COMPLEXITY OF PRODUCTION STRUCTURESfacta.junis.ni.ac.rs/me/me2009/me2009-10.pdfComplexity of...

FACTA UNIVERSITATIS Series: Mechanical Engineering Vol. 7, No 1, 2009, pp. 119 - 136

COMPLEXITY OF PRODUCTION STRUCTURES

UDC 658.51

Rado Maksimović1, Srdjan Petrović2

1Faculty of Technical Sciences, University of Novi Sad, Serbia 2Metals Banka, Serbia

E-mail: [email protected]

Abstract. The aim of this paper is to contribute to the development of procedures for the design of effective production structures of an enterprise. The paper considers the possibilities of making production structures more manageable by means of lowering the degree of complexity of those structures. Complexity of a production structure is a characteristic defined by the number of structural elements and their interdependence. Special attention is given to the influence of replacing the traditional approaches (individual and process) by modern approaches (group and product) on the complexity of production structures.

Key Words: Production Structure, Enterprise, Complexity

1. INTRODUCTION

Enterprise-environment relations and disorders in the work process, bearing in mind their accidental character, have lead to a situation in which industrial system structures - - enterprises develop in the following conditions:

uncertainty of the environment and lack of knowledge about the characteristics of enterprise-environment relation,

frequent changes in the development of technologies and changes in the approach to organization, from mechanistic - based on the principle

of division of labor and management suitable in cases of specified work conditions, to or-ganic - based on the principle of functioning of the living beings and on management based on feedback, which is suitable when the work conditions are not specified.

These conditions, as part of existence, survival and development of enterprises, are characterized by a high frequency of changes which lead to technological, organizational and management problems that need to be solved in real time [1]. Solutions to these problems, in turn, cause new changes and the process goes on continually.

Received February 20, 2009

120 R. MAKSIMOVIĆ, S. PETROVIĆ

The relations in the production program of enterprises [2] determine the basic types of production structures which are presented as Types I-IV in Fig. 1. They have the following characteristics:

Type I: The field of slow technologies and technological and spatial structures of general character

Type II: The field of technological and spatial structures of universal character Type III: The field of technological and spatial structures of productive character Type IV: The field of fast technologies and technological and spatial structures of

purposeful character.

Fig. 1 Relations in the production program of an enterprise

The presented relations and tendencies in the development of production, organiza-tional and management structures of enterprises increase the requirements concerning the characteristics of those structures. These requirements are presented in Fig. 1 and are re-flected in:

the need to achieve a high degree of integration of material, energy and information flows on the one hand, and of the functions of an enterprise on the other, for the purpose of developing the most suitable procedures of production, organization and management the tendency of constant increase in the complexity of elements and structures of an enterprise, expressed in the function of the characteristics of production programs; changes in the work process - from labor intensive to capital intensive to knowledge intensive processes the requirements to free the potential of employees by enriching the content of work and removing people from work that is mentally and physically strenuous and dan-gerous -automation of the work process [2], [3].

In the earlier research of production structures [2], [4], [5], the basis for the develop-ment of effective enterprises was formed. The idea of this basis (Fig. 2) is: a change of the flow and structure designing approach - from process to product.

Complexity of Production Structures 121

The result of the mentioned changes in the approach is the creation of the Working Unit, the basic module of an effective enterprise - designated as WU in Fig. 2. Working Unit is defined as part of the production structure of an enterprise capable to carry out a certain task which is part of the work program, should the conditions of adequate space, equipment and the required structure of employees be met.

Working Unit has the following characteristics:

it is independent of the other parts of the system's structure concerning the human resources and technical capacity, it is responsible for completion of part of a program, concerning the amount, quality and deadlines and it is suitable for process automa-tion.

2. ENTERPRISES COMPLEXITY: A BRIEF LITERATURE REVIEW

Earlier research of the complexity of production systems are characterized by different ways of looking at complexity and can be divided into four groups:

1) Theoretical considerations of production systems complexity The most recent theoretical views on the complexity of production structures are pri-

marily based on the general principles of the systems theory and mathematical modeling of a system's structure in general sense.

