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enterprises logistics

Agnieszka Stachowiak (eds.)

pyjvip

¡ S I

iUIS! MONOGRAPH

¡ M s

Publishing H ouse

of Poznan University of Technology

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Reviewers:

Prof. T om asz N ow akow ski, Ph.D. Eng.

Prof. R adosław P ytlak Ph.D . Eng.

Cover design, typesetting:

M arek D erbich

No part o f this book may be reproducer, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or other­

wise, without permission in writing from the author.

ISBN: 83-7143-856-1

Edition based on ready to print materials submitted by authors

Copyright © by Poznan University o f Technology, 2009

Publishing House o f Poznan University o f Technology pl. M. Skłodowskiej-Curie 2, 60-965 Poznań, Poland tel. +48 (0) 61 665 3516, faks +48 (0) 61 665 3583 e-mail: office_ed@put.poznan.pl

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C hapter IX

K lim arczyk G., H adas L., W yrw icka M.

M ulti - aspect A nalysis o f the Inventory m anagem ent system

in an A ssem bly C om pany ... I l l C hapter X

K ulinska E.

T he m odel o f logistics processes’ risk m a n a g e m e n t... 125 C hapter XI

O leskôw -Szlapka A ., Sobis J.

L ot sizing in lean m a n u fa ctu rin g ... 139 C hapter XII

Lubinski P., K lebaniuk-Lubinska A.

V ariants o f decupling points case s t u d y ...151 C hapter XIII

Bielecki M ., B oron K.

O rder handling as a quality factor o f w arehouse m anagem ent

in textile enterprises ... 161

ERP systems and artificial intelligence in logistics... 177

C hapter X IV

Z aw adzka L., B adurek J.

ERP m igration s tra te g ie s ... 179 C hapter X V

Fertsch M ., Paw lew ski P.

C om parison o f process sim ulation softw are technics ... 189 C hapter X VI

Pisz I.

A pplying fuzzy logic and soft logic to logistics projects m o d e llin g ... 201 C hapter X V II

Pruska Z., C yplik P.

A pplications o f selected tools o f artificial intelligence

in the field o f logistics and production r% a review ...2 1 1

A uthor’s index 223

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Chapter X

THE MODEL OF LOGISTICS PROCESSES’

RISK MANAGEMENT

E w a K U L IN S K A *

% INTRODUCTION

T his publication presents possibilities o f the application o f the principle o f V .A. G orbatova' specification for the purpose o f solving practical issues in the scope o f logistics processes m odelling.

O ne o f m ain assum ption o f logistics processes operation facilitating the im ple­

m entation o f objectives and influencing on adding values is the safety o f operation.

This safety is understood as efficient risk m anagem ent o f the process.

The m anagem ent consist in m odelling, arrangem ent, com position o f com plex process in cause and effect line o f logical structure facilitating the im plem entation o f objectives, delivery o f products o f as good added value as it is possible taken over from th e clients and com pany p oint o f view.

Each process characterizes by the fact that a set o f logically connected statem ents or actions are carried out to achieve som e result. T he replacem ent o f Input and O ut­

put characteristics is determ ined by a structure and operation. The structure provide expected functioning o f exam ined process, how ever the process operate adequately to as structure. Search o f structural and operation connections o f processes and opti­

mal logical structures form m ain assum ption o f specification principle.

2. ESSENCE OF CHARACTERIZATION PRINCIPLE

T he principle o f characterization consists in m utual interpretation o f operation m odel \|/a o f exam ined object (asset) w ith a m odel o f its structure \j/b. O btaining a result that is establishing m utual influence o f structures is obtained by the selection o f principles, rules o f pro per operation expressed by a m odel y a.

* Opole University o f Technology

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126 Kulińska E.

The suprem acy o f characterization over fam iliar m odels o f linear and dynam ic program m ing and others w hich for the purpose o f finding optim al variant o f a solutions im plicate the necessity o f generation and assessm ent o f a set o f all solu­

tions are m anifested in the analysis o f defined features o f solutions w ithout the need o f its subject generation. System interpretation o f tasks in accordance w ith the principle sw itches first o f all to the follow ing [5]:

1. determ ining (seeking) no t only the solutions bu t also characteristic features;

2. characteristics o f solutions should be referred to representatives (invariants) o f classes o f equivalent solutions;

3. class o f equivalent solutions is form ed as a result o f Input data interpretation o f solved group o f statem ents in categories o f solution s’ features.

