Completion Time of Fuzzy GERT-type Networks with Loops

Transcription

1 Completion Time of Fuzzy GERT-type Networks with Loops Sina Ghaffari 1, Seyed Saeid Hashemin 2 1 Department of Industrial Engineering, Ardabil Branch, Islamic Azad university, Ardabil, Iran 2 Department of Industrial Engineering, Ardabil Branch, Islamic Azad university, Ardabil, Iran Abstract In real world, many projects have uncertain parameters. In these projects, uncertainty can occur in realization of some activities and in duration of activities. The GERT networks can describe these projects. The GERT network can have six different kinds of logical nodes. In special kinds of research projects, only and only one path out of various paths in the network is realized. In addition, some of the activities of the project may be repeated. Therefore, these networks have one or more loops. Apparently, being subjected to the above-mentioned assumptions, these networks have only exclusive-or, probabilistic nodes. In these kinds of projects, project managers are interested to know the distribution function of the project completion time; because it affects the project execution cost. In this paper, it is assumed that the uncertainty occurs in activity duration with positive trapezoidal fuzzy numbers. Implementation of analytical methods requires too much computational effort, which is significantly time consuming. So, a heuristic algorithm has been developed to define the distribution function of project completion time. A computer program has been written based on the proposed heuristic algorithm. An example has been solved using the proposed algorithm. Keywords GERT-type networks; completion time; loop; trapezoidal fuzzy number; fuzzy random variable I. INTRODUCTION In some projects, the activity duration and occurrence of the activities are certain. In these cases, the critical path method (CPM) is used. PERT has the ability to analyze projects, which have activities with deterministic occurrence and stochastic times. GERT is a strong tool for analyzing the real-world projects and it has been used when both duration of activities and the occurrence of activities have uncertainty. Uncertainty in activity duration can be shown as fuzzy numbers or random variables. Here, activity durations are shown with positive trapezoidal fuzzy numbers. In special kinds of research projects, only one path out of various paths is realized. So, these networks have only exclusive-or, probabilistic nodes. GERT as one of the most effective project analysis tools was first time introduced by Pritsker in1966 [1]. He showed that in the GERT networks the occurrence of activities and the duration of activities are nondeterministic. Many studies have been conducted about GERT. GERT networks are used as a tool for planning and defining the project time as well as for estimating project costs [2]. A number of new analytical methods have been proposed to determine the completion time of the GERT networks as an effective factor in project returns [3, 4]. Fuzzy numbers have been used to describe project activity time. It has been shown that the above description is more simple and is closer to the real world activity times [5]. Fuzzy concepts in the GERT networks, for the first time, were used by Nishikawa and Itakura [6]. Using trapezoidal fuzzy numbers a new method for scheduling fuzzy GERT networks is presented in research projects [7]. Some scholars believed that conventional GERT networks cannot accurately reflect the characteristic of real-world networks; thus they used triangular fuzzy numbers to formulate fuzzy GERT networks which could solve the problem [8]. Although many fuzzy sets have been used to express uncertainty, triangular and trapezoidal fuzzy sets have been used to explain the uncertainty of the activity times [9]. The problem of determining the completion time of fuzzy GERT networks with exclusive-or, DOI:.23883/IJRTER INJT5 18