Methods of non-linear dynamics and simulation techniques are used in order to iden-tify the amount and quality of data required for the analysis of a system's structure [6]. There have also been attempts to reduce the chaos and miscellany that cause dynamic changes and behaviors in a system to the simple model of a production system that en-ables its stability.

Finally, complexity of a production system's structure is a key characteristic in the ap-proaches which introduce the concepts of knowledge management and organizational learning [7].

2) Measuring the complexity of production systems Theoretical models have already pointed to the need to measure the complexity of

production systems. Such a need is particularly significant in practical approaches which use the complexity of production systems in designing and managing their processes.

Fig. 2 The basic changes in approaches to

production structures designing


There is a connection between the complexity of a system and the system's perform-ances, and in the measuring methods, the following criteria are used most frequently: the number of elements in a structure, costs, manageability [8]. The systems of designating structural components lead to the concept of structural complexity. This concept intro-duces into the way of its measuring the interdependence between components and a vari-ety of information that they exchange between one another [8], [9]. There is also an inter-esting aspect that considers the so-called management complexity, but only in the case of industrial co-operation of systems from different lines of business, i.e. on the level of complex socio-technical systems.

3) Decreasing the complexity of production systems The need for decreasing the complexity of production systems has been widely ac-

knowledged. Hypothetical lean models are not applicable. A practical approach is being sought that would enable the transition from highly complex production systems to small scale systems (lean factory). Case studies have mostly used analysis models based on frameworks. The need for decreasing the complexity of a production structure is particu-larly evident when solving problems of planning and work distribution in the systems with a high product variety. In most of the case studies this problem has not been adequately solved [10].

4) The effect of complexity on effectiveness Lately, complexity has been observed as a key characteristic that determines the qual-

ity of production systems. There have been investigations into the effect of complexity of production systems on the character of production flows, organization of an enterprise, management actions, information support and total effectiveness of business.

Special attention is given to case studies which include: the structure of the so-called virtual enterprises, the complexity of the development process of a product, market re-search and limitations from the environment, managing an enterprise which is not based on hierarchical organizational structure [11]. The complexity of management procedures and appropriate management methods (ERP, MRP, JIT...) are also related to the complexity of the object that is being managed - the production system and its performances [12].

3. PRODUCTION STRUCTURES COMPLEXITY

3.1. A Definition

The measure of complexity of the structure of industrial systems-enterprises, defined as the degree of complexity, or variety, is extremely important. In accordance with the principle of the minimum necessary in the development procedures of production, organ-izational and management structures of a system, the complexity of the observed part of the structure represents: the measure of conditionality- interdependence between the ob-served part of the structure and its other parts, the ground for the development of proce-dures for simplification of elements, a connection between elements and the structure as a whole, and the ground for comparison with structures of similar characteristics.

Complexity is also a measure of quality of the procedures for the designing and ad-vancement of an enterprise's structures [13]. The degree of complexity of industrial system structures is determined by the characteristics and the number of structural elements, the


position of elements in the structure and the relations between the elements of the structure. Therefore, it is one of the basic general characteristics of industrial systems - enterprises.

In accordance with the character of flows in a system (material, energy and information) and of the structures of a system (production, organizational, management), complexity, as a general characteristic of an enterprise, can be measured by the degree of complexity of production structures, the degree of complexity of organizational structures and the de-gree of complexity of management structures of an enterprise [13].

The project of production structures of an industrial system basically defines the static structure. The production function is only made possible if resulting from the harmony of the other functions of an enterprise (determined by the project of organizational structures) to which control procedures (determined by the project of control structures) are applied.

The project is used to determine the characteristics and the number of elements of a structure (based on the elaboration of work procedures and calculations), to determine the position of elements in a structure upon the chosen approaches to flows designing, and to establish relationships between elements of a structure by designing of system's lay-out, i.e. to determine the causes of complexity of production structures.

