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Planning principles in metallurgy
In management: the planning systems help to improve the quality of decisions; faster identify and assess risks; provide more accurate and timely information. Increased structure and discipline in planning, reporting and forecasting activities improve control over production processes in general.
Conclusion
The automation of planning activities at metallurgical enterprises presents many challenges, since it involves a multitude of conflicting criteria and competing objectives
and also requires a great deal of expertise and knowledge, both of which are not easy to model and codify.
A properly selected, installed and operated planning system helps to speed up production, reduce costs and increase the profitability of the company.
References
1. www.psimetals.de.
2. Tony Arnold J.R., Chapman Stephen N., Clive Lloyd M. Introduction to materials management. 7th ed. p. cm.
3. Fawls Tom. A Business Primer for Understanding Integrated Planning, Reporting and Control Systems. www.SpinningDisc.com.
Polikarpova M.G.
FUZZY-LOGIC-BASED RISK MANAGEMENT OF M&A DEALS OUTCOME: A CASY-STUDY A LARGE RUSSIAN METALLURGIC HOLDING
Abstract. The paper researches the application of several fuzzy logic concepts to evaluating risk rating of M&A projects undertaken by a large Russian Metallurgic Holding: maxmin compression, fuzzy relationship of preferences, additive compression. The way of expert answer treatment is presented for the possibility of further fuzzy logic methods application. 20 M&A projects are used as the empirical basis for the research. The methods applied show consistency in final estimates proving the ability of their use in MA deals' risk outcomes evaluation. The proposed method can be used to evaluate risk consequences for M&A deals. Keywords: fuzzy logic, fuzzy set, membership functions, rule matrix, risk, M&A, metallurgy
Currently M&A is one of the most solicited ways of developing an industrial enterprise. Though M&A deals embed material risks they are efficient to achieve the objectives that are unattainable given other long-term development strategies.
Being highly risky M&A deals often result in losses for the acquirer. As McKinsey found in 2008 70% of M&A resulted in business value destruction. Same time Russian M&A differ in several ways from abroad ones:
■ no common regulator and no unique pricing procedure exist;
■ market is rather closed, no unified statistics available;
■ there legal blank points enabling raider activity etc.;
■ legal system drawback in corporate conflicts resolution [2].
Generally the corporate culture to dealing with M&A deal consequences is not well worked out. As the M&A deal associated risks need to be dealt with, the paper has its objective to present the way of evaluating M&A risks based on fuzzy logic concept.
M&A deal realization passes three stages of its live-cycle:
1) project integration (negotiation process);
2) company reorganization (sales-and purchase agreement execution);
3) company integration (incl. corporate cultures) [4].
The majority of M&A deals are subject to UK common law, including deals taking place in off-shore jurisdictions.
When working out methodological principles of M&A deal risks evaluation for an industrial enterprise
considering metallurgic holding as an example industry-specifics should be accounted for:
■ geographic distance of integrated companies and their corporate cultures difference;
■ high capital-intensity of metallurgy, demand for huge initial investments, long period of investment pay-back;
■ acquisition of current and developing new plants is subject to external groups of interest influence. Dealing with them is of objective necessity;
■ all large metallurgy plants in Russia provide employment for whole cities implying high social responsibility of M&A projects;
■ technological similarity needs to be accounted for when merging metallurgical companies.
The M&A process complexity is driven by a high number of involved parties. Thus different stakeholders' possible actions were analyzed to account for most of the M&A deal risks.
Figure below presents the worked out process of project gross risk evaluation. The mechanism is self-adaptive and self-regulative. As risks at each of the stages are difficult to qualify fuzzy logic is used to evaluate gross risk. The fuzzy logic permits us to treat heterogeneous factors given lack of sufficient quantitative data [5].
According to the proposed mechanism individual risks were evaluated based on expert judgments for alternative investment projects.
