DIVERSIFICATION PRODUCTIVE MODEL: CASE PERU Hctor Hurtado Bocanegra, Ulises Romn Concha, Luzmila Pr Concepcin, Percy De la Cruz Vlez de Villa

mathemathicas@hotmail.com, nromanc@unmsm.edu.pe, lproc@unmsm.edu.pe,

pdelacruzv@unmsm.edu.pe

Bellavista, March 05, 2015.

ABSTRACT

The Productive Diversification, developing the Institutions, aims to expand the range of

Products (Goods and Services), as is the case of Peru; to, preserve and improve

productivity, in order to sustain economic growth of the country. So, too, the Institutions

have in the Diversification of Production, a means to correct the internal deficiencies,

by integrating all production areas and articulated, institutional activities, akin to

achieve and consolidate, their economic expectations, the Institution in the near future.

Thus, the Institution is, for Productive Diversification various Associations, including its

production areas; for, direct and supervise the proposed objectives; additional, new

departments are created and reformed others, to ensure that the products have the

Quality and Innovation required, to enable them to venture into the operating markets.

Therefore, it is presented, the Productive Diversification Model; for, support

Institutions, the effectiveness of its meetings and how, reaches the expected success,

by developing Associative Structures, avoiding dispersions (conflicts, empty, i.e.) that

lead to failure in the objectives; and, in the control of Leadership, Efficiency,

Effectiveness, Productivity and Quality, the members participating in the Associations

(Commissions, Councils, i.e..) formed, through Associative Networks, to simulate the

movements in real time, of the activities undertaken by all members, involved in the

Diversification of Production.

The Productive Diversification Model, is a mathematical tool, which is based on "The

Theory of the Associations" intelligent and qualitative mathematical definitions, such as:

the Topology, the Category and Algebraic Structures, on meetings and activities

(mathematics associations), to be performed productively, members (humans)

Diversification of Production, to achieve its success.

Keywords: Mathematical Association, Topology, Category, Associative Structure,

Algebraic Structure, Associative Network.

RESUMEN

La Diversificacin Productiva, que desarrollan las Instituciones, tiene por objetivo

ampliar la oferta de Productos (Bienes y Servicios), como es el caso del Per; para,

preservar y mejorar la productividad, en aras de sostener el crecimiento econmico del

pas. As, tambin, las Instituciones tienen en la Diversificacin Productiva, un medio

para corregir las deficiencias internas, al integrar todas sus reas productivas y

articular, sus actividades institucionales, afn de lograr sus expectativas econmicas y

consolidar, a la Institucin en el futuro prximo.

Es as, que la Institucin constituye, para la Diversificacin Productiva diversas

Asociaciones, entre sus reas productivas; para, encaminar y supervisar, los objetivos

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propuestos; adems, se generan nuevos departamentos y reforman otros, para lograr

que los Productos tengan la Calidad e Innovacin necesaria, que les permita

incursionar en los mercados operativos.

Por eso, es que presentamos, el Modelo de Diversificacin Productiva; para, apoyar a

las Instituciones, en la efectividad de sus reuniones y qu, llegue al xito esperado,

mediante la formulacin de Estructuras Asociativas, evitando las dispersiones

(conflictos, vacos, etc. ) que conducen al fracaso en los objetivos propuestos ; as

como, en el control del Liderazgo, Eficiencia, Eficacia, Productividad y Calidad, de los

miembros que participan en las Asociaciones (Comisiones, Consejos, etc.,) formadas,

a travs de las Redes Asociativas, para simular los movimientos en tiempo real, de las

actividades que realizan todos los integrantes, que participan en la Diversificacin

Productiva.

El Modelo de Diversificacin Productiva, es una herramienta matemtica, que se

fundamenta en La Teora de las Asociaciones y las definiciones matemticas

inteligentes cualitativas, cmo: la Topologa, la Categora y las Estructuras

Algebraicas, sobre las reuniones y las actividades (asociaciones matemticas), que

deben realizar productivamente, los miembros (seres humanos) de la Diversificacin

Productiva, para lograr el xito del mismo.