2 Volume, Issue ; February [ISSN: ] probabilistic nodes, regardless of the loops in the network, has been investigated []. In recent years, some new methods are developed for analyzing the Boolean dynamical systems. Optimal estimation of the state of a Boolean dynamical systems is observed through correlated noisy Boolean measurements. An optimal minimum mean-square error filter is developed for a class of Partially- Observed Boolean Dynamical Systems (POBDS) with correlated Boolean measurements []. Partially-observed Boolean dynamical systems are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. A maximum-likelihood adaptive filter is proposed based on an efficient particlebased expectation maximization algorithm for the Partially-observed Boolean dynamical systems model, which is based on a modified forward filter backward simulation in combination with the auxiliary particle filter-boolean Kalman smoother []. In one of the recent researches, a novel uncertainty propagation approach is presented for multidisciplinary systems with feedback couplings, model discrepancy, and parametric uncertainty. In this research, the proposed method incorporates aspects of Gibbs sampling, importance resampling, and density estimation to ensure that, under mild assumptions, the current method is provably convergent in distribution [13]. The problem of stochastic control of gene regulatory networks observed indirectly through noisy measurements and with uncertainty in the intervention inputs is studied newly. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general. So, reinforcement learning and Gaussian process techniques to find a near-optimal solution are applied [14]. In this paper, GERT networks are combined with fuzzy theory to describe the projects that have uncertainty in activity realization and activity duration. It is supposed that the probabilities in output of nodes are known. Activity times are shown with positive trapezoidal fuzzy numbers. Also, it is assumed that the project network has one or more loops. By combining the analytical relations and simulation method, a new heuristic algorithm has been developed to compute the completion time distribution function of the project and completion time distribution function of each end nodes. In section, 3.3 will be shown that this new method is designed based on sampling. Also, mean and variance of above mentioned completion times can be computed. Finally, a numerical example has been solved with the new algorithm. II. WEAKNESSES OF PREVIOUS METHODS Generally, there are three methods for obtaining the transfer value between two nodes in a flow graph. These methods are topology equation, Maison rule and network simplification method. Topology equation is limited to closed flow graphs. If a flow graph is open, it should be first converted to a closed flow graph using a virtual activity, and then topology equation can be employed. Instead of converting an open flow graph to a closed one, we can use the Maison rule to determine the transfer value of the path in the open flow graph. The topology equation is a very useful technique, but the basic drawback is that if the flow graph is complex and has many loops, the analysis of the flow graph and the identification of the higher-order loops are both difficult. Using the network simplification method in large networks is very challenging. In addition; all abovementioned methods can be used when the activity durations are random variables with known moment generating function. III. PROPOSED METHOD The innovated algorithm in this research allows the analysis of large networks with many loops. This method can calculate the distribution function of the realization of each end node, the distribution function of the completion time of the network and the probability of realization of each path. A significant advantage of the proposed method is that, in order to calculate the expected value and variance of the completion time of network, there is no need to obtain the first and second derivatives of the moment-generating All Rights Reserved 19

3 Volume, Issue ; February [ISSN: ] 3.1. Assumptions The studied networks have a single start node and they can have one or more end nodes. The networks can have loops. The Networks contain exclusive-or, probabilistic nodes. The durations of the network activities are positive trapezoidal fuzzy numbers Notations In this research, the following notations have been used. N: Number of the activities M: Number of the end nodes n i : Number of paths, which start from start node and terminate in i-th end node A i : The event of realization of i-th end node A ij : The event of realization of i-th end node through the realization of j-th path that terminates in that node S ij : Activity set of j-th path which terminates in i-th end node q ij : Number of the occurrence of j-th path that leading i-th end node in simulation P : k Accomplishment probability of k-th activity, given that start node of this activity has already been realized P ij : Realization probability of j-th path which terminates in i-th end node P i : Realization probability of i-th end node T ij : Fuzzy completion time of network by realization of i-th end node through the realization of j-th path which terminates in that node t k : Fuzzy duration of k-th activity t: Due date of the project D: Fuzzy completion time of the network f ij : Estimate of P ij via simulation C ij : Crisp values corresponding to trapezoidal fuzzy time of j-th path which leading to i-th end node SN: Number of simulation runs I: Counter of the number of simulations E(D) R : Expected value of completion time of network using P ij values E(D) S : Expected value of completion time of network using f ij values Vactor EN: The vector EN is a column vector that each component of it, shows the end nodes of each path Matrix Pa: Each row of the matrix represents a path, in which the number of components of the row depends on the number of realized path activities Vector P: The vector P is a column vector that each component of it, shows the values of P ij Matrix T: Each row of the matrix represents the fuzzy completion time of each path Vector C: The vector C is a column vector each component of which, shows the values of C ij Vector F: The vector F is a column vector each component of which, shows the values of f ij Vector Q: The vector Q is a column vector each component of which, shows the frequency of repetition of each path 3.3. Steps of new algorithm Step1: simulate the network for first time and set I = 1 Step2: set the realized path in the first row of the matrix Pa Set the number of the end node of the realized path in the first row of the EN vector Set the probability of the first path in the first row of the vector P Set the completion time of the first path in the first row of the matrix All Rights Reserved 20

