Presenting Fuzzy Multi-Objective Mathematical Programming Model in order to Suppliers Selection and Allocating Orders in a Supply Chain

Transcription

1 Turkish Journal of Engineering and Technology. Vol., 3 (5), 75-88, 2 Available online at ISSN Presenting Fuzzy Multi-Objective Matheatical Prograing Model in order to Suppliers Selection and Allocating Orders in a Supply Chain Behjat Davarpanah *, Leila Lagzaie Departent Of Matheatics, Zabol Branch, Islaic Azad University, Zabol, Iran * Corresponding Author Eail: Davarpanah_Behjat@yahoo.co Abstract Issues of supplier selection play a key role in the context of supply chain anageent. In today's copetitive world, enterprises have paid special attention to choosing the right suppliers selection because this selection helps the to reduce their purchasing costs and iprove the quality of their final products and services. Supplier selection is an issue of ulti-criteria decision aking that includes both quantitative and qualitative criteria such as the cost of purchasing of each unit, tiely delivery, quality of service and the other factors. In this study, a fuzzy ulti-objective atheatical prograing odel was presented in order to supplier selection and allocating orders in a supply chain. In the proposed odel was used a copensatory and non-copensatory cobined approach, haronic collective, and taking into account satisfactory levels for degree of ebership or satisfactory functions and fuzzy constraints. The proposed odel was ipleented in an organization. Keywords: Fuzzy Multi-Objective Matheatical Prograing, Fuzzy Theory, Supplier Selection, Supply Chain Manageent. Introduction Supplier scoring and assessent is process that use to assess the perforance of suppliers. Suppliers are copared on the basis of the value added and the cost of the entire supply chain. Unfortunately, sourcing decisions are often only focused on price of incoing products fro suppliers. Many of the other characteristics of suppliers, such as lead tie, reliability, quality, and design capability that effect on the total cost of collaborate with a supplier are ignored. A good process of suppliers scoring and assessent should consider all aspects of supplier perforance that are affected the total cost of the suppliers. Supplier selection uses the output of supplier scoring and assessent in order to identify the appropriate suppliers. Then supply contract will negotiate with suppliers. A good contract explains all factors affecting on supply chain perforance and is designed in order to enhance the profitability of the entire supply chain so that to be aintained the interests of the parties. Considering that about 8 percent of the cost of a product is deterined by its design, it is vital that suppliers are actively involved in this process. Cooperation in designing allows to suppliers and producers that when designing the final product coponents work together. Also, cooperation in designing provides assurance that changes in the designing will notice effectively to all ebers involved in the chain. When the product is designed, supplies are the process by which suppliers sends its product in response to custoer order. The ai of supplies is fulfilling the orders and delivery of the according to a tie schedule with a iniu of cost. Finally, the role of sourcing planning and analysis is analysis of costs related to different suppliers and 75

2 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 identifying the opportunities in order to reduction the total cost. Effective sourcing processes in an enterprise can iprove profits and added value of supply chain. Issues the supplier selection plays a key role in the context of supply chain anageent. In today's copetitive world, enterprises have paid special attention to choosing the right suppliers selection because this selection helps the to reduce their purchasing costs and iprove the quality of their final products and services (Ozkok & Tiryaki, 2a). Supplier selection is an issue of ulticriteria decision aking that includes both quantitative and qualitative criteria such as the cost of purchasing of each unit, tiely delivery, quality of service and the other factors. In this kind of issues ay be a conflict between the objectives of the decision. In this kind of issues often follow two ain objectives, Firstly, which suppliers will purchase fro the? And second, how uch will purchase fro each selected supplier? Several studies was carried out on the identification of iportant criteria in the supplier selection, for exaple, Dickson (9) identified 23 criteria for supplier selecting. In another study was conducted in 99, Weber et al (99) studied 74 articles in the field of supplier assessent and were classified the in ters of the used criteria and analytical ethods (Weber et al., 99). Another category of study were conducted through representing appropriate ethod to assess their suppliers (Ain et al., 2). For exaple, Ghodsypour and O Brien (998) offered a cobinatorial approach of Analytic Hierarchy Process (AHP) and linear prograing in order to supplier selection. Erol and Jr (23) have developed a ixed integer nonlinear prograing approach to assess suppliers and orders allocation that including the qualitative and quantitative conflicting purposes. Aid et al (2) presented a fuzzy ulti-objective linear prograing odel in order to overcoe the abiguity of the inforation in the supplier selection. Deirtas and Austen provided an integrated approach using analytis network process (ANP) and integer linear prograing fuzzy to choose the best supplier. also, Wang et al (29) presented a hierarchical TOPSIS ethod to choose their supplier. In the research literature will be discussed the research of Chai et al that reviewed the articles in the field of supplier selection in 28 and 22 and presented the appropirate clasification. Therefore, the ai of the study was presenting the fuzzy ultiobjective atheatical prograing odel to supplier selecting and orders allocation in a supply chain. Methodology The studied copony Alpha Copany is coposed of three ain parts that is working in the petrocheical industry. Considering that the copany is in contact with any suppliers, requires the use of integrated and science process is assessted in order to iprove the syste of the purchase in the copany.coerce section is in contact with any internal and external suppliers in order to provide the piceses and always is looking for the best the purchase fro the best provider. Due to high extension of pieces and suppliers nuber in studied copany, researcher to test their proposed odel with the opinion of dear industry consultant selected eight pieces/ain products that both in ters of valuable will be strategic and also in ters of nature will be ultiple sourcing. This eans that several supplier to supply it. This research was a type of atheatical analysis and odeling, because it was followed the atheatical odeling and developent of existing procedures. In fact, in this research, in order to full study of fuzzy atheatical prograing techniques were studied the theoretical atheatical odeling, linear prograing, atheatical prograing under uncertainty conditions and siilar topics. The proposed atheatical odel in this study was as follows: n l Miniize Z pc x n l i j k n l i j k n i j i j k Miniize Z def (r ) x n 2 ij i j Miniize Z del(r ) x Subject to : j j n 3 ij i j pc x B x s.y ij j def (r ) x def in ij ij x Di,i,2,..., n x P, j,2,..., accepted x and integer,i 2,3,4,5 Y or (r ) x i \ 7

