Economic engineering study regarding Aeolian installation manufacturing system using CPM and pert methods.

Vartolomei, Mihaela ; Milos, Teodor ; Vartolomei, Mihael 等

1. INTRODUCTION

Solar energy is the first energy source used by humans. It represents essential element in mankind's development and there is no way to be life on Earth without sun energy (Lazarescu, 2003). The total solar energy intercepted by the Earth is 178 x [10.sup.9]MW, by 15.000 times more than mankind's current necessity. Medium density of radiant flux on horizontal area is between 250 W/[m.sup.2], in Sahara and 100W/[m.sup.2], in Central Europe (Ambros et al, 1999). The Partnership Project this paper has started is called "Energetic Supply for a Local Community Using Draughts". It will choose the optimum solution for Aeolian turbine which will be manufactured by a partner of the project. The peculiar of the project is the possibility to choose the configuration of the turbine palette with the calibration and simulation of the flow with the peculiar soft existent in the University. In this paper, our attention is fixed on planning and designing period of the Aeolian investment.

Non-fossil energy sources or energy renewable sources (ERS) represents the environment resources, that are continuously regenerating or in a certain periodicity and their consumption don't lead to a possible depletion. These kinds of ERS are constantly renewed or restored and include: sun (solar), internal heat of the earth (geothermal energy), wind (wind power), vegetation (biomass), falling water, tides, and wave motion (hydropower). A clear feature of ERS is their independent existence by any man's consistently activity (Ambros et al., 1999).

2. INVESTMENT DESIGNING PROCESS USING CRITICAL PATH METHODS (CPM)

2.1 CPM Principles

In this paper we call "work" the whole process of work and manufacturing activities targeted towards execution and setting the Aeolian investment.

The work has more activities. An activity represents the sum of rather homogeneous operations, which participate to the achievement of a part of the work.

The program is referring to tidy up activities executions, so that the work frames in planned terms, without surpass resources allocated. Every activity is formed by a throng of events (event is the physical stage an activity can be at a certain moment). Any activity is bordered upon two events: starting one and ending one. If the investment's work (W) has n activities then:

A=([a.sub.1], [a.sub.2], ..., [a.sub.i]); i=1...n (1)

Where: A=throng of activities [a.sub.i]=activity i

In this investment situation, we had identified 7 activities, from [a.sub.1] to [a.sub.7] (table 1). Furthermore, it is necessary to introduce a succession relation between these activities. Thus, the investment activities and events' graph (networks system of oriented arcs, bordered by knots) is showed in figure 1. The arcs represent the activities and the knots represent the start-end events. Looking figure 1, we can notice that there are more paths from event 1 to event 7: [P.sub.12357], [P.sub.12457] and [P.sub.1267] (so called full paths), the longest full path is called critic path:

[P.sub.12357]=180+30+360+60=630 days

[P.sub.12457]=180+30+300+60=570 days

[P.sub.1267]=180+360+0=540 days

[P.sub.cr]=max ([P.sub.12357], [P.sub.12457], [P.sub.1267])= [P.sub.12357]=630 days

[P.sub.12357] is the critical path ([P.sub.cr]) because it has the longest length. Thus, the uncritical path has time reserves (represents the difference between maximum terms till activity execution is accepted and possible minimum terms). There are four terms: minimum term of activity start ([t.sub.i]), maximum term of activity start ([T.sub.i]), minimum term of activity end ([t.sub.j]) and maximum term of activity end ([T.sub.j]).

The minimum and maximum terms are established using optimality principle (relation 2 and 3).

[FIGURE 1 OMITTED]

[t.sub.1]=max[P.sub.li] and [t.sub.j]=max[P.sub.lj] (2)

[T.sub.i]=[P.sub.cr]-max[P.sub.in] and [T.sub.j]=[P.sub.cr]-max[P.sub.jn] (3)

Where n represents the final event of the work

Using minimum and maximum term of the events we can calculate time reserve for each activity. So we have:

[t.sub.1]=0; [t.sub.2]=max[P.sub.12]= [P.sub.12]=180 days; [t.sub.3]=max[P.sub.13]= [P.sub.123]=180+30=210 days; [t.sub.4]=max[P.sub.14]= [P.sub.124]=180+30=210 days [t.sub.5]=max[P.sub.15]=max ([P.sub.1235]; [P.sub.1245])=max(180+30+360; 180+30+ +300)=max(570;510)=570 days [t.sub.6]=max[P.sub.16]= [P.sub.126]=180+360=540 days [t.sub.7]=max[P.sub.17]= [P.sub.15]+ [P.sub.57]=570+60=630 days [T.sub.7]=[P.sub.cr]-0=630 days [T.sub.6]=[P.sub.cr]-[P.sub.67]=630-0=630 days [T.sub.5]= [P.sub.cr]-[P.sub.57]=630-60=570 days [T.sub.4]=[T.sub.5]-[P.sub.45]=570-300=270 days [T.sub.3]=[T.sub.5]-[P.sub.35=570-360=210 days [T.sub.2]=min([T.sub.3]-[P.sub.23; [T.sub.4]-[P.sub.24]; [T.sub.6]-[P.sub.26]) = min (310-30; 270-30; 630-360) = min (180; 240; 270) = 180 days [T.sub.1]=[T.sub.2]-[P.sub.12]=180-180=0 days