4 Volume, Issue ; February [ISSN: ] Set the crisp values of trapezoidal fuzzy time of the realized path in the first row of the vector C Set the q 1 = 1 Step3: if I = SN, go to the step 5. Otherwise, set I = I + 1 and go to the step 4 Step 4: simulate the network again If the realized path is repetitive, add one unit to component of Q which is corresponding to the realized path. Otherwise, set the new path in the first empty row of the Pa matrix and set the number of end node of the new path in the new row of vector EN. Set the completion time of the path in the new row of vector T. Set the crisp values of trapezoidal fuzzy time of the newly realized path in the new row of the vector C. Set the new row of the vector Q equal to 1 and go back to step 3. Step 5: compute the values of vector F using by below equation:f ij = q ij SN E(D) R and E(D) S are defined as follows: i = 1,2,, M, j = 1,2,, n i M E(D) R = P ij T(A ij ), E(D) s = f ij T(A ij ) i=1 n i j=1 The variance of the completion time of network can be computed as follows: var(d) = E(D D) [E(D) E(D)] Step 6: compute the distribution function of the completion time of the network as follows: M n i j=1 P(D t) = i=1 P ij ; c ij t Probability function of random variable of D is defined as follows: P(D = T(A ij ) = P ij Compute the conditional distribution function of the completion time of the network as follows: P(D = T ij A i ) = P ij P i ; i = 1,2,, M, j = 1,2,, n i Based on the above algorithm, a computer program is written with C++. IV. NUMERICAL EXAMPLE In this section, an example has been solved and analyzed. By using the proposed algorithm and written computer program based on the proposed algorithm the random variable of the completion time of the network, the probability of realization of each node, the probability of realization of each path, the average and the variance of the completion time of the network have been calculated. Example: At the beginning of a production line a product is manufactured. The product is inspected before the final operation is performed. 25% of the products must be reworked. Production and inspection are called activity 1. Reworking is called activity 2. 30% of the reworked products are rejected at the next inspection (activity 4). These products are scrapped. If the product passes the above-mentioned inspections, it is sent to a completion operation (activity 3 and 5). The final inspection (activity 7) rejects 5% of the products due to product specifications contradiction. These are scrapped (activity 8). 15% of products are slightly different from the product specification and need to be re-inspected prior to activity 2 or 3 (activity 9). 80% of the products are accepted (activity ). Due date of the projects is 30 time units. Figure 1 shows the GERT network equivalent to the example. M i=1 n i All Rights Reserved 21

5 Volume, Issue ; February [ISSN: ] Fig 1: GERT network of the example Table 1: Durations of the activities as trapezoidal fuzzy numbers k a b c d Using the computer program introduced in section 3.3, the above example has been solved and the final results (values) are as follows. E(D) R = ( , , , ) E(D) S = ( , , , ) var(d) = ( , , , ) M n i P ij = i=1 j=1 M n i f ij = 1 i=1 j=1 t = 30 P(D 30) = P ( 1) = P ( 2) = P (D = T(A ij )) = P ij P (D = T(A ( 1)1 )) = 0.5 P (D = T(A ( 1)2 )) = 0.75 Type equation All Rights Reserved 22