C lasses o f equivalent solutions occu r usually in less am ount than solely solu­

tions and th e analysis o f solutions’ features can be conducted w ithout its direct (said issue) generation. The studies w hich are form al and are verified considering m ethodological m atter on given scope o f characterization principle construct the theory o f characterization. Its essence contains in m utual interpretation possibilities o f a m odel o f operation o f exam ined object w ith a m odel o f its structure. M utual interpretation possibilities o f m odels are obtained by the follow ing [5]:

• selection o f universal principles „correct operation” (expressed in a m odel o f operation),

• structural interpretation o f operation model.

U niversal principles „proper operation” are expressed by so called graph figures described as [13]:

• m andatory - abstract construction w hich in a form o f hom eom orphism should occur in a m odel o f operation „subject to” its error;

• forbidden - easily identifiable objects w hich isolation o r split (in a m odel o f operation) gives a guarantee o f obtaining a correctness o f object operation;

• neutral - are intended for performing transformations simplifying a model o f opera­

tion and as a result the forbidden figures and mandatory figures are not formed.

The object shall operate correctly i f m utually unique interpretation am ong rules o f its operation can b e defined and prove mutual unique interpretation betw een rules o f operation (described w ith operation model \j/a) and im plem enting structure (described w ith structure m odel \|/b) [13]. F or the purpose o f determ ination and prove unique interpretation o f these two m odels the follow ing assum ptions are taken:

• resources operate adequately to its structure,

• structure o f the resources is adequately to its expected m ethod o f operation.

T he essence o f characterization rules can be described in a general outline [5]:

< M'a, Vb, Po (Va, Vb) > (10.1) where:

\|/a- model o f operation,

\|/b~ model o f a structure,

Po (Va, M;b) is an atomic predicate which characterizes the possibility of the interpretation of a model of operation y a in categories o f structure model \|/b.

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The model o f logistics processes’ risk management 127 P ractical application o f characterization rule fo r the purpo se o f solving d eter­

m ined group o f tasks (problem s) require the preparation o f adequate theory ex­

pressed in detailed determ ination o f m odels v|/a> \|/b and a predicate Po [13].

3. THE APPLICATION OF CHARACTERIZATION PRINCIPLE

F or the purpose o f conducting researches and planning experim ents data ob ­ tained in the years 2003 - 2008 in tw o groups o f com panies w ill be applied. F irst group contains organizations w hich deal w ith risk m anagem ent; second group in­

cludes organizations w here risk control is no t applied. R esearches focused o n find­

ing com m on features for each o f group separately. The characterization referred to the following:

• m eters significant as far as form ing and realization o f added value for clients are concerned

• m eters significant as fa r as form ing and realization o f added value for a com ­ pany are concerned

• m eters o f logistics processes

• m eters applied in risk m anagem ent.

O n this basis a m odel o f assessm ent unlike m entioned above w as prepared, it is suitable only for axiological base o f risk m anagem ent o f logistics processes (it is no t applied to logistics processes m easurem ent, level o f added value neither risk m anagem ent).

T he application o f a principle o f V .A .G orbatov characterization used to solving research problem is presented in the diagram - fig. 1 0.1.

The application o f characterization principle in research problem solving consist in a preparation o f a theory w hich as far as axiological bases o f logistics processes conception o f risk m anagem ent is considered shall determ ine in detail the following:

• M odels o f com panies’ operation applying integrated system o f risk m anagem ent (\|/a) - include rules o f operation o f these com panies in 2003-2008.

• M odels o f com panies structure applying integrated system o f risk m anagem ent as w ell as com panies w hich do not apply integrated system o f risk m anagem ent (\[/b) - m odels com prising inform ation about com m on features o f these com pa­

nies in 2003-2008. O n the basis o f an analysis o f both m odels o f a structure a level o f form ed and im plem ented added value and actions influencing on it af­

terw ards w ill b e possible to determ ine.