1.INTRODUCTION

The National Plan for Productive Diversification, presented on July 28, 2014, by the

President of the Republic of Peru, aims to expand the country's export supply, to

strengthen economic growth, which for the past 10 years It has maintained and what, is

imperative, for the high level of informality and high heterogeneity, between production

regions; and the limited productive diversity, among others, which endanger economic

growth, obtained until 2013 [5].

The National Plan for Productive Diversification, makes an interesting proposal, by the

swarm of ideas presented, such as: Permanent Multisectoral Commission for

Productive Diversification, made up of seven (07) of the Peruvian State Ministers and

(01), representative Business Associations; in addition, it is important, the presentation

of three Axes or Lines of Action, namely: Shaft N 1: Promoting Diversification of

Production, Shaft N 2: Adaptation of Regulations and Administrative Simplification and

Shaft N 3 : Productivity Growth [5 ], although I differ somewhat from the names given,

not without interest and other concepts presented in the Plan for Production

Diversification, which will be subsequently discussed, related to complete our

contribution, to the success of the project that urges it made, because the country

requires it.

In the V Peruvian Congress of Operations Research and Systems, held from 3 to

November 7, 2014, in the auditorium "Elle Dumbar", National Major University of San

Marcos, during the round table No. 1: "Productive Diversification Efficient", was stated

that: The absence of Structures in the National Plan of Productive Diversification,

threatening that, it is efficient and what, lest Innovative "; which, it was received by

conference attendees, highlighting its importance, for the productive development of

the country.

Thus, that, the Productive Diversification Model, for, the Permanent Multisectoral

Commission: Case Peru; which, it is described by formulas ensemblistic, such as

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meetings (associations) among the members of the Permanent Multisectoral

Commission, so that they are productive, avoiding (detect and predict) conflicts,

dispersions, gaps, i.e., and, control the Leadership, Effectiveness, Efficiency,

Productivity and Quality of its members with: Order, Logic, Management and

Exactness, Topologies and Categories, described in the Structural Associative Ring,

which is configured to, the Permanent Multisectoral Commission for Productive

Diversification.

Also, it presents an Associative Structure, which corresponds to Associative Planning

(Strategic), of the three (03) Axes or Lines of Action, which has been based National

Productive Diversification Plan [2] is presented; through a formula ensemblistic,

emanating be a Topology and Category, describing the Associative Structure: Abelian

Group; for, properly addressing, human activities in all three shafts and achieve, the

objectives proposed, in time.

Consequently, the Model of Productive Diversification, aims to show how you can build

Associative Structures, on human groups and Activities, that people do to achieve the

proposed objectives, with: Order, Logic, Management and Exactness, through the

"Theory of the Associations [2] and give, smart qualitative mathematical definitions

mentioned, designing Associative Networks; for, detect and predict: contingencies,

conflicts, dispersions, mistakes, accidents, i.e., and control: Leadership, Productivity,

Efficiency and Quality: In addition, Innovation, through the Associative Mesh, to migrate

Associative Structure, among other situations, which shall be described later.

2.- MATERIAL AND METHOD

Since, the National Plan of Productive Diversification, as a strategy envisages, the

creation, of: the Permanent Multisectoral Commission for Productive Diversification; as,

implementation, give: three (03) Major Axes, for, the takeoff of the national productive

sector, in the coming years; where, these, involve people, to integrate the Permanent

Multisectoral Commission and, perform activities that correspond to the three Main

Axes, to be developed over time [5].

However, the humans are different each other, by: Age, Sex, Education, Family,

Knowledge, Political Function, Laboral Function, i.e., and, considering that by

integrating the Permanent Multisectoral Commission or some Great Axes and why, to

meet in joint sessions, are forming a Set Class, in which all members interact with each

other, forming a Fuzzy Set, anytime where, complexity is frequent and recurrent, giving

rise to chaos at all times, that is, conflicts, gaps, errors, dispersions, accidents, loss of

opportunities, i.e.,, because it is not taken into account, the implied laws exist

associations (meetings), which through "The Theory of the Associations" [2] and the

Intelligent qualitative mathematical definitions, such as: Topology, the Category [1] and

Algebraic Structures [4], it is possible to identify through the diagram, Associative

Network, which will allow; detect and predict, Contingencies, Failures, Gaps, Conflicts,

i.e., and, control Leadership, Efficiency, Effectiveness, Productivity and Quality, of all

members, with: Order, Logic, Direction and Exactness [3 ].

