MNRK-curs8&9.ppt

8/13/2019 MNRK-curs8&9.ppt

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COURSE NO. 7 DECREASING THE ACTION OF RISK FACTORSON BUSINESSES BY USING THE METHOD OF UTILITIESESTIMATION

CONTENTS:1. Introductory notions2. The algorithm of the method3. Case Study

Objectives:- understanding the necessity of using the modern calculation and optimization methodsfor managerial decisions taken in risky situations;

- learning the algorithm of the method and the specific mathematical model;- developing the abilities necessary to correctly solve some situations regarding

businesses in risky situations.

Recommended bibliography:Horobet A. - Managementul riscului n investiiile internaionale. Editura All. Bech, 2005, Bucureti Iliescu C. - Mangementul riscului, Editura Dacia, 2000,Bucureti Ilie L.,- Managementul firmei. Editura Dacia, 2003, Bucureti


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1. Introductory notionsThe manager (the managerial team) uses this method in order to choosean operating variant aut of many possible variants. The algorithm of themethod is based on the following axioms:a) If X and Y are the consequences of two operating variants, then thevariant with the consequence X is preferred to the one with theconsequence Y if and only if U(X)>U(Y),where: U(X) = the utility of the variant with the consequence X

U(Y) = the utility of the variant with the consequence Y

b) If the utilities of two variants of the multitude of possible variants areconsidered to be known, according to them, the utilities of the otherfunctions can be determined;

c) If the utility function has the properties a and b, then it can suffer a linearprofitiv transformation.

The consequence is a numerical value that is assigned to every criterionestablished by the decision body corresponding to every operating variant.The consequence is expressed in different measurement units (length,weight, time, quantity, etc.).

The utility is a numerical value permitting the unitary (non-dimensional)expression of the consequence (in order to be able to make arithmeticaloperations with the consequences).


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2. THE ALGORITHM OF THE METHOD Establish the variants of managerial operation. Establish the criteria according to which each variant is

analysed. Establish the consequences for every criterion and variant. Transform consequences into utilities. Rank the criteria. Calculate the importance coefficients for each criterion. Establish the utility function for each variant by weighting it

with the value of the importance coefficient. Choose the optimum variant (by applying the axiom a).


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3. CASE STUDY NO. 8 The company AGRO S.R.L. has prospected three possible markets so as to launch itsproduct TON -2000 (tuna fish can). The market analysis is based on the following criteria:

C1 = product quality;

C2 = product cost;C3 = sales average value per day;C4 = risk rate

The consequences for every criterion and variant are given by the following matrix (these values resulted by measurements, calculation and evaluation):

Ci

Vi C 1 C 2 C 3 C 4

V1 1.5/1 1.2/1 46 0.6

V2 1/1 0.8/1 80 0.4

V3 0.9/1 1.4/1 33 0.8

We have to establish the optimum variant for managerial operation for the company AGRO S.R.L. Solution:a) The operating variants are represented by the 3 markets which the product can be launchedon (V1 = market no. 1, V2 = market no. 2, V3 = market no. 3)b) The criteria for analysing every variant are established in such a manner that the most

relevant consequences for the company should result (product quality, product cost, salesaverage value per day, risk rate).


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c) The consequences resulted by measuring, evaluating and comparing, the mathematicalcalculation, are determined by specialists and written down for every variant and criterion. Inour case:

C11= 1.5/1 and it expresses the ratio between the (companys) product quality and

the quality of a similar product existing on the market no. 1.C12= 1/1 and it expresses the ratio between the (companys) product cost and the

cost of a similar product existing on the market no. 1.C13= 46, it represents the sales average value of the product / day;C14= 0.6, the risk coefficient assumed if it is decided to launch the companys

product on the market no. 1.d) In order to transform consequences into utilities, we use the following relations:

U(Cij) = , when the optimal condition is MINIMUM

U(Cij) = , when the optimal condition is MAXIMUM

Cij = the consequence for the variant i and the criterion jUij = the utility for the variant i and the criterion jIn order to apply one of the above relations, we need to write down in the matrix theoptimum type according to the nature and action of the corresponding criterion. Forinstance, for C1 (the product quality) we apply the MAXIMUM optimal type. For C4 (riskrate) the optimal type is MINIMUM.

CijCijmin

CijCijmin


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e) Criterion ranking is done by comparing them one to another in a comparing matrix, thus:

C1 C 2 C 3 C 4 RANK

C 1 1 0 0 III

C2 0 0 0 IV

C3 1 1 0 II

C 4 1 1 1 I

C1 product qualityC2 product costC3 sales average value per dayC4 risk rateC1 C2 (C1 is more important so we write the figure 1 in its corresponding box) C1 C3 (C3 is more important so we write the figure 0) - In this way, we continue till the end;- By summing up the points, we determine the rank of the criterion in the hierarchy;


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f) The importance coefficient Kj is determined for every criterion with the followingrelation:

where: j = the criterion no.; 2 = constant value; rank = the rank given to the criterion in thehierarchythus:

K1 = ; K2 =

2loc1

Kj

12.08

11

23

06.016

11

24

g) In order to establish the utility, in the given matrix we calculate the utilities according tothe relations given in point d, then we calculate the importance coefficients and wemultiply every utility with the value of the corresponding coefficient.

K 1C

1

0.12 K

2C

2

0.06 K

3C

3

0.25 K

4C

4

0.50 The sum of utilities

V1

1 0.12=

0.12 0.039 0.14 0.33 0.62

V 2 0.07 0.06 0.25 0.50 0.88

V3 0.07 0.03 0.17 0.25 0.52

In the end, the companys manager chooses the 2nd variant, as U(V2) > U(V1 and V3).

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MNRK-curs8&9.ppt