Available online www.ejaet.om European Journal of Advanes in Engineering and Tehnology, 207, 4 (2): 29-34 Researh Artile ISSN: 2394-658X Seletion of the Best Belt Conveyor using AHP Abhinendra Singh Dhakar, Vaibhav Shivhare and Dinesh Kumar Kasdekar Department of Mehanial Engineering, Madhav Institute of Tehnology & Siene, Gwalior (MP), India er.abhinendra@gmail.om ABSTRACT There are various riteria whih affet the performane of Belt Conveyor. The performane of Belt Conveyor in terms of Maintenane ost and Load apaity is an essential issue for Sreening Creaser. Seletion of Belt Conveyor is a Multi-Criteria Deision Making (MCDM) problem. In that respet there are many methods available for seletion of Best Belt Conveyor, however, this paper targets to investigate the appliability of AHP to solve Best Belt Conveyor seletion problem. AHP is a method that assists in hoosing greatest alternatives by pair wise omparison of eah other and their riteria artiulated as a matrix. In the Analyti Hierarhy Proess (AHP), deision maker primaries give linguisti pair wise omparisons and then obtain an arithmetial pair wise assessment by seleting a ertain numerial sale to measure them. After that, eah olumn of the substitutes is multiplied as per the priority of the orresponding riteria and lastly the ranks are alulated by adding eah row. The pair wise omparison is made with the standard sale. On the basis of giving riteria, whih onlude how muh one alternative is more important than other? Finally derives a priority vetor from the numerial pair wise omparisons. Key words: Multi-Criteria Deision Making [MCDM], Belt Conveyor, Analyti Hierarhy Proess [AHP] INTRODUCTION Convey is an important logisti ation in the prodution systems influening smoothness of the prodution proess. Belt Conveyor onveys system play an important role in Timber Industry, mining, handling of bulk material, stone industry and many additional fields where large quantities of goods have to be onveyed [-2]. The belt onveyor depends upon their presentation, no issue whether it is in metallurgial industry, in the mining industry or building industry. Seletion of best belt onveyor assembly is a Multi-Criteria Deision Making (MCDM) problem [3-4]. Multi riteria deision making initiates deision-making troubles whih the deisions are making effets, onsidered from the point of view of several riteria. As the deision making problems, it is ompulsory to take into onern all elements, whih influene the result of the investigation, the relation among them and the intensity by whih they inter relate. One of the ways how to demonstrate these fats is the formation of a ertain hierarhial struture. An MCDM method, as its own name suggests, is for use in situations when more than one deisive fator must be onsidered (example Base Length, Load Capaity, Material Cost, Roller Cost et.). Fundamentally, these methods work with the same fundamental tool deision matrix [5]. AHP method is flexible, intuitive appeal to the deision makers and it has an ability to hek the onsisteny ratio. There are several MCDM methods [6-7], but in this paper AHP has been used [3, 8] beause of its simpliity and appliability. In this study, the different possible alternatives are the four different Belt onveyor of sreening Creaser. In order to identify the riteria whih, the AHP model will be based on, we take the supervision from the engineers of sreening Creaser. The identified riteria were then validated by other sreening reasers. In the end, the riteria of the AHP struture we have developed are Base Length (BL), Load Capaity (LC), Material Cost (MC), and Roller Cost (RC). ANALYTIC HIERARCHY PROCESS [AHP] The Coneption and the Priniples of AHP AHP, whih is a type of method of multi-objetive deision and ombine qualitative and quantitative analysis, was initially reated by Amerian sholar Saaty. The basi theory of AHP is that the multifaeted problem was deom- 29