6 Volume, Issue ; February [ISSN: ] A simulation with one million iterations has obtained the above results. This simulation has recognized 133 paths. The specifications of these paths have been given in the appendix. V. CONCLUSION AND RECOMMENDATIONS In this paper, an algorithm has been proposed to calculate the cumulative distribution function of the completion time of GERT networks with fuzzy times. In this paper, the studied network has loops. So, the total number of the network paths is infinite. Therefore, the innovated algorithm identifies paths with higher probability of realization. Hence, those paths, which are not recognized in large simulation runs, have very low realization probabilities. The identification of these paths can be ignored. The proposed algorithm calculates the P ij and the estimation of P ij which is called f ij. When the network is simulated, the total sum of the estimated probabilities is always equal to one, and sum of the P ij of the realized paths is near to one. By increasing the simulation runs, the proposed algorithm identifies more paths. Consequently, difference of the sum of probability of realized paths ( P ij ) with 1 will be smaller. Also, using the proposed algorithm expected value and variance of the completion time of the network, distribution function of the network completion time and the distribution function of the completion time of each end nodes occurrence can be computed. In this paper, network activity durations are considered positive trapezoidal fuzzy numbers. It is suggested that other types of fuzzy numbers can be used in future researches. In this study, it is assumed that the nodes of GERT networks are exclusive0or, probabilistic. In future studies, the other types of nodes in GERT networks can be considered. In the proposed algorithm of this research, deffuzzification has been done using the maximum-average degree of membership method. Other deffuziffication methods can be used in future researches. Instead of converting fuzzy numbers to crisp values, fuzzy numbers can be ordered by using the fuzzy numbers ranking methods. Finally, results of the two above-mentioned methods can be compared. The new methods for analyzing the Partially-Observed Boolean Dynamical Systems (POBDS) can definitely give good insight of future investigation. REFERENCES I. A. A. B. Pritsker, GERT- Graphical evaluation and review technique, Memorandum RM-4973, II. B. W. Taylor, K. R. Davis, Evaluating time/cost factors of implementation via GERT simulation, Omega, 6(3), , III. S. S. Hashemin, S. M. T. Fatemi Ghomi, A hybrid method to find cumulative distribution function of completion time of GERT networks, Journal of Industrail Engineering International, 1(1), 1-9, 25. IV. A. P. Shibanov, Finding the distribution density of the time taken to fulfill the GERT network on the basis of equivalent simplifying transformations, Automation and Remote Control, 64(2), , 23. V. F. A. Lootsma, Theory and Methodology stochastic and fuzzy PERT, European Journal of Operational Research, 143(2), , VI. H. Itakura, Y. Nishikawa, Fuzzy network technique for technological forecasting, Fuzzy sets and systems, 14(2), 99-3, VII. M. K. Gavareshki, New fuzzy GERT method for research projects scheduling, In Engineering Management Conference, Proceeding. IEEE Intrnational, Vol. 2, pp , October. 24. VIII. S. Y. Liu, S. C.Liu, J. W. Lin, Model formulation and development of fuzzy GERT networks, Journal of the Chinese Institute of Industrial Engineers, 21(2), , IX. H. Zhang, C. M. Tam, H. Li, Modeling uncertain activity duration by fuzzy number and discrete-event simulation, European journal of operational research, 164(3), , 25. X. S. S. Hashemin, Fuzzy completion time for alternative stochastic networks,, 6(), 17-22, 20. XI. L. D. McClenny, M. Imani, U. M. Braga-Neto, Boolean Kalman filter with correlated observation noise, Acoustics, Speech and Signal Processing (ICASSP), 2017 IEEE International Conference on. IEEE, XII. M. Imani, U. M. Braga-Neto, Particle filters for partially-observed Boolean dynamical systems, Automatica 87 (2018), XIII. S. F. Ghoreishi, D. L. Allaire, Adaptive Uncertainty Propagation for Coupled Multidisciplinary Systems, AIAA Journal, Vol. 55, No. (2017), pp XIV. M. Imani, U. M. Braga-Neto, Control of Gene Regulatory Networks with Noisy Measurements and Uncertain Inputs, IEEE Transactions on Control of Network Systems (TCNS), All Rights Reserved 23