In that way the degree of complexity of production structures is determined by the quality of project of material flows and system's lay-out. The degree of complexity is a measure of quality of a project whereby the lower degree of complexity means a better quality of a product and vice versa.

Bearing in mind the need for flows simplification in a system (material, energy and information flows), whose variety generates limitations to the effective work process, the degree of complexity of production structures is determined by conditionality of flows in a sys-tem, as a relation between the total number of connections between ele-ments and the number of structural elements, as shown in Fig. 3 [13].

When the degree of complexity of production structures is consid-ered, in accordance with the defini-tion in Fig. 3, the elements of a structure are the basic parts of system-workplaces, and their interrelations are observed.

A more detailed analysis of the presented relation has shown [13] the existence of a connection between the degree of complexity (variety of production structures) and char-acteristics of certain types of material flows as follows:

Type I It represents a discontinuous flow and comprises several workplaces which are not

interrelated (Fig. 4a), resulting in the degree of complexity κI = 0 (Fig. 4b).

Fig. 3 Complexity Degree of the Production Flows


Fig. 4 Complexity degree for Type I of production flows

Type II It represents a discontinuous flow of process type and comprises all the workplaces in

a system (Fig 5a) which are not interrelated, resulting in the degree of complexity with these limits (Fig. 5b):

upper limit-maximum degree of complexity determined by the connection between one element and all other elements of a structure:

)1()1(max1)( −=−

=⎟⎠

⎞⎜⎝

⎛

≅κ∑=

= mmmm

m

mmi

ii

upII (1)

lower limit- the degree of complexity determined by the most complex type of flow, with two machines at every workplace (Fig. 5a):

mm

mm

ms

mi

ii

unII

95213242)5(51)( −≅⋅+⋅+⋅+−

≅⎟⎠

⎞⎜⎝

⎛

≅κ∑=

= (2)

Fig. 5 Complexity degree for Type II of production flows


Type III It represents a continuous flow and comprises workplaces distributed according to the

sequence of stages (Fig. 6a), resulting in the following degree of complexity (Fig. 6b): upper limit - the degree of complexity determined by the most complex type of a multi-product flow:

m

upIII

95)( −≅κ (3)

lower limit - the degree of complexity determined by the complexity of flow with two technological systems at ≈1/3 workplaces (Fig. 6a):

mm

mm

m

ms

mi

ii

unIII

35,212)

22(2)

22(3

1)( −≅⋅+

−+

−

≅⎟⎠

⎞⎜⎝

⎛

≅κ∑=

= (4)

Fig. 6 Complexity degree for type III of production flows

Type IV It represents a continuous flow and comprises several workplaces distributed accord-

ing to the sequence of stages (Fig. 7a) resulting in the degree of complexity in the fol-lowing limits (Fig. 7b):

upper limit - the degree of complexity determined by the complexity of flow with two machines at ≈1/3 workplaces:

m

upIIV

35,2)( −≅κ (5)

lower limit - the degree of complexity determined by the complexity of flow with one machine at every workplace (Fig. 7a):

mm

mm

ms

mi

ii

unIV

2212)2(21)( −≅⋅+−

≅⎟⎠

⎞⎜⎝

⎛

≅κ∑=

= (6)


Fig. 7 Complexity degree for Type IV of production flows

The relation between the degree of complexity and conditionality of flows, shown in Fig. 8, is determined upon:

the total number of structural elements determined upon the relation load/capacity the total number of connections between structural elements determined by the analysis of technological procedures.

This relation enables qualitative analysis of material flows types and the development of criteria for selection of the most favorable variant.

Fig. 8 Analysis of production structures complexity degree


3.2. Results of the research into production structures complexity

Research into the degree of complexity of production structures was conducted in more than thirty different cases-enterprises with different lines of work - production pro-grams, and gave results which are presented further on using the example of analyzing a machine tool manufacturing enterprise [13], [14].

The analysis of complexity was carried out by taking the following factors into con-sideration:

structures in state - production structures based on individual approach to material flows designing and process approach to production structures designing a certain number of newly projected possible variants of production structures in which, in accordance with the principles in Fig. 5, there was a switch to group ap-proach to material flows designing and product approach to structure designing.