Dhakar et al Euro. J. Adv. Engg. Teh., 207, 4 (2):29-34 posed into omposing fators, whih are grouped hierarhially aording to their administrative affiliation. It has partiular appliation in group deision making, and is used around the world in a spaious variety of deision situations, in fields suh as government, business, industry, healthare, shipbuilding and eduation. The establishment of judgment matrix is the key of the appliation of AHP [9]. The harateristi feature of AHP in human fators analysis is a quantitative analysis of the qualitative problem and mathemati modelling of reviewers put into effet Priority. So not muh quantitative data are needed by AHP, but all the related fators and their interrelation must be desribed, whih is a matter that the ultimate answer is orret or not. Methodology of AHP AHP has been designed to explain omplex problems involving multiple riteria [0-]. It allows deision-makers denote their preferenes using a status sale [2-3]. A representation flow hart desribing the methodology adopted shown in fig. Fig. Shemati Flow Chart Desribing the Methodology The analysis and basi steps of AHP Reognize the Problem Reognize the sope of problem and the relations between the fators. This thread is not only the basis of the approah for AHP, but also the key point of the entire proess. The orretness of the logial relations among fators in a straight line relates to the reliability of the final result. Originate Pairwise Comparison Matries In this step deision maker have to originate a pairwise omparison matrix of elements at eah level in the hierarhy, virtual to eah element at the next level. At AHP, if M is the alternative and N is the riteria, then the deision maker has to onstrut N judgment matries of alternative of M x M order and an M judgment matrix of riteria of N x N order. Lastly, the deision matrix of M x N order is formed by using relative sores of the alternative with respet to eah riterion. At AHP, Saaty s sale of the real number from -9 and their reiproals are used to assign importane in a systemati manner. Relational sale proposed by Saaty s [3, 8,, and 3] is shown in Table -. Table - Fundamentals of Saaty s Sale Intensity of Importane Definition Equal Importane 3 Moderate Importane 5 Strong Importane 7 Very strong or Demonstrated Importane 9 Extreme Importane 2,4,6,8 For ompromise between the above value Reiproal If ativity, I have one of the above number assigned to it when ompared with ativity j, then j has the reiproal value when ompared with I. 30
Dhakar et al Euro. J. Adv. Engg. Teh., 207, 4 (2):29-34 The Relative Importane of Different Criteria In this step, the relative importane of different riteria with respet to the goal of the problem and the alternative sore with respet to eah of the riteria is determined [4]. For N riteria the size of the omparison matrix (C) will be N x N and ij will denote the relative importane of riteria i with respet to the riteria j. In the matrix, ij = only when i = j and ij = ij. The relative importane of the i th riteria (Wi) is determined by alulating the geometri mean of the i th row and then normalizing the geometri means of the row from the above matrix. Then matrix C3 and C4 are alulated suh that C3 = CxC2 and= C 3 Where, C2 = [W, W2 WN] T C 2 C ij = [ 2... N Prinipal Eigenvetor (λmax) of the original pairwise omparison matrix (C) is alulated from the average of matrix C4. To hek the onsisteny in pairwise omparison, judgment, onsisteny index (CI) and onsisteny ratio (CR) are alulated. RCI is a Random Consisteny Index and its value ould be found out from Table -2. The value of CR should be equal to or less than 0. for onsidering the judgment is onsistent or aeptable. Otherwise the judgment will be inonsistent and unaeptable. In this situation deision maker has to add some hange in the pairwise omparison matrix. 