3 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 Paraeters and variables of research are expressed in Table. Table. Introduction of odel coponents. Model indices I J K Model paraeters pc def (r ij) del(r ij) B s ij accepted def (r i) Di in P ij Decision variables of odel x y j Definition Coponents Suppliers Discount conditions Definition The cost of purchasing the piece i fro supplier j in discount conditions k Defective rate the piece i purchased fro supplier j Lead tie the piece i fro the supplier j The total purchase budget Supplier capacity j to supply the piece i Acceptable the defective rate of piece i The total deand for piece i The iniu aount of supplied piece i fro supplier j Definition The total aount of the purchase of the piece i fro supplier j in discount conditions k Selecting or deselecting of supplier j th The approach of proposed solution There are several solving ethods of ulti-objective probles. The first way was Zieran ethod that he considered equal the objective functions and constraints in his odel which is not always in this way in real world issues. Tivari presented a collective odel that λ k and λ r variables indicated the level of achieveent to fuzzy objective functions and fuzzy constraints, respectively. They resolved the proble of Zieran odel by adding weight to the objectives and constraints. Lai and Hwang (993) offered a odel in which an overall λ were added for the ax-in to the Tivari odel. Ozkok and Tiryaki (2b) presented a odel in which there was possibility for copensatory or non-copensatory control. By exaining all these ethods and odels and considering their strengths, a odel is represented that had all the following features: being copensatory being non-copensatory possibility for being copensatory or non-copensatory control being haronic ebership functions weighting the ebership functions existence of threshold for the degree of acceptance of ebership function The approach of proposed solution is presented as follows: j K P j j J K Zj gk P K xi, i, 2,..., n 77 j K j K j k Maxiise ( w ) S.t, (x), j, 2,..., J (x), k, 2,..., K g (x) b, p, 2,..., M J K j j K K j k و 2,k,...,,,, j, 2,..., J K or w, w,

4 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 Logarithic fuzzy preference technique There were two types of technique to extract the weight fro paired coparisons. The first of the was techniques that obtained weights are in the for of real nubers such as fuzzy preference prograing technique (FPP) and logarithic fuzzy preference prograing (LFPP). The second of the was techniques that extract the weights in the for of fuzzy nubers. LAMBDA-Max and logarithic fuzzy least squares techniques are in this type. In this study, in particular LFPP ethods will be used to analyze data and obtain the values of weights. As well as to solve the LFPP proble, WINQSB software will be used to obtain the exact answers without error. LFPP ethod described as in the following: Most people initially looking for second ways due to being easier to calculate a definite nuber as weight. The first technique fro this type was developed analytical ethod that was proposed by Chang and was proved by Wang soon that weights derived fro this ethod are invalid and will not be able to properly deonstrate the iportance of the relationship between decision variables or replaced. In fact, this ethod should not be used to extract the weights. Also, fuzzy preferences prograing technique that was introduced by Mikhailovich, had considerable weaknesses. For exaple, we ay use this technique to deterine priorities and reach to contradictory vectors or vectors that are subultiples together. This non-uniqueness of in the solution challenges the use of this ethod in deterining the priority. By an equivalent aking, LFPP technique or logarithic fuzzy preference prograing were obtained based on nonlinear logarithic and was proved that do not have drawbacks of old ethods. The objective functions and constrains of the FPP procedure were as follows which can extract the a Fuzzy pair-wise coparison atrix by solving the: Maxiize By two equivalent aking:,, FPP was converted to LFPP. In fact, nonlinear equations were converted to logarithic nonlinear equations, and finally the objective function and new constrains will obtain as follows:, But again in the above calculation there were possibility for being negative λ; therefore two non-negative variable η and δ for i and j fro to n enters to equations and objective function and constraints of logarithic fuzzy preference prograing (LFPP) technique was obtained as follows: 78