Thus, that, Productive Diversification Model, presents the Associative Structure: RING

WITH IDENTITY or INTEGRAL DOMAIN (to the Theory of Associations, have the

same interpretation), for the Permanent Multisectoral Commission (CM), which means,

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the existence two Nucleus ( Hub or Nodes) and consequently, two Binary Operations,

one generating an Abelian Group and the other, a Monoid, both have a Topology and

an implicit Category; in addition, two all different Empty Associations and two Universal

Associations, because the Permanent Multisectoral Committee, is chaired by the

Minister of Production (P) and therefore, is the main Nucleus and integrates the

President of the Council of Ministers (PCM), as a secondary Nucleus, for political office

representing investiture.

2.1 ASSOCIATIVE STRUCTURE: RING WITH IDENTITY (4), of the Permanent

Multisectoral Comission for Productive Diversification, Case: PER, is as follows:

CM: Multisectoral Commission; P: Minister of Production

PCM: President of the Council of Ministers.

COM: Minister of Foreign Trade; ECO: Minister of Economy and Finance.

E: Minister of Energy and Mines; A: Minister of Agriculture

G: Representative Business Associations. T: Minister of Transport. ;

The Associative Structure, is attached the formulas ensemblestic, with the respective

sessions, citing some activities that are required to perform; to avoid: Conflict, Empty,

among others, and control, in all Member: Leadership, Effectiveness, Productivity,

Efficiency and Quality, using a spreadsheet and indicators, calling the members, just

finished each session (meeting). The formulas ensemblestic of Associative Structures,

are as follows:

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2.2 STRATIFICATION OF THE ASSOCIATIVE STRUCTURE

I. E(CM,P)={ , {P}, {{P}, PCM}, {{{P}, CPM}, COM}, {{{P}, CPM}, ECO}, } [2]

It is an Associative Structure: Abelian Group, comprising Associations:

1. {P} - The Minister of Production (P), prepares the meetings

holding in the day, with: PCM, COM and ECO, which

means, review the objectives of the day and mad, the day

above.

2. {{P}, PCM} - The Minister of Production (P), meets with

PCM; to, review the objectives of the day and confirmed,

Activities and results, of: COM and ECO, the previous day,

as well as, projections of the day, which has previously been

submitted by virtual means, to their offices.

3. {{{P}, PCM}, COM} - Session, enter: P, PCM and COM, which is

directed by: P, in which PCM, has the task, ask

to: COM about the activities undertaken the previous day; for,

be collated, with which previously were referred

above day, by: E and A, as well as, those made by: COM.

Also, the planned activities of the day, for : COM,

E and A, after the meeting, P will evaluate : PCM and COM.

. 4. {{{P}, PCM},ECO) - Session, enter: P, PCM and ECO, which is

directed by: P, in which PCM has the task, ask

to: ECO about the activities the previous day; for,

be collated, with which previously were referred

previous day, by: T and G, as well as, those made by; ECO.

Also, the planned activities of the day, both for: ECO,

T and G, after the meeting, valued at P: PCM and ECO.

5. CMP - Universal Association, which is set every two

weeks, to outline the strategy to perform, during the

fourteen days and revise, the proceedings in two weeks;

directed by: P, which is the moderator between PCM:

ECO and COM, and maintaining equidistant to avoid

empty.

II. E(CM, PCM)= { , {PCM}, {{PCM}, P}, {{{PCM}. P}, {COM, ECO}}, } [2]

It is an Associative Structure: Monoid, comprising, Associations:

P

P

P

P

P

PCM

M

ECO

PCM

M

PCM

M

COM

PCM

M

COM

ECO

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6. {PCM} - The Presidency of the Council of Ministers (PCM)

prepares holding meetings three times a week,

he directs, with: P, COM and ECO, which means review

secondary objectives of the week and to practice, in the

next week.