7 Volume, Issue ; February [ISSN: ] Appendix Table 2: Results of 1 million simulation runs in the numerical example Row Pa EN P ij T ij C ij q ij f ij 1 1_2_4_ _3_7_ _3_7_ _2_4_5_7_ _2_4_5_7_ _3_7_9_3_7_ _3_7_9_2_4_ _3_7_9_3_7_ _2_4_5_7_9_3_7_ _3_7_9_2_4_5_7_ _2_4_5_7_9_2_4_ _3_7_9_2_4_5_7_ _2_4_5_7_9_3_7_ _3_7_9_3_7_9_3_7_ (6,9.5,16.5,20 ) (5.5,9,14,17.5 ) (5,8.5,14,17.5 ) (9,14,22,27) 18.0 (8.5,13.5,22,2 7) (,17,24.5,3 1) (.5,17.5,27, 33.5) (9.5,16.5,24.5,31) (13.5,22,32.5, 4 (13.5,22,32.5, 4 (14,22.5,35,4 3) (13,21.5,32.5, 4 (13,21.5,32.5, 4 (14.5,25,35,4 4.5) P(D = T ij A 5.32E E E E E E E E E E E E E E All Rights Reserved 24

8 Volume, Issue ; February [ISSN: ] 15 1_3_7_9_3_7_9_2_4_ (15,25.5,37.5, 47) E _3_7_9_3_7_9_3_7_ (14,24.5,35,4 4.5) E _2_4_5_7_9_2_4_5_7_ (17,27,40.5,5 0) E _2_4_5_7_9_2_4_5_7_ (16.5,26.5,40. 5,) E _2_4_5_7_9_3_7_9_2_4_ (18.5,30.5,45. 5,56.5) E _2_4_5_7_9_3_7_9_3_7_ (18,30,43,54) E _3_7_9_3_7_9_2_4_5_7_ (18,30,43,54) E _3_7_9_2_4_5_7_9_2_4_ (18.5,30.5,45. 5,56.5) E _3_7_9_2_4_5_7_9_3_7_ (18,30,43,54) E _3_7_9_2_4_5_7_9_3_7_ (17.5,29.5,43, 54) E _2_4_5_7_9_3_7_9_3_7_ (17.5,29.5,43, 54) E _3_7_9_3_7_9_2_4_5_7_ (17.5,29.5,43, 54) E _3_7_9_3_7_9_3_7_9_3_7_ (19,33,45.5,5 8) E _3_7_9_3_7_9_3_7_9_2_4_ (19.5,33.5,48, E _3_7_9_3_7_9_3_7_9_3_7_ (18.5,32.5,45. 5,58) E _3_7_9_2_4_5_7_9_2_4_5_7_ (21.5,35,51, All Rights Reserved 25

9 Volume, Issue ; February [ISSN: ] 31 1_2_4_5_7_9_2_4_5_7_9_3_7_ _2_4_5_7_9_3_7_9_2_4_5_7_ _2_4_5_7_9_2_4_5_7_9_2_4_ _2_4_5_7_9_2_4_5_7_9_3_7_ _3_7_9_2_4_5_7_9_2_4_5_7_ _2_4_5_7_9_3_7_9_2_4_5_7_ _3_7_9_2_4_5_7_9_3_7_9_2_4_ _2_4_5_7_9_3_7_9_3_7_9_3_7_ _3_7_9_2_4_5_7_9_3_7_9_3_7_ _3_7_9_3_7_9_2_4_5_7_9_3_7_ _3_7_9_3_7_9_2_4_5_7_9_2_4_ _3_7_9_3_7_9_3_7_9_2_4_5_7_ _2_4_5_7_9_3_7_9_3_7_9_2_4_ _3_7_9_3_7_9_2_4_5_7_9_3_7_ _2_4_5_7_9_3_7_9_3_7_9_3_7_ ) (21.5,35,51, ) (21.5,35,51,6 3.5) (22,35.5,53.5, 66) (21,34.5,51,6 3.5) (21,34.5,51,6 3.5) (21,34.5,51,6 3.5) (23,38.5,56,7 0) (22.5,38,53.5, (22.5,38,53.5, (22.5,38,53.5, (23,38.5,56,7 0) (22.5,38,53.5, (23,38.5,56,7 0) (22,37.5,53.5, (22,37.5,53.5, E E E E E E E E E E E E E E E All Rights Reserved 26

