# The Nonlinear Optimisation and Time Scheduling on the Basis of by pptfiles

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```									The Nonlinear Optimisation and Time Scheduling on the Basis of Cash Flow
Doc. Ing. Václav Beran, DrSc., CTU in Prague

Optimisation in time
• optimisation categories are time dependent applications on the bases of a limited budget (TDK – Time-Dependent Knapsack Problem) • To realize production activities so that their production speed can satisfy optimal cash flow is one of the basic ideas of any supplier and any investment subject
.

Tools for formation of steering interference (t, P, L) are for real process (P) and steering processes (L) illustrated as:
• search for satisfaction of goals by means of solutions regardless restrictive conditions, • search for solutions on the basis of simulations, • search for an optimal solution, • search for solutions in virtue of factual conception of future solution along scenarios,

kspeed= 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

T= 25 Max Q´ permited 150 21,42857 130 18,57143 160 22,85714

Section A
15 15 15 15 15 15 15 15 15 15

Action B Section A
13 13 13 13 13 13 13 13 13 13

Action C Section A
16 16 16 16 16 16 16 16 16 16

Section D
44 44 44 44 44

221,4286 44,28571 Section E
52 52 52 52 52 52 52 52 52 52

520 74,28571 120 17,14286 140 20

Action F in E
12 12 12 12 12 12 12 12 12 12

Action G in E
14 14 14 14 14 14 14 14 14 14

Action H in E
9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6

240 34,28571

Cash flow
100

m il. Kč

80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

m onths

t. EUR

0 1 3 5 7 9

20

40

60

Basis for credit creation

17

months

15

Optimal solution

11

13

19

21

23

25

It is worthy of note that any decision rule influences the structure (location in time and placement of implementation) of P. We speak about  dispersion in time,  value change of implemented action (activities) in time,  present value change according to profit rate (discounted value),  changed value in time according to construction of decision rule,  changed value in time according to stick to memory of input data.

The experience up to optimisation results is described as improvement against empirical results (up to 30 %). The experience in students groups is on the level up to 10-15 %). Serious comparison on the basis of large industrial projects might be interesting, however data are less reliable. Project have during elaboration so fundamental changes in size, time and costs that comparison are not serious.

160 140 120 100 80 60 40 20 0 1 2 3 4 5 6

Cash flow (project production speed)

t. EUR

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

months Fig. 3 Cash flow for optimal solution given in fig. 2

Optimal solution

The goal is reach total capacity (demand capacity) Dt under a minima discounted costs.

min  p j 
t 1 j 1

T

N

t 1

x jt

 
T t 1

N j 1

c j x jt  Dt

where xjt reach values {0, 1, 2, …} for all j and t . Parameter  is there a discounting factor (0   1) and xjt is the searched production speed characteristic for production technology and production activity j in time interval t.

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