7. {{PCM}, P} - The President of the Council of Ministers (PCM),

he meets with Minister of Production (P); to, establish

Objective of the proposed agreements with: COM and ECO, and in

the three days of the week and confirm, the results of the week.

8. {{{PCM}, P}, {COM, ECO}} - Session, concluded between: PCM,

P, COM and ECO, set out three days a week; to, check out,

secondary objectives, of the National Plan of Diversification

Productive, that have been achieved and that, they be held in the

next week; still, P who asks what, corresponds to

P ECO

PCM COM

UCM.PCM - Universal Association, which articulates members:

PCM, P, COM and ECO, on the progress of the secondary objectives

and projections, the following week.

III. E(CM,COM)={ , {COM}, {{COM}, E}, {{COM}, A}, } [2]

It is an Algebraic Structure: Abelian Group, comprising, the Associations:

9. {COM} - The Minister of Commerce: COM, prepares the

daily meetings, with: E and A, which means, review the

objectives for the day and made, the day before.

10. [{COM}, E} - The Minister of Commerce: COM, meets with

Energy Minister: E; to, confirm the information,

the day before, who they have been referred by virtual means

and the activities, to develop in the day, reviewing the proposed

objectives, at the end, the Association, COM must

evaluate: E.

PCM

PCM

P

COM

COM

E

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11. {{COM}, A} - The Minister of Commerce: COM, meets with

Minister of Agriculture; A; to, confirm the information,

the day before, who they have been referred by virtual means

and activities, to develop in the day, reviewing the proposed

objectives. At the end, the Association, COM must

evaluate: A.

12. CM.COM - Universal Association, which articulates members:

COM, E and A, about the progress makes in two weeks

and the projection, of the objectives, for two weeks.

IV. E(CM,ECO)={ , {ECO}, {{ECO}, T}, {{ECO}. G}, } [2]

It is an Associative Structure. Abelian group, comprising, Associations:

13. {ECO} - The Minister of Economy and Finance: ECO, prepares

daily meetings with: T and G, which means, reviewing

Objectives of the day and made, the day before.

14. {{ECO}, T} - The Minister of Economy and Finance: ECO, meets

with the Minister of Transport, T; to, confirm the information

the day before, that have been timely submitted, by

virtual means and activities, to develop in the day,

reviewing the proposed objectives. At the end, the Association,

COM must evaluate T.

15. {{ECO}, G} - The Minister of Economy and Finance. ECO, meets

with the Representative of Employers' Associations: G; for,

confirm the information the day before, which have been

timely submitted, by virtual means and the

activities, to develop in the day, reviewing the objectives

proposed. At the end, the Association, COM must evaluate G.

16. CM.ECO - Universal Association, which articulates members:

ECO, T and G, about the progress makes in the two weeks

and projection, of the objectives, for the next two weeks.

ECO

A

COM

COM

ECO

ECO

COM

A E

T

G

G T

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Then, the Associative Structure, of the Permanent Multisectoral Commission

for Productive Diversification, presents: 4 Topologies, 4 Categories, 4 Binary

Operations, 4 Empty Associations, 4 Universal Associations and 4 Algebraic

Structures, which Integral Network, it is:

NOTE. For esthetic reasons, it is not possible to represent all the articulations, which

are seen in the dotted lines, in the Associative Structure; therefore, we left to the

reader, the hypothetical idea, that all intelligent articulations are represented.

Finally, the plenary session, which corresponds to what is usually done, regardless of

associative implications, correspond to the session 17, would be the Universal

Association of all its members, which could be related to that described Integral

Network, to realize the need to Structure the Permanent Multisectoral Commission and

thus, the success of the National Plan of Productive Diversification, a monthly meeting

is suggested and agenda, Objectives achieved in the past month and Projection, the

following month.

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The National Productive Diversification Plan [5], also contains three main lines, for

takeoff of the national productive sector, in the coming years and what are the

following:

Shaft No. 1. Promoting Productive Diversification.