10 Volume, Issue ; February [ISSN: ] 46 1_3_7_9_3_7_9_3_7_9_2_4_5_7_ _3_7_9_2_4_5_7_9_3_7_9_3_7_ _3_7_9_3_7_9_3_7_9_3_7_9_2_4_ _3_7_9_3_7_9_3_7_9_3_7_9_3_7_ _2_4_5_7_9_2_4_5_7_9_2_4_5_7_ _3_7_9_3_7_9_3_7_9_3_7_9_3_7_ _2_4_5_7_9_2_4_5_7_9_2_4_5_7_ _3_7_9_2_4_5_7_9_3_7_9_2_4_5_7_ _2_4_5_7_9_2_4_5_7_9_3_7_9_3_7_ _3_7_9_2_4_5_7_9_2_4_5_7_9_2_4_ _3_7_9_3_7_9_2_4_5_7_9_2_4_5_7_ _2_4_5_7_9_2_4_5_7_9_3_7_9_2_4_ _2_4_5_7_9_3_7_9_2_4_5_7_9_2_4_ _2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_ _2_4_5_7_9_3_7_9_2_4_5_7_9_3_7_ _2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_ (22,37.5,53.5, (22,37.5,53.5, (24,41.5,58.5, 74) (23.5,41,56,7 1.5) (25,40,59,73) 49.5 (23,40.5,56,7 1.5) (24.5,39.5,59, 73) (26,43,61.5,7 7) (26,43,61.5,7 7) (26.5,43.5,64, 79.5) (26,43,61.5,7 7) (26.5,43.5,64, 79.5) (26.5,43.5,64, 79.5) (26,43,61.5,7 7) (26,43,61.5,7 7) (25.5,42.5,61. 5,77) E E E E E - 1.E - 1.E - 2.E - 2.E - 4.E - 2.E - 4.E - 4.E - 2.E - 2.E E All Rights Reserved 27

11 Volume, Issue ; February [ISSN: ] 62 1_3_7_9_2_4_5_7_9_3_7_9_2_4_5_7_ (25.5,42.5,61. 5,77) E _2_4_5_7_9_3_7_9_2_4_5_7_9_3_7_ (25.5,42.5,61. 5,77) E _3_7_9_3_7_9_2_4_5_7_9_2_4_5_7_ (25.5,42.5,61. 5,77) E _3_7_9_2_4_5_7_9_2_4_5_7_9_3_7_ (25.5,42.5,61. 5,77) E _2_4_5_7_9_2_4_5_7_9_3_7_9_3_7_ (25.5,42.5,61. 5,77) E _2_4_5_7_9_3_7_9_3_7_9_3_7_9_2_4_ (27.5,46.5,66. 5,83.5) E _3_7_9_3_7_9_3_7_9_2_4_5_7_9_3_7_ (27,46,64,81) E _3_7_9_3_7_9_3_7_9_2_4_5_7_9_2_4_ (27.5,46.5,66. 5,83.5) E _3_7_9_3_7_9_2_4_5_7_9_3_7_9_2_4_ (27.5,46.5,66. 5,83.5) E _3_7_9_2_4_5_7_9_3_7_9_3_7_9_2_4_ (27.5,46.5,66. 5,83.5) E _3_7_9_2_4_5_7_9_3_7_9_3_7_9_3_7_ (27,46,64,81) E _3_7_9_3_7_9_3_7_9_3_7_9_2_4_5_7_ (27,46,64,81) E _3_7_9_3_7_9_2_4_5_7_9_3_7_9_3_7_ (27,46,64,81) E _2_4_5_7_9_3_7_9_3_7_9_3_7_9_3_7_ (27,46,64,81) E _3_7_9_2_4_5_7_9_3_7_9_3_7_9_3_7_ (26.5,45.5,64, 81) E _2_4_5_7_9_3_7_9_3_7_9_3_7_9_3_7_ (26.5,45.5,64, All Rights Reserved 28

