguistics and spelling rules for words and

sentences. In addition, there are such options as

animated display, multimedia assembly

(dismantling) of product component parts,

blocks, units and mechanisms. The cost of

developing interactive electronic technical

manuals is included in a set of integrated

logistics support measures for knowledge-

intensive products. It is paid by the customer

separately, under a contract related to the

development of technical operation documents.

The generation of the Maintenance and Repair

cost includes calculations of material, labor,

financial resources. The Maintenance and

Repair cost is included in a set of integrated

logistics support measures for knowledge-

intensive products.

2.1.2. Formation of the Material and Technical

Maintenance Cost

The second export problem is the planning and

management of Material and Technical

Maintenance (MTM) processes. The MTM

management includes:

1. spare parts planning needs and spare

parts consumption forecast;

2. management algorithms for warehouse

stocks;

3. procurement management;

4. supplies transportation and delivery

organization, options for the element

distribution in repair and mechanical

shops, warehouse distribution; storage;

5. resources replenishment; resources

extension;

6. issue records for supplies, issue

records for spare parts (electronic

catalogs); report generation.

The Material and Technical Maintenance

cost formation includes calculations of a

resources cost, a maintenance and application

cost for each resource type. The Material and

Technical Maintenance cost is included in a set

of integrated logistics support measures for

knowledge-intensive products.

2.1.3 Formation of an After-Sales Service

Business Model

Exporting countries impose requirements for after-

sales service business model organization.

Integrated logistics support includes typical business

models for supplier-customer interaction. The

confluence of supplier and customer interests is

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reflected in export contracts. The main international

standards are as follows: DEF STAN 00-60, MIL

STD-1390D (used by the Indian Navy), STANAG

4427 (configuration management for supplied

products), MIL-STD 1369, SPEC 1000D, SPEC

2000M, SPEC S3000L (LSA), SPEC S4000M. An

individual business model for a certain exporting

country requires the development of:

1. management methods and technologies for

stocks, orders, supplies of spare parts,

accessories and repair consumables;

2. management methods and technologies for

Material and Technical Maintenance;

3. management methods and technologies for

Maintenance and Repair (M&R);

4. standardization of procedures and

technologies, harmonization of data and

document exchange formats.

The After-Sales Service Business Model cost

includes calculations for the management methods

and technologies development . The After-Sales

Service Business Model cost is included in a set of

integrated logistics support measures for

knowledge-intensive products.

2.1.4. Formation of an Investment Management

Strategy

Exporting countries impose investment management

requirements for the organization. Integrated

logistics support includes investment management

for spare parts replenishment, specifically:

1. a strategy for maximum financial

management;

2. a direct strategy;

3. a strategy for a consolidated balance sheet.

A maximum financial management strategy suggests

that: a budget is divided into parts, only a 1/12 (12

months a year) part of the budget can be spent

within one period of time. The maximum financial

management strategy is considered to be an

operator, it neglects the stochastic nature of demand

and consumption. A lack of this maximum financial

management strategy results in a situation where a

budget is not used to the maximum extent and has

certain restrictions.

A direct strategy is each request for a spare parts

catalog item, which results in its order and a full

payment. There are no time or cost restrictions when

it comes to an order item. There is no hindrance to

the budget spending. A lack of this direct strategy

results in a possible lack of budget and stocks

(shortage), leads to an imbalance in supporting the

efficiency of knowledge-intensive products.

A consolidated balance sheet strategy combines the

advantages of both maximum financial management

and direct strategies. It prevents any stock instability

at the end of the budget year. The main idea of this

consolidated balance sheet strategy is a maximum

balance in stocks.

We can draw the following conclusions: efficient

stock management and resource optimization

require the development of conceptual and

functional integrated logistics support schemes for

knowledge-intensive products. Integrated logistics

support measures are based on the principle of

central management. The development of a set of

integrated logistics support measures is aimed at

improving the efficiency of after-sales service for

knowledge-intensive products. The efficiency of a

set of integrated logistics support measures is based

on the global information network, which allows for

operational management. Information and computer

support is an integral part of a measure effectiveness

set. The reliable functioning of information and

computer support ensures timely operational

interaction in logistics objectives by supply chains.

The authors study of system integrated logistics

support in military products considers additional

features of after-sales service organization for

knowledge-intensive products [5].

2.1.5. Formation of the Insurance Cost

Foreign export customers insure orders (purchases)

against losses. Insurance is applicable to the

following types of losses: transportation; stock

maintenance; downtime and unserviceability of

knowledge-intensive products; low level of

maintenance and repair; low level of technical staff

human potential. The exporter's insurance support is

the provision of insurance tools to protect export

credits and investments, which includes:

1. deferred payments insurance;

2. deferral insurance (insurance indemnity);

3. credit insurance to replenish the exporter's

circulating assets;

4. export factoring insurance (a risk factor of

non-payment);

5. Russian outward investments insurance;

6. short-term accounts receivable insurance;

7. supplier's credit insurance against a risk of a

foreign buyer's payment failure.