The research is based on expert judgments for 20 M&A deals of one of the largest Russian metallurgy enterprises. 51 risk criteria have been chosen. Nine topmanagers were questioned to obtain their expert judgments.
As expert judgment might are subjective and are reasonably different from manager to manager the Delfi-method is used to iteratively process the filled-in questionnaires.
When ranking alternatives experts tend to provide different opinions. Therefore it becomes necessary to estimate consistency on expert judgments (the degree of expert concordance). Arriving at the quantitative measure of expect non-concordance helps to analyze the reasons for differences in opinions.
To measure expert judgments degree of concordance following measures are often used [7] :
■ spearman rank correlation coefficient;
■ dispersion concordance coefficient (Kendall rank correlation coefficient);
■ entropy concordance coefficient.
Non-parametric module of Statistics software was
used to estimate experts concordance within identified criteria of M&A deals risks. x2-Pearson criteria for Kendall rank correlation coefficient was used. For all risk
Final estimates are presented in Table 1. When the 1st iteration is accomplished, the following condition was checked:
max
i =1, m
{IK) - K01}< 0,0001.
(4)
Table 1
1st iteration results for Rykov algorithm are presented
>4.(0,05;19)
Thus
criteria the following holds: — ,bKp
the null hypothesis of expert judgments being consistent is not rejected.
Expert competence coefficients were estimated given ex post data on questionnaire output [6]. Rykov iterative algorithm was used to obtain competence coefficients.
Let's take as an example the case of country risk at the third statge of M&A deal estimation. Firstly take a look at the ranks of all M&A deals for each expert.
Secondly, at zero stage prior expert competence coef-
AK1 = 0,196 K1* = 0,307 K1 = 0,139
AK 1 = 0,117 K1* = 0,228 K1 = 0,103
AK3 = 0,108 K1* = 0,219 K3 = 0,099
AK 1 = 0,105 K* = 0,216 K1 = 0,098
AK5 = 0,120 K1* = 0,231 K5 = 0,105
AK 1 = 0,099 K* = 0,211 K1 = 0,095
AK} = 0,142 K 7 = 0,253 K1 = 0,114
AK8 = 0,153 K8* = 0,264 K3 = 0,119
AK 9 = 0,171 K9* = 0,283 K9 = 0,128
ficients are estimated: K^ average group estimated
= — = 1. Then m 9
are calculated:
x1 = ^ K{0 ■ Xj . Then adjusted expert
i=1
competence coefficients were obtained given the below formula:
As condition (4) does not hold, then 1st iteration steps are repeated once more. To accomplish the procedure 11 steps were needed. Final output by iteration is presented in Table 2. Expert competence coefficients on other risks were estimated similarly.
Table 2
Rykov algorithm application for expert competence coefficients estimation for country risk
AK1 =
1
max
j=1,n
{I x1 - Xj IF
(1)
i = 11, m,s = 0,001. Coefficient add-ons were based on the values of |x1 — xj |. Additive approach was
used to estimate adjusted competence coefficients:
K1 =K0 +AK1
(2)
Iteraion No. Deviation from previous iteration Expert competence coefficients
K1 K2 K3 K4 K5 K6 K7 K8 K9
1 0,02768 0,139 0,103 0,099 0,098 0,105 0,095 0,114 0,119 0,128
2 0,01208 0,151 0,099 0,093 0,091 0,102 0,087 0,116 0,124 0,137
3 0,01294 0,138 0,103 0,099 0,097 0,107 0,096 0,113 0,120 0,126
4 0,01255 0,150 0,100 0,093 0,091 0,103 0,088 0,115 0,124 0,136
5 0,00534 0,156 0,098 0,089 0,087 0,102 0,084 0,116 0,127 0,141
6 0,00235 0,158 0,097 0,087 0,086 0,102 0,082 0,116 0,128 0,143
7 0,00111 0,159 0,097 0,086 0,085 0,102 0,081 0,116 0,129 0,144
8 0,00056 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
9 0,00027 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
10 0,00015 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
11 0,00009 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
As the sum of coefficients needs to equal to unity, the obtained values were normalized using the following formula (3):
Generalized rank is obtained accounting for expert competence based on the ranking of risk sums for all objects (competence coefficients are used as the weights):
K1 =
1* K1
IK1*
i = 1
(3)
Riskk ( j) = £ K* Riskk ( j),
(5)
k = 1,51, j = 1,20.