• A tom ic predicate P0(y a, Yb) - determ ining a possibility o f an interpretation o f operation m odel in categories o f structure model.

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128 Kulińska E.

Fig. 10.1. A model o f the application o f characterization principle of V.A.Gorbatov for the purpose of research problem solving Source: own study

A level o f form ed and im plem ented added value w as described w ith the aid o f adequate meters. A base o f construction o f operation m odel and a structure is de­

term ination o f direction o f value change (increase o r decrease) o f each m eter in 2003-2008. Searched solution o f research problem is a set o f structure m odels (\|/b) w hich for a given case o f a com pany shall determ ine the following:

• level o f form ed and im plem ented added value o f logistics processes in com pa­

nies applying risk m anagem ents and in com panies w hich do n o t deal w ith risk m anagem ent;

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The model o f logistics processes’ risk management 129

• influence o f risk m anagem ent on the level o f form ed and im plem ented added value on the basis o f an analysis and com parison o f structure m odels in both group o f com panies.

Search o f optim al solutions is im plem ented on the basis o f research experim ents conducted in the follow ing phases:

1. C onstruction o f a set o f logic propositional function fo r tw o groups o f com pa­

nies - a function w as recorded and expressed in a language o f characterization principle the inform ation o f a level o f form ed and im plem ented added value.

2. S et o f graph m odels o f propositional functions for tw o groups o f com panies, it is a graph presentation o f logic propositional functions. In graph m odels in logic propositional function occur so called im possible objects w hich should be cleaved to obtain operation model.

3. Set o f operation m odels for tw o groups o f com panies M they represent rules o f operation o f tw o groups o f com panies as fa r as form ing and im plem enting added value through logistics processes is concerned.

4. S et o f structures’ m odels fo r tw o groups o f com panies - m odels are solutions o f form ed research problem . O n this basis it is possible to assess a level o f bank­

ruptcy risk and determ ining preventive actions.

C hanges in econom y and finance condition should b e w ritten in a language o f characterization principle in the follow ing form:

• set o f logic propositional functions - first phase brings result in a form o f pro- positional function for each o f com panies groups;

• graph m odels o f propositional functions - second p h ase brings resu lt in a form o f graph m odels for each o f com panies group;

• set o f graph m odels o f operation - third phase brings result in a set o f graph m odels o f operation for each com panies group;

• graph m odels o f a structure - forth phase brings result in a set o f graph m odels o f structures for each group o f com panies. R esults o f this phase are a solution for research problem .

Form al record o f solutions o f research problem is the follow ing relation:

where:

X - a set o f companies tested in respect o f risk management on forming added value of logistics processes Xj.

Z - set of companies using rules o f integrated risk management Zj R — set o f companies which do not use a system o f risk management R,

X = Z U R

V

A

s . ¿=1

x\*x

, W — all analyzed companies, (1 0 .3 )

v z

Z t

e

Z

, n -

amount o f companies with implemented system o f risk management, (

10.4)

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130 Kulinska E.

l | J i ^ ^

^

amount o f companies without implemented system o f risk management ( 1 0 . 5 )

b u t assu m in g th a t X = Z U R am ou n ts to w = m + n.

The influence o f risk management on forming and implementation o f added value through logistics processes shall be examined on the basis o f prepared m easures M.

- amount of considered measures. ( i o i |

T he application o f rules o f characterization principles require taking into ac­

count rules o f algebra o f logic, therefore M variable can assum e only value 0 or 1 (falsehood or truth). The application o f these rules force correct w ay o f interpreta­

tion o f analyzed m easures.

Therefore:

value 0 - M; variable takes, as value o f m easure decreased in tim e t;+1 in com ­ parison w ith preceding period t;.

value 1 ** Mi variable takes, as value o f m easure increased in tim e ti+i in com ­ parison w ith preceding period tj.