The data presented about a structure in state are: the number of different work objects: 123, the number of elements (workplaces): 30, values that characterize the state of pro-duction structure - a list of workplaces (Table 1) and load/capacity ratio (Fig. 9).

Table 1 Data About Production Structure- State

Workplace (Code)

Load [min/year]

Capacity [min/year] No Loading

degree ηii 0120 255,368 180,000 2 0.71 0150 46,885 180,000 1 0.26 0160 94,205 180,000 1 0.52 0170 75,305 180,000 1 0.42 0180 57,695 180,000 1 0.32 0230 152,228 180,000 1 0.85 0240 176,997 180,000 1 0.98 0250 112,528 180,000 1 0.63 0260 1,282,187 180,000 8 0.89 0320 257,512 180,000 2 0.72 0330 170,409 180,000 1 0.95 0340 25,268 180,000 1 0.14 0350 150,817 180,000 1 0.84 0390 194,658 180,000 1 1.08 0420 123,111 180,000 1 0.68 0430 1,233,318 180,000 7 0.98 0490 347,685 180,000 2 0.97 0710 69,215 180,000 1 0.38 0810 31,660 180,000 1 0.18 0820 155,020 180,000 1 0.86 0840 548,328 180,000 3 1.02 0850 509,912 180,000 3 0.94 0870 170,685 180,000 1 0.95 0920 185,380 180,000 1 1.03 1010 585,035 180,000 4 0.81 2510 64,600 180,000 1 0.36 2520 336,610 180,000 2 0.93 2530 113,861 180,000 1 0.63 6010 180 180,000 1 0.01 6020 180 180,000 1 0.01

Fig. 9 Loading degree for the example of

state of production structure


By revitalization procedure two variants of production structure were designed. They had the following characteristics:

Variant 1: - number of working units: 2 - number of different work objects: WU 1: 85; WU 2: 38 - number of elements (workplaces): WU 1: 19; WU 2: 20 - characteristics of Variant 1 of the production structure: * for WU 1: specification of the workplaces (Table 2) and load/capacity ratio (Fig. 10) * for WU 2: specification of the workplaces (Table 3) and load/capacity ratio (Fig. 11).

Table 2 Data About Production Structure - Variant 1, WU 1 Workplace

(Code) Load

[min/god] Capacity [min/god] No Loading

degree ηii 0240 176,997 180,000 1 0.98 0840 196,473 180,000 1 1.09 2530 70,106 180,000 1 0.39 0850 461,634 180,000 3 0.85 0260 1,137,697 180,000 7 0.90 1010 208,258 180,000 2 0.58 6010 180 180,000 1 0.01 0320 257,512 180,000 2 0.72 0120 181,427 180,000 1 1.01 0430 325,110 180,000 2 0.90 0490 347,685 180,000 2 0.97 0820 155,020 180,000 1 0.86 0250 112,528 180,000 1 0.63 6020 180 180,000 1 0.01 0150 46,885 180,000 1 0.26 0230 152,228 180,000 1 0.85 0810 31,660 180,000 1 0.18 0920 185,380 180,000 1 1.03 0870 170,685 180,000 1 0.95

Fig. 10 Loading degree for the example of WU 1 in Variant 1

Table 3 Data About Production Structure - Variant 1, WU 2

Workplace (Code)

Load [min/year]


degree ηii

0120 73,942 180,000 1 0.41 0430 908,208 180,000 5 1.01 1010 376,778 180,000 2 1.05 0330 170,409 180,000 1 0.95 6020 180 180,000 1 0.01 0840 351,891 180,000 2 0.98 2530 43,755 180,000 1 0.24 0420 123,111 180,000 1 0.68 6010 180 180,000 1 0.01 0260 144,490 180,000 1 0.80 0710 69,215 180,000 1 0.38 0170 75,305 180,000 1 0.42 0160 94,205 180,000 1 0.52 2510 64,600 180,000 1 0.36 0180 57,695 180,000 1 0.32 2520 336,610 180,000 2 0.93 0850 44,278 180,000 1 0.25 0390 194,658 180,000 1 1.08 0350 150,817 180,000 1 0.84 0340 25,268 180,000 1 0.14