5 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 و Required certain weights will obtained fro fuzzy pair-wise coparison table by solving this proble. Results Deterine the degree of iportance of objectives and constraints Fuzzy pair-wise coparison atrix was fored by experts in order to deterine the degree of iportance of objectives and constraints. Each of the experts copare the objectives and constraints together by using the following range (Table 2): Table 2. Fuzzy range for the copletion of paired coparisons. Reverse of triangular fuzzy nubers Triangular fuzzy nubers (.9,.9,.9) RES (9, 9, 9) ES(Extreely Strong) It have absolutely preference (.9,.8,.7) RIVS (7, 8, 9) IVS(Interediate) Interediate (.8,.7,.) RVS (, 7, 8) VS(Very Strong) It have a lot of preference (.7,.,.5) RIS (5,, 7) IS(Interediate) Interediate (.,.5,.4) RS (4, 5, ) S(Strong) It have preference (.5,.4,.3) RIMS (3, 4, 5) IMS(Interediate) Interediate (.4,.3,.2) RMS (2, 3, 4) MS(Moderately Strong) It have a little preference (.3,.2, ) RIES (, 2, 3) IES(Interediate) Interediate (,, ) E (,, ) E(Equally Strong) It is equal By using arithetic ean of the pair-wise coparison atrices of experts, atrix of cuulative fuzzy pair-wise coparison was obtained as follows (Table 3): Table 3. Matrix of cuulative fuzzy pair-wise coparison between the criteria L Budget constraints u L Deand constraints u Maxiu acceptable defective rate constraints L u Total purchase cost (first objective function) L u The cuulative defective rate (second objective function) L u The cuulative lead tie (second objective function) L u Logarithic fuzzy preference prograing technique was used in order to extract the absolute weight fro the above atrix that according to this technique ust be solved the non-linear odel for obtaining the weights. In following odel was considered and M paraeter equal to : 79

6 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 After solving the above power of square, weights of criteria were calculated as follows (Table 4): Table 4. The degree of iportance of criteria. X exp(x) Final weight Budget constraints.388 Deand constraints Maxiu acceptable defective rate constraints Total purchase cost (first objective function) The cuulative defective rate (second objective function) The cuulative lead tie (second objective function) The weights derived fro this stage can be used as input in the proposed odel. Solving the proposed odel Before solving the odel should be solved a separate odel for each of the objective functions till iniu and axiu aount of the will achieve according to the different eberships. The results of these three objective functions associated with soe fuzzy constraints were shown in the following table (Table 5): Table 5. The degree of iportance of criteria. µ= µ = µ = Total purchase cost Min Z The cuulative defective rate Min Z The cuulative lead tie Min Z Budget B Deand for product i D i D i-.5(d i) D i D i+.5(d i) Acceptable defective rate of coponent i def ac.(ri) def ac.(ri)-.5(def ac.(ri)) def ac.(ri) def ac.(ri)+.5(def ac.(ri)) Budget, deand and acceptable defective rate are fuzzy. Each of the objective functions was solved by using lower and upper liits of the fuzzy nubers, and iniu and axiu values of objective functions were calculated objective functions. In the proposed odel in order to weighting the desirability of different ebership functions in the objective function of the proposed odel, were used fro obtained weights fro logarithic fuzzy preference prograing technique. Different scenarios are shown in Table : 8

7 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 Table. Different scenarios for solving the proposed odel. W Scenario s γ Total purchase cost cuulativ e defective rate cuulativ e lead tie Budget Deand acceptabl e defective rate Explanation s S S S S S S S S S S S Equal weight S Ephasis on the objective functions S Ephasis on the 8