Objective: To expand the export basket of Economics.

Shaft No. 2. Adequac of Regulations and Administrative Simplification.

Objective: Increase profitability and investment, of the

enterprises by adapting the Regulations and

Simplification, of the procedures with the state

institutions.

Shaft No. 3. Productivity Expansion.

Objective: Increase Productivity, Economy and reduce

Heterogeneity.

where, the Strategic Planning, of the National Plan of Productive Diversification; it, has

to start with the Shaft N 3, to leverage the Shafts N 2 and N 1, respectively, that

corresponding to the Associative Structure: Abelian Group:

E(PA,3) = { , { 3 }, { { 3 }, 2 }, { { 3 }, 1 }, } [2] whose Associative Network, is the diagram:

3. NUMERICAL TESTS

For, Production Diversification Model: Case PERU, has been considered the following

diagrams:

3.1. TABLE NUMBER OF ASSOCIATIONS VERSUS OBJECTS, detailing in each

numbered Association N 1 to N 17, the Objects: P, PCM, COM, ECO, E, A, T and G,

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corresponding members of the, Permanent Multisectoral Commission of Productive

Diversification.

3.2. TABLE OF OBJECT VERSUS OBJECT, indicating the number of times the

objects: P, PCM, COM, ECO, E, A, T and G, members of, The Permanent

Multisectoral Commission of the Diversification of Production, involved in 17

Stratification Associations, of: the Associative Structure - Ring with Identity.

3.3. TABLE OF SIMULATION, considering the 17 Associations,of: The Associative

Structure Stratification - Ring with Identity, has been partitioned into four (04)

Associative Categories:

. HIGHEST - are daily meetings or associations, Monday through Friday, to be

performed simultaneously, how:

N 1 N 9 and N 13

N 2 N 10 and N 14

N 11 and N 15

N 3

N 4

. HIGH - meetings or associations, which are held three days a week,

alternating and independent, how:

N 6

N 7

N 8

. LOW - meetings or association, every two weeks, preferably on Saturdays and

independent, how they perform:

N 5

N 12

N 16

. VERY LOW - meetings or associations, they must be performed once per

month and are, kind of information about the development, of the National Plan of

Productive Diversification and the projection, of the month following:

N 17

3. 4. TIME TABLE SIMULATION, allows us to quantify, the time required for the

Stratification of the Associative Structure: Ring with Identity, Productive Diversification

Model - Case PERU; whereas, in a first case the factor for five (5) minutes in, a second

case, the factor for ten (10) minutes, by session. Therefore, for an approximately 243

meetings (associations) monthly, it required 12 hours 35 minutes and 25 hours 10

minutes, by month respectively.

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3.1 TABLE OF NUMBER OF ASSOCIATIONS VS OBJECTS

Associations/

Objects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total (%)

P 1 1 1 1 1 1 1 1 8 18.18%

PCM 1 1 1 1 1 1 1 1 8 18.18%

COM 1 1 1 1 1 1 1 1 8 18.18%

ECO 1 1 1 1 1 1 1 1 8 18.18%

E 1 1 1 3 6.82%

A 1 1 1 3 6.82%

T 1 1 1 3 6.82%

G 1 1 1 3 6.82%

TOTAL 44 100%

3.2 TABLE OF OBJECT VS OBJECTS

Objects /

Objects P PCM COM ECO E A T G

P 6 5 3 3 1 1 1 1

PCM 2 3 1 1

COM 4 2 2

ECO 4 2 2

TOTAL 8 8 8 8 3 3 3 3

Legend:

P: Production Minister PCM: President of Council of Ministers

COM: Minister of Foreign Trade ECO: Minister of Economy and Finance

E: Minister of Energy and Mines A: Minister of Agriculture

T: Minister of Transport G: Representatives of Business

Associations

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3.3 SIMULATION TABLE BY CATEGORIES

3.4 SIMULATION TABLE BY TIME

12 hours 35 min. 25 hours 10 min.