2 Similarly, N numbers of pairwise omparison matries, one for eah riteria of M x M order are formed where eah alternative is used against all of its ompetitors and then the pairwise omparison is made with respet to eah for the deision riterion. The eigenvetor of eah of these N matries represents another performane sore in the orresponding riteria and a olumn of the final deision matrix is formed [5-6]. The deision matrix (Table -3) resembles the following: M i= a ij = () Determine the Final Priority of All the Alternatives In this step, determine the final priority of all the alternatives [7-8], onsidering the alternative sares (aij) in eah riteria and (Wj) weight of the orresponding riteria using the following equation [9-20] N 2...... N 2N... ] AAHP = max For i=, 2, 3 M (2) Table -2 Random Consisteny Index (RCI) Value N 2 3 4 5 6 7 8 9 0 2 3 4 5 RI 0 0 0.52 0.89..25.35.4.45.49.5.54.56.57.59 Table -3 Deision Matrix of AHP Criteria Alternatives C C2 C3 C4 CN W W2 W3 W4 WN A a a2 a3 a4 an A2 a2 a22 a23 a24 A2N AM am am2 am3 amn RESULT AND DISCUSSION The belt Conveyor problem is deomposed into a hierarhy as shown in fig. To do this, first level is the goal, next level is the riteria and the level is the five alternatives (belt onveyor) whih are to be evaluated. Criteria to the Belt Conveyor are: Base Length (BL) 2. Load Capaity (LC) 3. Material Cost (MC) and 4. Roller Cost (RC). Table -4 shows the pairwise omparison of matrix of the riteria in ase of the Performane of Belt Conveyor. Table -6 established the global priority of the Belt Conveyor for Performane. Final ranking sore of alternatives on the basis of Performane are as shown in Fig. 4. In this figure it an be seen that Belt Conveyor is the best Conveyor. 3
Dhakar et al Euro. J. Adv. Engg. Teh., 207, 4 (2):29-34 Fig. 2 Deomposition of Belt Conveyor Problem into a Hierarhy for Performane Table -4 Pair-Wise Comparison Matrix Performane BL LC MC RC Priority BL 0.6 0. 0.33 0.05 LC 6 0.33 2 0.22 MC 9 3 3 0.53 RC 3 0.05 0.33 0.6 λ max = 4.09, CI = 0.03 and CR = 0.033 Table -5 Shows Pair-Wise Comparison Judgment of Belt Conveyor of Alternative BL BC- BC-2 BC-3 BC-4 Priority BC- 0.2 0.33 3 0.32 BC-2 5 3 7 0.562 BC-3 3 0.33 5 0.262 BC-4 0.33 0.4 0.2 0.052 λ max = 4.4, CI =0.040, CR =0.044 LC BC- BC-2 BC-3 BC-4 Priority BC- 0.4 0.25 0. 0.042 BC-2 7 3 0.33 0.252 BC-3 4 0.33 0.4 0.05 BC-4 9 3 7 0.588 λ max = 4.3, CI =0.045, CR =0.0505 MC BC- BC-2 BC-3 BC-4 Priority BC- 2 5 8 0.529 BC-2 0.5 2 7 0.289 BC-3 0.2 0.5 3 0.30 BC-4 0.2 0.4 0.33 0.048 λ max = 6.092, CI =0.0076, CR = 0.0086 RC BC- BC-2 BC-3 BC-4 Priority BC- 7 4 9 0.648 BC-2 0.4 0.33 3 0.03 BC-3 0.25 3 5 0.228 BC-4 0. 0.33 0.2 0.049 λ max = 4.075, CI =0.0358, CR = 0.0402 Table -6 Loal and Global Priorities Performane BC LC MC RC Sore BC- 0.32 0.042 0.529 0.648 0.399 BC-2 0.562 0.252 0.289 0.03 0.253 BC-3 0.262 0.05 0.30 0.228 0.4 BC-4 0.052 0.588 0.048 0.049 0.65 32