Based on the proposed adaptively regulating mechanism of gross risk evaluation next step would be to estimate the M&A deals gross risk.
Fuzzy logic concept is an approach enabling to process information when purely quantitative data in not available . To mention it is possible to proceed from conventional models in theory of probability and expert judgments to fuzzy sets descriptions. As an example traditional distribution can be substituted by a distribution with fuzzy parameters. Expert judgments might be interpreted like membership functions that form the fuzzy classificatory [1].
Consequently membership functions for 51 criteria were formulated (expert values of [1;9] were mapped to unit interval [0;1]). As the risk criteria was a monotonical-ly increasing function, the following transformation took place:
x = = 1(X_1). (6)
x - x 8
max min
As a result risk was scaled to [0;1] values where the minimal ones corresponded to minimum risk and vice versa.
Four methods of fuzzy sets orderings were used in the paper based on:
1) maxmin compression;
2) fuzzy relationship of preferences;
3) additive compression.
1. Multivariate choice of alternatives based on max-min compression
Let trace the algorithm for M&A deals ranking based on fuzzy logic:
1. As the maximum values of membership function should correspond to the best alternative, it was transformed as follows:
(ai) = 1 -^(a, ).** (7)
2. Relative importance coefficients co . are obtained
on the basis of the first eigenvalue of the rule matrix. Rule matrix is produced with respect to the indicator hierarchy. The degree of indicator significance is determined according to the principles presented in Table 3.
a>J = ma2j , (8)
where aj is eigenvalue of the first eigenvector.
3. The alternatives ranking rule given different indicator significance is determined as the fuzzy sets intersection:
d = c? n c2ffl2 n...n camm. (9)
* Fuzzy logic was actively applied after Lotfi Zadeh published his article in 1965 (Zadeh, 1965). The motivation for the paper was to process complex and difficult-to-formalize real-world problems that conventional methods of systemic analysis fail to deal with.
** To mention new membership functions produce the non-riskiness measure.
Several approaches can be used to intersect the fuzzy sets. Nevertheless mostly the minimum is taken:
Hd(ar) = min(u (a)YJ,i =1 n. (10)
j =1,m J
4. The best alternative ai* is characterized by the highest value:
/Ud (a*) = max /Hd (a,). (11)
i=1,n
5. The values of juD (a*) correspond to non-riskiness level of M&S deals. Considering our objective of risk measurement the inverse values should be taken:
Vdfinal (a*) = 1 -Md (a*) (12)
Table 3
Table of indicator significance
Degree of significance Definition Description
1 Equal significance Both indicators equally contribute to the outcome
3 Immaterial significance dominance of parameter One of the indicators is somewhat more important, though it is immaterial
5 Strong significance Clear evidence is to choose on of the indicators
7 Very strong significance Strong evidence exists to prefer one indicator to another
9 Absolute significance One indicator should be definitely preferred to another
2,4,6,8 Intermediary values
Inverse to values presented above When i-th indicator is compared to j-th indicator the above presented values are assigned, when on opposite j-th indicator is compared to i-th the inverse of the above values are assigned
Then the higher is ¡j.dfinal" (a* ) value, the higher is the risk of deal.
When characteristic equation was solved, first eigenvalue for the rule matrix was \ = 63,386. Solving for the equation (8) relative importance coefficients ® . were
also obtained.