M j = {0,1} (1 0 .7 )

In such term s, Mj variable shall reflect a direction o f changes (increase or de­

crease) o f added value im plem ented through logistics process. It w ill be a basis o f assessm ent:

• correctness o f integrated system o f risk m anagem ent,

• size o f form ed and im plem ented added value trough logistic processes in both types o f com panies,

• characteristic features for a state o f the application o f a system o f risk m anage­

m ent in form ing and im plem entation o f added value trough logistics processes,

• characteristic features for a state w hen a system o f integrated risk m anagem ent is not applied in form ing and im plem entation o f added value trough logistics processes,

• verification and quantification o f an influence o f logistics processes form ing added value on designing a system o f risk m anagem ent,

• verification and quantification o f an influence o f risk m anagem ent on form ing added value through logistics processes,

• preparation o f a m odel o f quantification o f a change o f a level o f m easures o f added value o f logistics processes as a tool supporting decision process in risk m anagem ent o f com panies.

Taking advantage o f rules o f reliability theory bases for a generation o f group o f adequate m easures w ere applied. A ssum ing that process risk is a sum o f unreliabil­

ity (Z) and reliability (N) o f a system o f actions com posing on the process the equation w ill be true [1]:

R = Z U N = 1 (

10

.

8

)

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The model o f logistics processes’ risk management 131 and

R = 1 - N (1 0 .9 )

The risk o f logistics process is influenced b y the reliability structure determ in­

ing the reliability relation o f the process w ith the state o f actions reliability in­

cluded in the com position. T herefore, the analysis m ust take into consideration a division o f a process on individual sub-processes and actions th at is com ponents o f sub-processes. D ecom position follow s to isolate such sequence o f actions w hich characterizes w ith serial system . In such system a reliability structure o f individual actions is its product, hence the m ore actions in sub-process the less reliability oc­

cur. R eliability o f logistics sub-process o f serial system shall be defined w ith the follow ing formula:

N pL = N , N2...N n (1 0 .1 0 ) where:

Ni N2... Nn - reliability o f individual actions (component o f a sub-process).

Therefore, total risk o f the sub-process shall am ount as follows:

l i i - S M - f i W f i S (1 0. H >

where:

Rjl R2, Rn - risk occurring in individual actions o f logistics sub-process.

F or n num ber o f com ponent actions o f such logistic sub-process the am ount o f risk can b e calculated as follows:

Rn =--- | | ---

¡PfH ^1 *^2 —‘S'n-l ( 1 0 .1 2 )

where:

Sn -? means loss in n amount o f actions caused by occurrence o f risk factor in this domain rn, WPL - means analyzed index from determined domain or logistics function [6], [11].

Sn loss in individual actions depend on tim e loss caused by expansion o f dura­

tion o f logistics process due to risk factor occurrence. Logistics process accom ­ plishes assum ed objective, how ever it requires m ore tim e fo r com pletion. L oss in objective accom plishm ent o f logistics process caused b y risk factor occurrence will be presented as follow s [1]:

1 (10.13)

where:

At„ - time loss refer to given action (delay),

T - period determined for objective accomplishment.

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132 Kulinska E.

Therefore, total risk Rc for logistics process o f n actions w ill am ount to the fol­

low ing accordingly [1]:

Rc

= 1_[(1_^L)(1_^1)...(1--- )]

T T (10.14)

A m ount o f m easures for the analysis o f axiological dim ension o f risk m anage­

m ent o f logistics processes w ill depend on num bers considered in W Pl-

C onsidering synthetic character o f the preparation, a m ethod o f m odel im ple­

m entation on the basis o f exem plary transport process w ill be presented.

F or sim plification purposes, to explain a sense o f characterization principle, w e can assum e that a m ap o f risk distribution o f exam ined transport process is a table o f bivalent distribution {0,1} w here 0 m eans a risk o f little probability o f occur­

rence and little effects, easy to control, o f lo w cost; 1 - h igh risk o f high occurrence probability, extensive effects and the reduction o f effects w ill require great invest­

m ents; table fields w here is a relation betw een an action and given type o f risk are filled w ith a line.