Dhakar et al Euro. J. Adv. Engg. Teh., 207, 4 (2):29-34 Fig. 3 Sore of Belt Conveyor for Performane CONCLUSION The main goal of the appliation of multi riteria deision-making methods is that all obstales the deision-maker has solved of the deision-making problem were onstantly managed. In pratie the emphasis is often put on the seletion of the best option, the best solution at the large amount of information. Analytial hierarhial proess (AHP) belongs to frequently used multi riteria, methods, whih are used in more omplex deision-making tasks. The method an be used not only for the situation of preferenes among riteria, but also among variants. In this Paper, a ase study was performed to hoose the best belt onveyor assembly. The importane of the dimensions was evaluated by industry experts. In our study AHP method is used. Belt Conveyor- was found to be the suitable Belt Conveyor among the given four alternatives. The results point out that this optimization method heavily depends on global priorities of the riteria and the alternatives of the problem. One of the advantages of the proposed method is its ability and flexibility with the different appliations. REFERENCES [] Miriam Andrejiova, Zuzana Kimakova, Daniela Marasova. Using AHP Method at the Determination of the Optimal Seletion Criteria of Conveyor Belts. International Journal of Engineering, 203, 2 (TomeX) 55-60. [2] TL Saaty Axiomati foundation of the Analyti Hierarhy Proess Management Siene 983, 32 (7) 84-855. [3] TL Saaty, Highlights and Critial Points in the Theory and Appliation of the Analyti Hierarhy Proess, European Journal of Operational Researh, 994, 74, 426-447. [4] YZ Mehrjierdi, Strategi System Seletion with Linguisti Preferenes and Grey Information Using MCDM, Applied Soft Computing, 204, 8, 323-337. [5] Y Deng, TS Chan Felix, Y Wu and D Wang, A New Linguisti MCDM Method based on Multiple- Criteria Data Fusion, Expert System with Appliation. 20, 38 (6) 6985-6993. [6] S Fienrek and J Zak, planning of an Integrated Urban Transportation System based on Maro-Simulation and MCDM/A Method, Proedia- Soial and Behavioural Sienes, 202, 54 (4) 567-579. [7] L Anojkumar, M Ilangkumaran and V Sasirekha, Comparative Analysis of MCDM Method for Pipe Material Seletion in Sugar Industry, Expert System with Appliation, 204, 4 (6) 2964-2980. [8] TL Saaty, Axiomati Foundation of the Analyti Hierarhy Proess, Management Siene, 986, 32 (7) 84-855. [9] Chen Lijuana and Chang Shinanb, An Approah of AHP for Human Fators Analysis in the Airraft Iing Aident. Elsevier, Proedia Engineering, 20, 7, 63-69 [0] TL Saaty, How to Make a Deision: The Analyti Hierarhy Proess, European Journal of Operational Researh, 990, 48, 9-26. [] TL Saaty, Priority Setting in Complex Problems, IEEE Transations Engineering Management, 983, 30, (3) 40-55. [2] TL Saaty, The Analyti Hierarhy Proess, MGraw Hill, New York; 980. [3] TL Saaty, Fundamentals of Deision Making and Priority Theory with AHP, RWS Publiations, Pittsburgh, 2000. [4] W Pedyez and MA Song, Granulation of Linguisti Information in AHP Deision-Making Problems, Information Fusion, 204, 7, 93-0. [5] HH Goh, BC Kok, BC Yeo, Combination of TOPSIS and AHP in Load Shedding Sheme for Large Pulp Mill Eletrial System, Eletrial Power and Energy System, 203, 47, 98-204. [6] Giuseppe Bruno, Esposito Esposito, Andrea Genovese, Renato Passaro AHP-Based Approahes for Supplier Evolution, Problem and Perspetives. Journal of Purhasing Supply Management, 202, 8 (3) 59-72. 33
Dhakar et al Euro. J. Adv. Engg. Teh., 207, 4 (2):29-34 [7] A Ishizaka and NH Nguyen, Calibrated Fuzzy AHP for Current Bank Aount Seletion, Expert Systems With Appliations, 203, 40 (9) 3775-3783. [8] MP Amiri, Projet Seletion for Oil-Field Developed by Using the AHP and Fuzzy TOPSIS Method, Expert Systems with Appliations, 200, 37 (9) 628-6224. [9] Katarzyna Nosal and Katarzyna Soleka, Appliation of AHP Method for Multi-Criteria Evaluation of Variants of the Integration of Urban Publi Transport, Transportation Researh Proedia, 204, 9 (4) 83-96. [20] Amrita Singh, Sharad Agrawal, Dinesh Kumar Kasdekar and Chandra Shekhar Malvi, Seletion of R4-Tyres using Analyti Hierarhial Proess on the Basis of Uniformity and Strength, Sientist, Tehnial and Medial 204, 2 () 7-7. 34