enterprises logistics
Agnieszka Stachowiak (eds.)
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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
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
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.
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.
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;
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 . ¿=1x\*x
, W — all analyzed companies, (1 0 .3 )v z
„ Z te
Z, n -
amount o f companies with implemented system o f risk management, (10.4)
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
)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.
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
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
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]
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
h°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
h°
Q 0 0 0 0 0 0 0 1 0 0t-
1 0 0 0A 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)
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
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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