12 Volume, Issue ; February [ISSN: ] 78 1_3_7_9_3_7_9_3_7_9_3_7_9_2_4_5_7_ _3_7_9_3_7_9_2_4_5_7_9_3_7_9_3_7_ _3_7_9_3_7_9_3_7_9_2_4_5_7_9_3_7_ _3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_3_7_ _3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_2_4_ _2_4_5_7_9_3_7_9_2_4_5_7_9_2_4_5_7_ _3_7_9_2_4_5_7_9_2_4_5_7_9_2_4_5_7_ _2_4_5_7_9_2_4_5_7_9_3_7_9_2_4_5_7_ 86 1_2_4_5_7_9_3_7_9_2_4_5_7_9_2_4_5_7_ 87 1_3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_3_7_ 88 1_3_7_9_2_4_5_7_9_2_4_5_7_9_2_4_5_7_ 89 1_2_4_5_7_9_2_4_5_7_9_2_4_5_7_9_3_7_ 90 1_3_7_9_3_7_9_2_4_5_7_9_3_7_9_2_4_5_ 7_8 91 1_2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_9_2_ 4_6 92 1_2_4_5_7_9_2_4_5_7_9_3_7_9_3_7_9_3_ 7_ ) (26.5,45.5,64, ) (26.5,45.5,64, 81) (26.5,45.5,64, 81) (28,49,66.5,8 5) (28.5,49.5,69, 87.5) (29.5,48,69.5, 86.5) (29.5,48,69.5, 86.5) (29,47.5,69.5, 86.5) (29,47.5,69.5, 86.5) (27.5,48.5,66. 5,85) (29,47.5,69.5, 86.5) (29,47.5,69.5, 86.5) (30.5,51,72,9 (31,51.5,74.5, 93) (30,.5,72, E E E E E E E E E E E E E E - All Rights Reserved 29

13 Volume, Issue ; February [ISSN: ] 93 1_3_7_9_2_4_5_7_9_3_7_9_2_4_5_7_9_3_ 7_ 94 1_2_4_5_7_9_3_7_9_2_4_5_7_9_3_7_9_3_ 7_ 95 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_2_4_5_ 7_ 96 1_3_7_9_2_4_5_7_9_3_7_9_3_7_9_2_4_5_ 7_ 97 1_3_7_9_2_4_5_7_9_2_4_5_7_9_3_7_9_3_ 7_ 98 1_3_7_9_3_7_9_2_4_5_7_9_2_4_5_7_9_3_ 7_ 99 1_2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_9_3_ 7_ _2_4_5_7_9_3_7_9_3_7_9_3_7_9_2_4_5_ 7_ 1_3_7_9_3_7_9_2_4_5_7_9_3_7_9_2_4_5_ 7_ 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_3_7_9_ 3_7_8 1_3_7_9_2_4_5_7_9_3_7_9_3_7_9_3_7_9_ 3_7_8 1_3_7_9_3_7_9_2_4_5_7_9_3_7_9_3_7_9_ 3_7_ 1_3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_2_4_ 5_7_ 1_3_7_9_3_7_9_3_7_9_3_7_9_2_4_5_7_9_ 3_7_ 1_2_4_5_7_9_3_7_9_3_7_9_3_7_9_3_7_9_ 3_7_ 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_3_7_9_ 3_7_ (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (30,.5,72,9 (31.5,54,74.5, (31.5,54,74.5, (31,53.5,74.5, (31,53.5,74.5, (31,53.5,74.5, (31,53.5,74.5, (31,53.5,74.5, E - 1.E E E E E E All Rights Reserved 30