In addition, export control procedures related to

foreign economic activities are accompanied and

supported. Methodological support in the currency

control field allows us to comply with the foreign

exchange legislation requirements for the currency

earnings repatriation. Methodological support in the

currency control field includes the exporters

responsibility for violating the foreign exchange

legislation requirements, analyzing sanctions,

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minimizing risks, as well as interacting with an

authorized bank.

The identified Maintenance and Repair, Material

and Technical Maintenance, Business Model of

After-Sales Service, Formation of the Cost of

Insurance and Investment Management Strategy

cost value formation problems show a necessity for

systematic analysis. Integrated logistics support

measures systematic analysis. The modeling of the

exporting knowledge-intensive products energy

costs is a system of technical and economic

indicators and costs dependence. The more complex

a knowledge-intensive product is and the higher the

systems reliability is, the higher the total cost of

integrated logistics support is. Let us try to identify

main mathematical dependencies.

3 Mathematical Modeling of Export

Energy Costs m Solution

It has been established that "the more complex a

knowledge-intensive product is and the higher the

systems reliability is", reliability indices are basic.

3.1. System Reliability, System Failure

Interval

3.1 Reliability requirements distribution and a

calculation method for the "average system failure

interval" coefficient (for one system element):

Т0 = Т0k.1/(γn (n+1)!Cn+1N ) (1)

where Т0k is a system element failure interval; γ is a

ratio of the system element recovery time and

system failure interval; n is an allowed number of

system elements that are simultaneously in a state

of failure.

3.2. Technical Readiness and Availability

Coefficients

Technical readiness coefficient characterizing the

sample readiness depending on the failure-free

operation and labor intensity of maintenance and

repair is calculated according to the formula:

Ktr = Kau * Kpa (2)

where Kau is an indicator (availability coefficient is

a probability that the planned time of sample

intended use will not be delayed beyond the

permissible time or canceled due to failure); Kpa is

an indicator (planned applicability coefficient is a

proportion of operation definite period during which

the product is not under planned maintenance and

repair).

Kpa =1-Kd *  (3)

where  – severity of use defined as a ratio of

product operating time during its intended use (in

hours, kilometers, starts, cycles, shots, etc.) per

calendar year and an estimated annual time reserve

(in hours); Kd is a sum of specific aggregate

duration of planned maintenance category Kdm and

specific aggregate duration of recovery Kdr

Kd = Kdm + Kdr (4)

where Kdm is the specific maintenance (repair)

duration, a ratio of the total maintenance (repair)

duration mathematical expectation and the sample

operating time during its intended use for a certain

operation period; Kdr is specific recovery duration.

The Kpa, Kd, Ktr coefficients are determined at the

estimated (normalized) operation intensity based on

actual operation data. The Kau indicator (availability

coefficient is a probability that the planned time of

sample intended use will not be delayed beyond the

permissible time or canceled due to failure) is

evaluated according to the formula:

Kau = Ka + (1- Ka)* Pr, (5)

where Pr is a probability of the sample recovery at a

given time during its preparation for intended use;

Ka is an availability factor.

This probability of the sample recovery at a given

time is determined taking into account the standard

duration of preparation for intended use, the

permissible time for delaying the start of use taking

into account the possibility of intended use with

separate failures according to the following

formulas:

Pr = 1-eхр(-tp /tr), (6)

tp = tdp +  tdp, (7)

where tdp is the standard duration of preparation for

intended use (at the beginning of a working day or

between cycles of intended use), hour; tr is a mean

time to recovery, hour.

Let us carry out the mathematical modeling of

dependencies. Using the numerical values and

products technical characteristics, we have

dependency graphs.

Let us evaluate the actual readiness level of Product

1 by using the following numerical values:

(8)

where T is the duration of an operation period

during which the actual number of serviceable

products is analyzed at the specified periodicity t;

m=[T/t] is the number of analysis cycles (the square

brackets denote a whole part of division [15/t]); 30

days are one month, a year is 365 days, then t =

0.082); n is the number of serviceable products at

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the i-th cycle equal to 1; N is the total number of

products in a sample (group) equal to 1.

Fig. 1: Dependence of the actual product readiness

level on the operation period duration according to

the formula (8).

Table 1. Calculation of the actual product readiness

level dependence on the operation period duration

(Fig. 1).

(years)

conversio

n into

days

t = 30

days

m =

T/t

K = 1/m

5475

182.5

0.005479

5475

91.25

0.010959

5475

120

45.625

0.021918

5475

180

30.416

0.032877

5475

365

0.066667

EXIT

5. Composite indicators

0,699 ≤ Ktr ≤ 0,865

0,963 ≤ Kau ≤ 0,986

0.01 ≤ Kp ≤ 0.07

Ka (real conditions) = КЭГ, at

m = [T/t] is the number of analysis cycles [15/t where 30 ≤ t ≤ 365 (days)]

Entry

1. Fault tolerance indicators:

Not determined, not calculated

2. Realiability indices:

1. PCP mean time to recovery ТВч - 30 min., (N = 18 units)

2. table of the numerical values of Product 1 component parts mean time to failure dependence, at the coefficient Твч (mean time to

recovery) equal to 30 minutes, taking into account multichannel structures.