Table 10.1. Decision table - risk identification for actions (components) o f transport process. Source: own study

Actions, process components

RISK TYPE

XI X2 X3 X4 X5 X6 X7

PI 1 1 - 0 - - 1

P2 - - 1 - - 1 -

P3 0 - 1 1 1 - 1

P4 - 1 - - 0 1 0

P5 0 - - 0 1 1 -

Presented decision table 1 allow s for form ulation the follow ing logic sentence describing risk m anagem ent o f transport process [1 2]:

F(Pal,P c22,..„ Pa55) = P,P3 P5VP,P4VP2P3V P,P3 P5VP3 P4P5VP2P4P5VP,P3P4 (10.15) M odelling consists in finding logic structure \|/b, w ith the aid o f the above de­

tailed function is im plem ented. O peration m odel vj/a, is specified as th e follow ing statem ent:

v|/a- < M ,S 2 ,S 3 > (10.16) where:

M - set o f propositional variables;

52 -:set o f relation defined with 2-elements alternative terms;

53 - set of relation defined with 3-elements alternative terms.

i f o . i S

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The model o f logistics processes’ risk management 133 S 2 = { { P1P4 }2 { P2P3}3} (10.18) S3 = { { P /P3 P5 }i{PiP3 Ps }4{P3 P4P5 M P2P4 P5 }6{ P1P3P4 }7} (10.19) On searched structure is imposed a condition so that its elements P01¡ could cre­

ate a partially ordered set a set which elements satisfy a relation o f partial arrange­

ment. it is described with the following properties:

• reflexivity:

• antisymmetry:

• transitivity:

Graphic illustration o f a partially ordered set is Hasse diagram which is a directed graph which was deprived o f all loops (property o f reflexibility) and closing bows (transitivity property). Examined possibilities o f creation o f logic structure (model are implemented in the scope o f the following phases:

• construction o f a model o f propositional function,

• determination and elimination o f forbidden figures from graph model o f pro- positional function (semantic table),

• construction o f graph model o f operation \|/3),

• construction graph model o f a structure \|/b.

Fig. 10.2. Graph model o f a function Source: own study

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134 Kulińska E.

T he analysis o f all possible variants o f H asse diagram (2! *2! *3! *3! *3! *3!* 3!=

236196) do no t bring to finding correct m odel o f a structure \|/a, because such solu­

tions do not exist for the sake o f the occurrence in graph m odel \j/a forbidden graph figures in a form , graph sub-m odels Qa and Q b.

Q a figure is graph sub-m odel recorded in a form o f cycle o f odd length w hich vertexes-w eighted are pairs o f changing in cycle’s w eight being indexes o f correct alternative term s [13].

Qb figure is graph sub-m odel recorded in a form o f triangle w ith pendulous ver­

texes. V ertexes o f a triangle have the sam e w eight and each o f them have addi­

tional w eight equal to pendulous vertex w eight. A vertex o f a triangle can also be one o f tw o rem aining vertexes o f a triangle [13].

G raph m odel o f propositional function includes (fig. 10.2) forbidden connec­

tions w hich do not correspond to any alternative term o f logic statem ent that is contain forbidden sub-m odels Qa and Qb.

F orbidden graph figures o f Q a and Q b types in analyzed exam ple are as fol­

lows:

Fig. 10.3. Forbidden graph figures. Source: own study on the basis: [6]

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The model o f logistics processes’ risk management 135 V ariables splitting should b e conducted in a w ay to elim inate all forbidden graph figures. F o r this purpose sem antic table is constructed - table.3 w hich w ith the aid o f 1 num ber designated occurrence o f a propositional variable that is a vertex in forbidden graph figure.

Table 10.2. Semantic table. Source: own study on the basis [12]

a,

ft 2)

Pi (1, 7)

Pi A 7)

a

P i

«)

Q,

P3 4)

Ps

0,

5)

a

Ps 7)

Pb (4>

55

ft

(4, 7)

P4

a

6) f l l S

(5, 7)

Pfc

<5, 6)

i t s ■'

a

4) P I QA7)

p5

<3,45, 7)

