Logic Control in Management

Logical, continuous (analog) and discrete binding behavior in the organization

• It is possible to identify three fundamentally different types of links in terms of the type of relationships between components of the organization (eg employees, control and controlled systems, etc.). There are logical types, analog and discrete types of links.

Logical links in managemento The logical relationship is built on the principle

of distinction only two states: it is necessary to intervention / intervention is not necessary, etc.

Such an approach to the relations of the components in the mangement organization is possible when:

o The observed state of the real binary nature (such as job accounting occupied or if the place is not occupied)

o Binary data reflects the fact that the organization components is above or below a reference value (eg setpoint). The condition is that this component is a time-continuous.

• Quantification of an organization state is conventionally expressed

values 0 and 1, and as such variables are formally analogous to the variables of propositional logic.

Continuous (analog) link in management

• It is everywhere action intervention is superior to the time continuous monitoring of the organizational behavior of his subordinate - controlled entity.

• Analog link occurs in situations that require spontaneous response from the controller to the controlled error. For example, there is a situation where advanced colleague teaches a new team member to use a computer program .

Discrete link in management

• In the management of some slower processes can bee soon realized that it is not necessary to continuously monitor the process variable and constantly respond to it continuously.

• In fact, we should to check a process regularly, and also check the status of its development (from a previous state), and accordingly adjust the position of its regulator.

• A fundamental question is: How long can we keep a controlled system without control?

Application of logic control in management decision-making

• The main purpose of the application logic control in management's decision is to simplify procedures and allow a natural decentralization of decision-making powers within the structure.

• The principle of logic control application explains the following illustrative example:

Illustrative example• Claims head of the insurance company has in its

working group 3 subordinates (liquidators). His personal role interprets to find situations where you need to make personnel changes in the working group - which has to hire a new employee. This is necessary in two cases:

• First, he is interrupted by the ability to work in a workgroup. (The cooperation is needed at least 2 workers).

• The second case that requires special action group leader is in a situation when the working group is not sufficient to perform required tasks (not enough to liquidate damages in a given time).

The task is:

• To find all possible situations that may arise.

• This survey represents the general form can be found managerial procedures to simplify manager's decision whether is necessary his personal intervention.

• Firstly, we define the inputs to the diagnostic system in binary format:

• Input parametres:•  •  • ;•  

• Output parametre• Manažer pracovní skupiny M

Siolution

present is

presentnot is 1,2,3worker

1

03,2,1 P

sufficient is

ysufficientnot is group theof eperformanc

1

0H

nothing performs

action theperforms group workingofManager

1

0M

• and we can satisfy every possible case, that may arise.• The maximum number of possible situations which might

occur, if we have n inputs, is given by the sum of the binomial coefficients:

HPPPfM ,,, 321

n

n

n...

nnN 2

10

So we find three functions of four input variables:

• So the maximum number of possibilities for n=4 is . A summary of all possible conditions is shown in table No 1, where it is indicated whether manager should perfor the action or not ( =0) .

1624

state P1 P2 P3 H M

1 0 0 0 0 0

2 1 0 0 0 0

3 0 1 0 0 0

4 0 0 1 0 0

5 0 0 0 1 0

6 1 1 0 0 0

7 0 1 1 0 0

8 0 0 1 1 0

9 1 0 0 1 0

10 1 0 1 0 0

11 0 1 0 1 0

12 1 1 1 0 0

13 0 1 1 1 1

14 1 0 1 1 1

15 1 1 0 1 1

16 1 1 1 1 1

Combinational values

Basic operations of Boolean algebra

• Negation: ; assigns the opposite value to the variable negated

• Disjunction (logical sum): assigns the value of y such that for all combinations of inputs are results equal to y = 1, except when:

• Conjunction (logical product): assigns the value of y such that for all combinations of inputs are results equal to y = 0, except when:

ay

... cbay

1 1... yiscba... cbay

0 i0... yscba

According to table No 1, synthesis in the form of the sum of the products has only four combinational lines, compared to 12 lines synthesis in the form of the product of the sums.

• Consider the 12th, 13th, 14th, 15th and 16th lines of table 1. We combine the requirements expressed by lines 12, 13, 14, 15 and 16 for combination function of managerial actions.