3. Ka зип ≥ 0.9

4. ТPCP = 30 minutes

5. t = 21.6 hours per day

6. mean time to failure Т0 = 2,500 hours

7. service life = 15 years

8. warranty service life Г = 10 years

9. operation life Р = 130,000 hours

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3. processability (maintainability) operational indicators

Does not depend on the values of indicators 2 (reliability) and 5 (complex)

4. Testability measure

Not determined, not calculated

5. Composite indicators

0,699 ≤ Ktr ≤ 0,865

0,963 ≤ Kau ≤ 0,986

0.01 ≤ Kp ≤ 0.07

Ka (real conditions) = КЭГ, at

m = [T/t] is the number of analysis cycles [15/t where 30 ≤ t ≤ 365 (days)]

EXIT

Fig. 2: Dependence of the actual product readiness level on the operation period duration according to the

formula (8).

The first calculation indicates that if the product

operation period is 15 years, and the analysis cycles

are 30≤m≤365, the actual readiness level increases.

We determined the maximum possible product

readiness analysis cycle once a year, with a 15-year

product operation guarantee.

Using mathematical modeling, we will analyze the

dependencies of the Technical Readiness

Coefficient depending on the failure-free operation

and labor intensity of maintenance and repair

according to the formulas (2)-(5). Mathematical

modeling of a large number of indicators cannot be

displayed by one graph. In this case, the Ishikawa

method ("skeleton of fish") is used, a method of

systematic analysis for the visualization of data and

relations.

Parameter input (left), output data (right).

Parameters are arranged from left to right in order of

importance – the formulas (2)-(5). To clarify, the

parameters can be written inside the "skeleton of

fish".

Table 2. Calculation of product recovery probability

at a given time (Fig. 3)

Рв

t в

0.632

0.5

0.798

0.8

0.5

The formulas (6) and (7) allow for a separate

calculation of the product recovery probability at a

given time, taking into account:

 the standard duration of preparation for

intended use;

 the permissible time for delaying the start

of product use;

 the possibility of intended use with

individual product failures.

During modeling, we selected an intended

product use standard duration interval from 30 to 48

minutes. With the time interval of 30 minutes and

48 minutes, the numerical probability values remain

high, the difference in probability values Рв is as

follows:

0,798103482-0,632120559=0,165982923≈ 0.2.

 ≈ 0.2 - this indicates that it is not advisable

to change the established tactical and technical

characteristics of the product. The parameters of

product component parts mean time to recovery are

equal to 30 minutes, it is not advisable to change

them, a probability gain is low: ≈0.2. Under an

export contract, it is not allowed to increase the

permissible time for delaying the start of intended

product use since there is a risk of penalties for its

downtime. It is legally difficult to prove and

distinguish between the physical meaning of product

downtime and that one due to the planned time

allowed for the start of intended product use. A ratio

of a risk price (penalties) and a time difference of 30

to 48 minutes is not comparable with the probability

 Рв≈0.2. In other words, "the game is not worth the

candle".

4 Conclusion

The author's mathematical modeling of knowledge-

intensive products export costs involves calculating

the integrated logistics support costs. Exporting

countries require a high level of technical products

efficiency. Mathematical tools are provided to

ensure a high level of technical readiness. It has

been established that "the more complex a

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Veretekhina Svetlana V.

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Volume 17, 2022

knowledge-intensive products is, the higher the

reliability of systems is". Reliability indices are

basic and are calculated according to the formulas

(1)-(8). Core indicators are used, then export of

knowledge-intensive products energy costs is

modelled: a system of technical and economic

indicators and a cost value dependence:

Maintenance and Repair, Material and

Technical Maintenance, Business Model of After-

Sales Service, Formation of the Cost of Insurance

and Investment Management Strategy. The more

complex a knowledge-intensive product is and the

higher the systems reliability is, the higher the total

cost of integrated logistics support is. The author

developed a set of integrated logistical support

measures for knowledge-intensive products.

Scientific research confirms the hypothesis of

feasibility of exporting knowledge-intensive

products only with high reliability and efficiency

factors. The study is original, financial university

higher doctorate. Mathematical modeling is carried

out by author at the Faculty of Information

Technologies of Russian State Social University,

Moscow. The numerical values of tactical and

technical characteristics belong to a real knowledge-

intensive product. Mathematical modeling using

artificial intelligence algorithms was considered in

the previous work of the author [6]. The theory of

economic doctrines and the horizons of the Russian

economy were considered in the works of Kleiner

G.B. [7- 10]. The author developed a set of

integrated logistical support measures for

knowledge-intensive products.

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