Variant 2: - number of working units: 4 - number of different work objects: WU 1: 62; WU 2: 23, WU 3: 26; WU 4: 12 - number of elements (workplaces): WU 1: 16; WU 2: 18, WU 3: 11; WU 4: 16 - characteristics of Variant 2 of the production structure: * for WU 1: specification of the workplaces (Table 4) and load/capacity ratio (Fig. 12) * for WU 2: specification of the workplaces (Table 5) and load/capacity ratio (Fig. 13) * for WU 3: specification of the workplaces (Table 6) and load/capacity ratio (Fig. 14) * for WU 4: specification of the workplaces (Table 7) and load/capacity ratio (Fig. 15).


(Code) Load

[min/year] Capacity

[min/year] No Loading degree ηii

0240 155,822 180,000 1 0.87 0840 170,545 180,000 1 0.95 2530 58,091 180,000 1 0.32 0850 108,903 180,000 1 0.61 0260 547,025 180,000 3 1.01 1010 163,513 180,000 1 0.91 6010 180 180,000 1 0.01 0320 195,022 180,000 1 1.08 0120 92,981 180,000 1 0.52 0430 237,805 180,000 2 0.67 0490 321,940 180,000 2 0.89 0820 45,185 180,000 1 0.25 0150 46,885 180,000 1 0.26 0250 73,625 180,000 1 0.41 0230 37,315 180,000 1 0.21 0870 8,265 180,000 1 0.05



(Code) Load

[min/year] Capacity

[min/year] No Loading degree ηii

0120 88,446 180,000 1 0.49 0250 38,903 180,000 1 0.22 6020 180 180,000 1 0.01 0320 62,490 180,000 1 0.35 6010 180 180,000 1 0.01 0820 109,835 180,000 1 0.61 0840 25,892 180,000 1 0.14 0850 352,742 180,000 2 0.99 0260 590,672 180,000 4 0.82 2530 12,015 180,000 1 0.07 0240 21,175 180,000 1 0.12 0430 87,305 180,000 1 0.49 1010 44,745 180,000 1 0.25 0490 25,745 180,000 1 0.14 0230 114,913 180,000 1 0.64 0810 31,660 180,000 1 0.18 0920 185,380 180,000 1 1.03 0870 162,420 180,000 1 0.90




Workplace (Code)

Load [min/year]


degree ηii

0120 73,942 180,000 1 0.41

0430 642,288 180,000 4 0.87

1010 254,458 180,000 2 0.71

0330 103,950 180,000 1 0.58

6020 180 180,000 1 0.01

0840 243,405 180,000 2 0.68

2530 43,755 180,000 1 0.24

0420 14,330 180,000 1 0.08

6010 180 180,000 1 0.01

0260 8,670 180,000 1 0.05

0710 54,135 180,000 1 0.30



Workplace (Code)

Load [min/year]


degree ηii

0170 75,305 180,000 1 0.42 0160 94,205 180,000 1 0.52 2510 64,600 180,000 1 0.36 0180 57,695 180,000 1 0.32 0330 66,459 180,000 1 0.37 0430 283,920 180,000 2 0.79 2520 336,610 180,000 2 0.93 0420 108,781 180,000 1 0.60 0710 15,080 180,000 1 0.08 0840 108,486 180,000 1 0.60 1010 122,320 180,000 1 0.68 0260 135,820 180,000 1 0.75 0850 44,278 180,000 1 0.25 0390 194,658 180,000 1 1.08 0350 150,817 180,000 1 0.84 0340 25,268 180,000 1 0.14


What follows for the given example are the results of the analysis of complexity de-gree for all the considered variants of production structures.

The existing variant of production structure (state)


The observed variant of production structure was designed according to process prin-ciple which generated relations between the elements and the degree of complexity pre-sented in Fig. 16.