2.2 PERT Principle

The essential difference between CPM and PERT (Program Evaluation and Review Technique Methods) is the execution period evaluation: CPM the period is evaluated in a certain number of days, PERT the period is appreciated in three situations: optimistic (the shortest, "a"), pessimistic (the longest, "l") and probable ("b"). The average value is calculated with relation 4 (Dogaru, 2004):

[[bar.d].sub.ij] = a + 4b + l/6 (4)

[square root of [[sigma].sup.2]] = l--a/6 (5)

z = [d.sub.p]--[[bar.d].sub.n]/[[sigma].sup.2] (6)

Where: [[square root of [[sigma].sup.2]]--represents Average Squared Deviation

[[sigma].sup.2]--represents Dispersion

z--represents probability factor

[d.sub.p]--represents planned duration of investment

[[bar.d].sub.n]--investment average duration

If planned term of investment execution is 366 days, the probability factor is 0.127 (using relation 6).

Then using Laplace function and interpolation methods we obtain the probability of 54.09% that indicate a proper programming (under 25% it means very short term and above 60% indicates many time reserves, so it will be redacted).

2.3 PERT/time

After program finalizing in its optimum variant, we'll elaborate Gantt graphic.

2.4 PERT/cost

A very important facility of this method is that prolonging execution dates of some activities, in the framework of time reserves, it is possible to obtain cost reduction linked by the work deployment (Buglea, 2002). This is why this model is known in scientific literature as cost-time function optimization. In some condition, the investment execution period can be shorted, but this supposes cost increase (urgency cost). But also, an exaggerated prolonging can produce certainly cost increases (figure 2) (Popa, 2005).

[FIGURE 2 OMITTED]

2.5 Work launching and execution

After the convenient variant is chosen, and after all terms was established, we go to the investment launching process, redrawing Gantt graphic depending by chosen variant, needed resources and mean for achieve any activity in established terms, passing, step by step Gantt graphic. Any modification in the system leads to the program re-optimization.

3. CONCLUSIONS

In planning and designing process of our project Aeolian investment in good conditions, we use Critical Path Methods. First we ordered different activities so that the final results to correspond with the main target of the project, from terms and resources allocation points of view (Anton et al., 2007). The designing process supplies data about economic and technical optimum and the planning process bunches economic and technical optimum with social optimum.

4. REFERENCES

Ambros, T.; Arion, V.; Gutu, A.; Sobor, I.; Todos, P.; Ungureanu, D. (1999). Energy Renewable Sources, Tehnica-Info Publishing House, Chisinau, ISBN 9975-91079-3

Anton, L.E.; Baya, A.; Milos, T.; Stuparu, A. (2007), Experimental Hydrodynamics, "Orizonturi Universitare" Publishing House, ISBN 978-973-638-330-4.

Buglea, A. (2002). Investments and Their Financing, West University Publishing, Timisoara, ISBN 973-8433-13-4

Dogaru, V. (2004) Statistics in Economy, Eurostampa Publishing House, Timisoara, ISBN 973-687-269-6

Lazarescu, S. (2003). Energetic Concepts and Wind Energy Utilization, Orizonturi Universitare Publishing House, Timisoara, ISBN 973-638-039-4

Popa, A. (2005). Investments Efficiency, Sitech Craiova, ISBN 973-746-059-6

Tab. 1. Investment activities and execution time.

Activity Start-end Activity name Activity Symbol
 symbol events time (in of right
 days) preceding
 activity

[a.sub.1] 1,2 Execution 180 --
 project
 elaboration

[a.sub.2] 2,3 Work space 30
 organization

[a.sub.3] 3,5 Building 360 a2
 execution

[a.sub.4] 2,4 Equipments 30 a1
 contraction

 4,5 Equipment 300 a4
 acquisition

[a.sub.6] 5,7 Equipment 60 a3
 assembling

[a.sub.7] 2,6 Prepare for 360
 manufacturing

Tab. 2. Average Squared Deviation and Dispersion

Act. Activity duration [square [square
symb root of root of
 [[sigma] [[sigma]
 a b 1 [d.sub.n] .sub.2]] .sub.2]]

1 2 3 4 5 6 7
[a.sub.1] 160 175 220 180 10 100
[a.sub.2] 20 30 40 30 3.33 11
[a.sub.3] 300 360 420 360 20 400
[a.sub.4] 20 30 40 30 3.33 11
[a.sub.5] 250 290 390 300 23.33 544
[a.sub.6] 40 60 80 60 6.67 44
[a.sub.7] 300 360 420 360 20 400
Tot. 520 625 760 630 x 555