Examples of Boolean algebra identities

Dual pairs páry a+0=a a1=1

a+b=b+a ab=ba

a + ab=a a(a+b)=a

ab + ac=a(b+c) (a+b)(a+c)=a+bc

1aa 0aa

ba ba babaa babaa

cbacba cbacba

bacacaba bacacaba

ba ba

Combination function: A Synthesis: form the sum of

the products

• Based on the properties of the logical product is the result y = 1 only when multiplied by all the variables = 1 If eg in the thirteenth row of the table requires y = M = 1, it is possible to meet this requirement the product of the inputs so that the inputs represented by the value 0 to negate and others are included intact.

Combination function: B Synthesis

• is based on the properties of the logical sum of the result y = 0 only in one case, where all addends variable = 0 (conjunctions 0).If eg the first row of the table combination requires states y = M = 0, it is possible to fulfill this requirement by the sum of the inputs so that the inputs are represented by 1 and negate the others are included intact.

state

P1 P2 P3 H M B Synthesis

1 0 0 0 0 0

2 1 0 0 0 0

3 0 1 0 0 0

4 0 0 1 0 0

5 0 0 0 1 0

6 1 1 0 0 0

7 0 1 1 0 0

8 0 0 1 1 0

9 1 0 0 1 0

10 1 0 1 0 0

11 0 1 0 1 0

12 1 1 1 0 0

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

HPPP 321

state

P1 P2 P3 H M A Synthesis

13 0 1 1 1 1

14 1 0 1 1 1

15 1 1 0 1 1

16 1 1 1 1 1

HPPP 321

HPPP 321

HPPP 321

HPPP 321

From the previous table, we see that A synthesis of combinatorial covers only 4 lines as opposed to 12 rows B synthesis.

Synthesis of combinatorial functions

• Consider the 12th, 13th, 14th, 15th and 16th lines of table 1. We combine the requirements expressed by lines 12, 13, 14, 15 and 16 for combination function of managerial action:

• The shape of the combinatorial function (resulting logical product of sum) is very complex (for managerial decision-making).We can use Boolean identities and members of these redundant operations removed.

HPPPHPPPHPPPHPPPMy 321321321321

1aa

Minimization of logic function

321321321321 PPPPPPPPPPPPHMy

213132

213331223211

PPPPPPH

PPPPPPPPPPPPH

H

y=M

P1

P2

P1 P3

P3

P2

Utilization of logic function in managemen

• The specific effects are these three:• may increase its natural spread of control

without effect on the quality of the performance of other management functions

• is easier to delegate decision-making power (decentralization)to the child and contribute to greater decentralization of organizational structures,using combinational function can easily build a back-up worker

• The resulting combination function is to see that progress removing redundant members, which is based on the rules of Boolean algebra is quite complicated and not very reliable procedure (in terms of possible errors).

• Much can be illustrated by the following simplifications made Karnaug maps (abbreviated as K - Maps - M. Karnaugh, * 1924, an American mathematician).

Its principle is based on the representation of the set K. (any combination of situations), which is defined a binary variable output pair 0 and 1

a

K - maps for 2, 3, 4 members of the entry criteria decision-making situation will create 4, 8, 16 boxes of possible situations according to the following files:

aK

a a=0

a=1

b=0 b=1

a=0

a=1

n=2

b=0 b=1

a=0

a=1

c=0

c=1 c=0

n=3

In our illustrative example we have four input variables,

HPPP ,,, 321

so we use the diagram of K-maps forn = 4

K-map for n = 4

0a

1a

0b 1b

0d

1d

0d

0c 1c 0c

28

So for our case seems to be fit the following map:

0 0 0 0

0 0 1 0

0 1 1 0

0 0 1 0

01 P

11 P

03 P 13 P

02 P

12 P

02 P

0H 1H 0H

0 0 0 0

0 0 1 0

0 1 1 0

0 0 1 0

01 P

11 P

03 P 13 P

02 P

12 P

02 P

0H 1H 0H

HPP 21 HPP 21HPP 32

y

• By the K-map simplification we choose the box with 1 or 0, depending on which are less according to their distribution.

• We try to bounded the area where 1 or adjoin. 0 and, together pairs of size two to the n-th degree (n=1,2,3,…)

• We are trying to find the largest these areas (larger area provides better simplification).

• When these areas are marked (we have three areas) we can merge fields by this way:

• If some variable occurs in both normal and negated form, we drop this variable.

y = M = + +HPP 21 HPP 31 HPP 32

213132 PPPPPPHMy

We reached the same result as in simplification using Boolean identities, but with using much convenient way.