14 Volume, Issue ; February [ISSN: ] 9 1_3_7_9_2_4_5_7_9_3_7_9_3_7_9_3_7_9_ 3_7_ (31,53.5,74.5, E - 0 1_3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_3_7_ 9_2_4_ (33,57.5,79.5, 1) E - 1 1_2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_9_2_ 4_5_7_ 1) _3_7_9_2_4_5_7_9_2_4_5_7_9_3_7_9_2_ 4_5_7_ 1) _2_4_5_7_9_2_4_5_7_9_2_4_5_7_9_3_7_ 9_3_7_ 1) _3_7_9_2_4_5_7_9_3_7_9_2_4_5_7_9_2_ 4_5_7_ 1) _2_4_5_7_9_3_7_9_2_4_5_7_9_3_7_9_2_ 4_5_7_ 1) _2_4_5_7_9_2_4_5_7_9_3_7_9_3_7_9_2_ 4_5_7_ 1) _3_7_9_3_7_9_2_4_5_7_9_2_4_5_7_9_2_ 4_5_7_ 1) _2_4_5_7_9_2_4_5_7_9_3_7_9_2_4_5_7_ 9_3_7_ 1) _3_7_9_2_4_5_7_9_3_7_9_2_4_5_7_9_3_ 7_9_3_7_ (35,59,82.5,1 ) E _2_4_5_7_9_2_4_5_7_9_3_7_9_3_7_9_3_ 7_9_3_7_ (34.5,58.5,82. 5,1) E - 1 1_3_7_9_2_4_5_7_9_3_7_9_3_7_9_2_4_5_ 7_9_3_7_ (34.5,58.5,82. 5,1) E - 2 1_3_7_9_2_4_5_7_9_2_4_5_7_9_3_7_9_3_ 7_9_3_7_ (34.5,58.5,82. 5,1) E - 3 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_3_7_9_ 2_4_5_7_ (34.5,58.5,82. 5,1) E - 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_2_4_5_ (34.5,58.5, All Rights Reserved 31

15 Volume, Issue ; February [ISSN: ] 4 7_9_3_7_ 1_2_4_5_7_9_3_7_9_3_7_9_3_7_9_3_7_9_ _4_5_7_ _2_4_5_7_9_3_7_9_3_7_9_3_7_9_2_4_5_ 7_9_3_7_ 1_2_4_5_7_9_2_4_5_7_9_2_4_5_7_9_3_7_ 9_3_7_9_3_7_ 1_3_7_9_3_7_9_3_7_9_3_7_9_3_7_9_3_7_ 9_3_7_9_3_7_ 1_2_4_5_7_9_2_4_5_7_9_3_7_9_2_4_5_7_ 9_3_7_9_3_7_ 1_2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_9_2_ 4_5_7_9_3_7_ 1_2_4_5_7_9_3_7_9_3_7_9_2_4_5_7_9_3_ 7_9_3_7_9_3_7_ 1_3_7_9_3_7_9_3_7_9_2_4_5_7_9_2_4_5_ 7_9_3_7_9_3_7_ 1_3_7_9_3_7_9_2_4_5_7_9_3_7_9_3_7_9_ 3_7_9_3_7_9_2_4_ ,1) (34.5,58.5, ,1) (34.5,58.5,82. 5,1) (38,63.5,90.5, 3.5) (36.5,64.5,87. 5,2) (38,63.5,90.5, 3.5) (38,63.5,90.5, 3.5) (39,66.5,93,1 17.5) (39,66.5,93,1 17.5) (41,70.5,98,1 24) E E E E E E E E E All Rights Reserved 32