1Qa 0 0 0 1 0 0 0 0 0 1 0 u . 1 1 1

Q* 1 0 0 g i g 1 0 0 0 0 1 0 0 1 0 0

3Qa 1 0 0

0 • 0 0 0 1 0 1 0 1 1 0 0

Qa

A 0 0 0 j j g j 0 0 0 0 0 0 . 0 1 0 0 1

Qa 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0

aQa 0 1 0 - 0 0 0 0 0 1 0 0 0 1 0 0

Qb 0 0 0 I 0 0 0 0 0 1 0 1 0 0 0

b2Q 0 0 0 0 0 0 0 0 0 0 1 0 1 1

Q

I»3 0 1 0 0 | 0 0 1 0 0 0 1 0 0 0 0

b4Q 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0

hsQ 0 1 0 0 0 0 0 0 1 0 ' T - 0 0

0 0

Q 0 0 1 . O' 0 0 0 0 1 0 1 0 0 0 0

hQ 7 0 0 0 0 0 0 0 0 0 0

1 1 0 0 1

Q

b3 0 0 0 0 0 1 0 0 0 0 1 0 0 0

Q 0 0 0 0 0 0 0 1 0 0

t-

1 0 0 0

A s the forbidden figures are elim inated the splitting o f a diagram can be com ­ pleted. In this case three variables replica w as form ed: P2(3,6); P4(5,7); P5(l,4 ).

F unction F(P0li Po22). . P r55) takes the follow ing form:

F (P °\P a22>..., Pa55) =? P1P3 P5 V P,P4V P2P3 V P,P3P5> V P3 P4P5V P2-P4 P5VP,P3FV (10.23)

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136 Kulińska E.

Fig. 10.4. Hasse diagram after the disposal o f Qa and Qb figures in a operation model \|/a Source: own study on the basis [12]

A s result o f splitting three propositional variables new m odel o f operation was obtained \|/a, w hich corresponds to H asse diagram and provides correct realization o f propositional function. It m eans th at the conform ity o f structure functioning obtained as result o f the application o f characterization theory expressed with a procedure o f predicate im plem entation Po (\|/a, \|/b) for a propositional function described w ith a m odel \|/a and logic structures described w ith a m odel \|/b. N ew m odel \|/a’ takes the follow ing form:

\j/a’ = < M ,,S2,5S3’> (10.24) M ’ » { P ,’ P | P 2’P Í P3’P3’P4’ P4’ P5’ P5’ } (10.25) S2’ = { { P ,’P4’ }2 { P2’P3’ }3 } (10.26) W = {{ P i’Ps’ ^ | i { P p f f | f }4{P3’ P4T5’ }5{P2’P4’ P5’ }6{ P ,’P3’P4’ }7}(10.27)

D ue to the application o f characterization principle it m anager to change a process o f generation, searching and analyzing o f 236196 variants o f logic structures in the analyze o f sim ple sem antic table. The result was possible as a result o f preceded preparation o f a theory o f conditions transform ation o f a m odel y a in a m odel \|/b.

4. SUMMARY

A s the exam ple presents it, for the interpretation purposes - in the scope o f characterization principles — detailed theory o f forbidden, m andatory and neutral graph figures is form ed w hich are used to hom eom orphic transform ations. D ue to

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The model o f logistics processes’ risk management 137 these transform ations com plex and expensive processes o f alternative solutions testing are converted w ith p ro o f o f correctness o f the operation.

Besides, the application o f solutions on the basis o f algebra o f logic provides the possibility o f other view on research problem s solution, other than applied until now and these are greatly statistic m ethods. They can contribute to problem s iden­

tification w hich w ere no t noticed by schem atic o f applied solutions. In effect, is caused the increase o f calculation possibilities o f a change o f added value produced by the im plem entation o f a system o f risk m anagem ent.

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[8] Kulińska E., Meaning of orientation on processes in creation and realization of the value added, Foundations o f Management, vol.2/2009.

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publika Czeska, Malenovice 2009.

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[12] Kulińska E., Krupa T., Model oceny aksjologicznego wymiaru zarządzania ryzykiem procesów logistycznych,, p.80-86, Logistyka 4/2009.

[13] Nazaretów W.M, Kim D.P, Krupa T., Robotyka i elastycznie zautomatyzowana pro­

dukcja. Techniczna imitacja intelektu., WNT, Warszawa 1991.

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