STATE

m = 32; ∑mi = 361; κ = 11,28

Fig. 16 Complexity degree for the state of production structure

Project - Variant 1 of the production structure

The observed variant of production structures was designed according to product principle with two WUs which generated relations between the elements and the degree of complexity presented in Fig. 17.

Project - Variant 2 of production structure

The observed variant of production structure was designed upon the product principle with four WUs which generated relations between the elements and the degree of com-plexity presented in Fig. 18.


Variant 1 - WU 1

m = 21; ∑mi = 190; κ = 9,05

Variant 1 - WU 2

m = 22; ∑mi = 130; κ = 5,90

Fig. 17 Complexity degree for Variant 1 of production structure - project


Variant 2

WU 1

WU 2

m = 18; ∑mi = 68; κ = 3,78 m = 22; ∑mi = 60; κ = 3,00

WU 3

WU 4

m = 13; ∑mi = 34; κ = 2,61 m = 18; ∑mi = 56; κ = 3,11

Fig. 18 Complexity degree for Variant 2 of production structure - project


The analysis of the values in Figs. 16, 17 and 18 and dependency (m-κ) in Fig. 19 for the observed example of production structure shows that:

by projecting production structures of an enterprise on the basis of group approach in flows designing, transformation from process to product flows designing is made possible, by designing more variants of production structures, their degree of complexity can be significantly managed and the degree of complexity of a certain variant of production structure is determined by the quality of project of working units (WU) concerning their structure and size.

Fig. 19 Complexity degree for all the observed structure variants

3.3. The possibilities of designing production structures of lower complexity

Experience in development of production structures with WU as the core has shown that this approach enables the transformation from the most widespread process flow de-sign into the more effective product flow design [13], [14], [15], [16], [17]. The depend-ency (m-κ) which was analyzed in real enterprises [18], [19] shows that additional analysis is needed towards the selection of the most adequate variant of production structure, in the sense of moving towards the lower limit of the degree of complexity of flows. The possibilities of lowering the degree of complexity of production structures are reduced to projects shown in Fig. 20.


Fig. 20 The possibilities of lowering the complexity degree of production structures

4. CONCLUSION

The contribution of this paper is in the definitions and determination of the measures of the enterprise's production structures complexity. Production structures complexity is defined by complexity degree. While in the great body of literature complexity is measured by size (number of structural elements), this paper observes the complexity degree as comprising a number of interrelationships between the elements of a structure, beside the number of elements. Complexity of production structures is thus identified as complexity of a network of flows in a system.

Analyses of complexity of production structures performed on thirty different produc-tion programs gave results which mostly coincide with the results presented in this text. Therefore, the following can be concluded:

"Unlike in process flow designing, designing production structures of an enterprise on the principles of group and product approach, as independent working units, form the basis for lowering the degree of complexity of structures".

Complexity research results in defining and measuring the key performances which illustrate the quality of the structure of an enterprise. In this way, through different analyses, the basis has been formed for quality evaluation as well as for comparison of real enterprises' structures.

However, flexibility and complexity characteristics of enterprises' structures, the way they are defined in this paper, could be used in future research as criteria for the analysis and choice of the optimum variant in the procedures of designing structures of enterprises.

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SLOŽENOST PROIZVODNIH STRUKTURA

Rado M. Maksimović, Srdjan Petrović

Rad predstavlja doprinos razvoju postupaka oblikovanja efektivnih proizvodnih struktura preduzeća. Razmatraju se mogućnosti povišenja pogodnosti upravljanja proizvodnih struktura putem sniženja njihovog stepena složenosti. Složenost proizvodnjih struktura je karakteristika definisana putem beoja elemenata i njihove međusobne povezanosti. Posebna pažnja usmerena je na uticaj zamene tradicionalnih (individualnih i procesnih) modernim (grupnim i predmetnim) prilazima u projektovanju na složenost proizvodnih struktura.

Key words: Proizvodna struktura, preduzeće, složenost

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