Having analyzed the outcome of m . expert values
third stage risks as the most important. Inter alia country risk, risk of the duties not accomplishment, and risk of company goods price decrease were considered to be the most important with the respective values assigned ®46 = 7,0895, ®50 = 7,0648, ®49 = 6,0752.
Finally all projects were ranked based on /uDFINAL(a*). First place corresponds to the highest risk, last - to the minimal. Based on the ranking Pakistan, Canada, Germany, Turkey were the riskiest M&A deals.
2. Multivariate choice of alternatives based on fuzzy relationship of preferences
When the alternatives are compared with respect to preference relationship, it is logical to assume non-dominating alternatives to be preferred. Mathematically speaking the problem converges to tracing out no dominating subset of alternatives within the fuzzy set.
Given R three corresponding fuzzy relationship can be formulated [3]:
■ fuzzy relationship of indifference:
Mr (ap, at) = max
(13)
(14)
MqMp, a) = = min
in {Mr, (ap,a,), Mr, (ap,a,),..., MRm (ap,a,)}.
(16)
2. Subset of non-dominated alternatives is chosen {A, n(Qj) for all p and i (i = 1, n; p = 1, n):
(ap) =
= 1 - sup a (ap, ai) - nQi (a, ap)}Vp,i, p * i
ap eA
3. Fuzzy relationship Q2 is obtained:
m
MQl(.ap,at) = Hri (ap,at).
J=i
(17)
(18)
4. Subset of non-dominated alternatives is found for {A,^(Q2)} for allp and i (i = 1,n;p = 1,n).
5. Final subset of non-dominating alternatives is found as the intersection of subsets {A,/u(Q,)} and {A,/u(Q2)} :
MND (a) = ^ n = mm«, Q).
Q2
Qi ' ^Q,
(19)
6. The most rational alternative to choose is the one having the highest degree of non-dominance:
min {1 -Mc, (ap x1 -MC, a)}, iin {^c](aPX MC] (a)}
■ fuzzy relationship of quasi-equivalence:
Mr1 (ap,a,) = min{mc1 (ap),McJ (a,)} ;
■ fuzzy relationship of strong preference: Mr, (ap , at) =
\Mc1 (ai) - Mc1 (ap ),if Mc1 (ai) ^ Mc1 (ap ) . (15) 10, if flc(ai) <Vc1(ap
As the obtained alternatives are non-dominated given the available information, they are considered to be the best.
Let there is A set and each alternative has several features J = 1, m . Information on pairwise comparison for all alternatives is presented in Rj relationship. The rational choice needs to be done given m relationships Rj on A set.
Matrixes of fuzzy relationships are formulated for all the fuzzy relationship R,,R2,...,Rm according to formula (15).
1. Fuzzy realtionship Q1 is constructed that symbolizes the intersection of relationships Q, = R, R2 H... H Rm :
„ND
a =<a | a e A, fj. (a) = sup fj. (a)k (20)
[ aeA J
To note not only aND alternatives are the best, sometimes weekly dominated alternatives might be of interest, i.e. the ones belonging to /uND (a) given the degree of confidence is no less then preapproved.
For 20 alternatives' membership functions 51 matrixes R,,R2,...,R51 of fuzzy relationship were constructed. Based on formula (16) Q, fuzzy relationship was obtained as the intersection Qx = Rx R2 H...HRm. Based on formula (17) subset of non-dominated alternatives was found {A, ^(Q,)} . Referring to principle (20) the final set was obtained.
Similar to maxmin compression four deals were considered as the most risky being assigned respective values of riskiness: Canada (/uND (a20) = 0,9593 ), Germany
(fiND(a17) = 0,9335), Pakistan (/uND(a4) = 0,8870), Turkey (/uND (a,) = 0,7915).
3. Multivariate choice of alternatives based on additive compression
Current method presents expert judgments as fuzzy numbers having membership functions of triangular form.
1. To estimate the importance parameters a linguistic variables are used: «not very important», «important», «very important». Linguistic variables are represented by the fuzzy numbers from the membership functions of triangular form.