*Biweekly

Legend:

P: Production Minister PCM: President of Council of Ministers

COM: Minister of Foreign Trade ECO: Minister of Economy and Finance

E: Minister of Energy and Mines A: Minister of Agriculture

T: Minister of Transport G: Representatives of Business

Associations.

Categoras NN de

AsociacinP PCM COM ECO E A T G Factor

1, 2, 9, 10, 11,

13, 14, 152 1 3 3 1 1 1 1 3

3 1 1 1 1

4 1 1 1 1

Alta 3 6, 7, 8 2 3 1 1 3

Baja 3 5,12,16 1 1 2 2 1 1 1 1 2

Muy Baja 1 17 1 1 1 1 1 1 1 1 3

17 Total 8 8 8 8 3 3 3 3

Muy Alta 10

Categories Factor 5 MINUTES 10 MINUTES Number of

Monthly Associations Daily Weekly Monthly Daily Weekly Monthly

Highest

3 15 75 300 30 150 600 160

1 5 25 100 10 50 200 20

1 5 25 100 10 50 200 20

High 3 15 45 180 30 90 360 36

Low 2 30* 60 60* 120 6

Very Low 3 15 30 1

Total: 755 Total: 1510 243

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4. RESULTS

The analysis, of Tables Productive Diversification Model, you can detach the following:

1. That, the number of basic meetings (assemblies, associations): 17; 243, are

performed monthly about.

2. The Associative Structure: Ring with Identity, has two (02) Principals Nucleus and

two (02) Secondary Nucleus; hence, the very high category, which corresponds to

perform 200 meetings, i.e., the 82.38% of total meetings.

3. To consider, as a factor of time: 5 minutes for meetings; we, will comparing, with the

time factor: 10 minutes, it is the most appropriate.

4. Is possible, to Detect and Predict, contingencies and conflicts (Empty) among the

members of the Permanent Multisectoral Commission, being targeted or specific

meetings.

5.The performance of each of the members, of the Permanent Multisectoral

Commission, it is possible to verify the Efficiency, Effectiveness, Productivity,

Leadership and Quality.

6. The Associative Structure: Ring with Identity, is flexible to expand the number of

objects (behavior, as a binary tree).

5 CONCLUSIONS

Productive Diversification Model: PERU Case, presents the Association Structure: Ring

with Identity, and that, has two Nucleus: P and PCM, with two Operations produced by

Nucleus; therefore, the Stratification Model of Productive Diversification, comprises 17

Associations or Meetings, categorized, like: VERY HIGH, HIGH, LOW and VERY LOW,

for the eight members of the Permanent Multisectoral Commission; where, the

following characteristics were observed:

- OPTIMIZATION OF TIME, although the Stratification of the Partnership Structure

It corresponds to 17 Associations, suggesting a longer time; however, it is not, because

they are made in some cases, simultaneously three- and two-Associations, in others,

biweekly or monthly; still, the simulation of five (05) minutes per meeting, as

appropriate, taking into account that the Associations are preprogrammed.

- AUDIT, the Stratification of the Associative Structure: Ring with Identity, to be specific

Associations, can, confirm the activities and the projection, of the actions to be taken,

the members of the Multisectoral Commission and thus, size: Leadership,

Effectiveness, Efficiency, Productivity and Quality, in each Association and thus,

averaging their results monthly.

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- DETECT AND PREDICT, empty (Contingency, Errors, Dispersions, Accidents,

Conflicts, i.e.), which are normally produced in an Universal Association, or Plena

Meeting, all members of the Permanent Multisectoral Commission of Productive

Diversification.

6 BIBLIOGRAPHIC REFERENCES

[1] Eilemberg Steenrod: Foundations of Algebraic Topology 1952

[2] Hurtado Hctor: Principles of the Theory of the Associations 2013

[3] Hurtado Hctor: Towards Mathematics Science 2010

[4] Sze-Tsen-Hu: Element of Modern Algebra 1965.

[5] National Plan of Productive Diversification: New Engines for development. Ministry

of Production. 2014, Lima - Peru. (www.produce.gob.pe).

{6} Deming W. Edwards, Quantity, Productivity and Competitiveness 1989.