Respectively:
1) not very important (HOB): n „™=<!0'—
HCB |0 0,2 0,4
2) important (B): n =]—;—; —
[0,3 0,5 0,7
3) very important (OB): ^ = {_^;_L;_1 1.
OB 10,6 0,8 1,0J
2. To estimate criteria Rj linguistic variables are also used: «very low risk», «low risk», «medium risk», «high risk», «very high risk».
Respectively:
1) very low risk (OH): n = \
OH 10 0,2
2) low risk (H): » ={ 1;
[0 0,2 0,4J
3) medium risk (C): „ = JA-_LAI;
[ 0,2'0,4'0,6 J
4) high risk (B): Mb = {A;_L;AI;
[0,4 0,6 0,8J
5) very high risk (OB): ^ = JA;_L;A1 .
OB {0,6 0,81,0 J
3. Criteria values for alternatives and their importance parameters are recorded.
4. Weighted estimates Ri are obtained as follows:
m ___
R *RJ, 1 = 1n, J = 1m.
J=1
5. When weighted estimates Ri are obtained, objects are compared. For the purpose fuzzy set I is introduced with values following the below rule:
¡uI (af) = sup min ¡uR (r).
r > r i=1,n 1
p-h
The best alternative is the one having the highest H1 (ai) value. I function values are interpreted as the
alternative level of riskiness.
Similarly to the previous approaches the metallurgy holding experts would treat the following projects as the most risk: Pakistan (^(a4) = 1) , Canada (^(a20) = 0,9260),
Turkey (M(a1) = 0,9240) , Germany (^(a17) = 0,9200).
The findings suggest fuzzy logic is a useful tool to evaluating gross risk of M&A projects. The gross risk estimate obtained enables to forecast the outcome of M&A deal, adjust the key financials and make the decision on whether to proceed with the deal or not during the first stage of M&A process.
Currently risk-management becomes an invaluable resort of strategic planning of Russian industrial enterprises that impacts the company value and might imply the rise of productivity. The proposed algorithm of M&A deals gross risk evaluation at OJSC Magnitogorsk Metallurgy Plant has proven its applicability and might be advised for further implementation at industrial enterprises in order to:
■ Identify and classify risks mostly impacting M&A deal outcome;
■ Provide complex and regular work on risk-management when running M&A deal to separate the duties within the Divisions and Levels of Management;
■ Improve the KPIs of M&A deals by decreasing the associated risks and optimizing costs to handle risk minimization;
■ Increase the efficiency of M&A project management by introducing additional criteria for decision-making and by receiving and analyzing feedback on M&A deals realization;
■ Support the growth in market capitalization, increase in credit and investment ratings;
■ Achieve the most beneficial state and to protect the current market niche.
References
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2. Bogatikov A.A. Why raiders and corruption prospers in Russia? M&A Journal, 2010, no. 7-8, pp. 91-95 (rus).
3. Borisov A.N., Alekseev A.V., Merkurieva G.V. et al. Fuzzy information treatment within the decision-support systems. Moscow: Radio and communication, 1989 (rus).
4. Polikarpova M.G. Current status and trends of integration in the Russian economy. ECO, 2010. no. 2, pp. 75-84 (rus).
5. Polikarpova M.G. Economic and mathematical analysis of the integration activities of the economic sectors of the Russian Federation. Vestnik Mag-nitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Noso-va. [Vestnik of Nosov Magnitogorsk State Technical Univeersity]. 2010. no. 3(31), pp. 73-77 (rus).
6. Rykov A.S. Systemic analysis: models and methos of decision-making and search optimization. Moscow: MISiS Publishing House, 2009.
7. Shmoilova R.A., Minashkin V.G., Sadovnikova N.A., Shuvalova E.B. Ed. Shmoilova R.A. Theory of statistics textbook. Moscow: Finance and Statistics Publ., 2003.