8 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 budget S Ephasis on the quality S Ephasis on the deand S Ephasis on the lead tie Constraints and the objective function were written based on a scenario 5 that desired code shown in the following to clarify the issue: fn.. Maxiize Z=.5*l+.8227*l+.737*l2+.927*l3+.94*l4+.927*l5+.892*l; Constraints of acceptable defective rate c...3*(x+x2+x3+ x2)+.*(x3+x32+x)+.*l+.*l5 <=2.; c2...5*x24+.5*x25+.7*x2+.*x27+.24*l+.24*l5<=5.4; c3...*x38+.*x39+.4*x3+.4*x3+.2*l+.2*l5<=3.95; c4...2*x42+.5*x43+.*x44+.2*l+.2*l5<=4.2; c5...7*x55+.*x5+.35*l+.35*l5<=7.35; c...4*(x7+x+x73)+.2*(x8+x82+x83)+.5*(x9+x92+x93)+.4*l+.4*l5<=7. 9; c7...2*x+.3*x+.7*x2+.2*l+.2*l5<=2.52; c8...*(x823+x8232+x82)+.2*(x824+x8242+x8243)+.8*l+.8*l5<=.8; Constraints of deand c9.. *x+*x2+*x3+ x2+*x3+*x32+*x+2*l+2*l<=42; c.. *x+*x2+*x3+ x2+*x3+*x32+*x+2*l+2*l>=38; c.. x24+x25+x2+x27+3*l+3*l<=3; c2.. x24+x25+x2+x27+3*l+3*l>=57; c3.. x38+x39+x3+x3+4*l+4*l<=79; c4.. x38+x39+x3+x3+4*l+4*l>=7; c5.. x42+x43+x44+4*l+4*l<=84; c.. x42+x43+x44+4*l+4*l>=7; c7.. x55+x5+7*l+7*l<=47; c8.. x55+x5+7*l+7*l>=; c9..*x7+*x+*x73+*x8+*x82+*x83+*x9+*x92+*x93+7*l+7*l <=58; c2..*x7+*x+*x73+*x8+*x82+*x83+*x9+*x92+*x93+7*l+7*l >=43; c2.. x+x+x2+2*l+2*l<=42; c22.. x+x+x2+2*l+2*l>=38; c23.. *x823+*x8232+*x82+*x824+*x8242+*x8243+*l+*l<=2; c24.. *x823+*x8232+*x82+*x824+*x8242+*x8243+*l+*l>=9; Constraints of iniu purchase c25.. x2>=2; c2.. x2>=5; Constraints of production power c27.. *x+*x2+*x3<=5; 82

9 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 c28.. x2<=4; c29.. *x3+*x32+*x<=; c3.. x24<=5; c3.. x25<=7; c32.. x2<=; c.. x27<=7; c.. x38<=8; c35.. x39<=9; c.. x3<=7; c37.. x3<=; c38.. x42<=2; c39.. x43<=75; c4.. x44<=9; c4.. x55<=2; c42.. x5<=25; c43.. *x7+*x+*x73<=8; c44.. *x8+*x82+*x83<=7; c45.. *x9+*x92+*x93<=9; c4.. x<=5; c47.. x<=; c48.. x2<=7; c49.. *x823+*x8232+*x82<=5; c5.. *x824+*x8242+*x8243<=3; Constraints related to discounts c5.. x<=4*y; c52.. x2>=5*y2; c53.. x2<=*y2; c54.. x3>=35*y3; c55.. x3<=49*y3; c5.. x3<=4*y3; c57.. x32>=5*y32; c58.. x32<=*y32; c59.. x>=35*y; c.. x<=59*y; c.. x7<=74*y7; c2.. x>=75*y; c3.. x<=24*y; c4.. x73>=25*y73; c5.. x73<=79*y73; c.. x8<=74*y8; c7.. x82>=75*y82; c8.. x82<=24*y82; c9.. x83>=25*y83; c7.. x83<=9*y83; c7.. x9<=74*y9; c.. x92>=75*y92; c73.. x92<=24*y92; c74.. x93>=25*y93; c75.. x93<=49*y93; c7.. x823<=4*y823; c77.. x8232>=5*y8232; c78.. x8232<=*y8232; c79.. x82>=35*y82; 83

10 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 c8.. x82<=49*y82; c8.. x824<=9*y824; c82.. x8242>=*y8242; c83.. x8242<=9*y8242; c84.. x8243>=2*y8243; c85.. x8243<=29*y8243; c8.. *y+*y2+*y3<=; c87.. *y3+*y32+*y<=; c88.. *y7+*y+*y73<=; c89.. *y8+*y82+*y83<=; c9.. *y9+*y92+*y93<=; c9.. *y823+*y8232+*y82<=; c92.. *y824+*y8242+*y8243<=; Constraints of budget c93.. 8*x+75*x2+7*x3+ *x2+9*x3+88*x32+85*x+3*x24+5*x25+4*x2+35*x27+85*x38+2*x39+*x3+5*x 3+75*x42+9*x43+8*x44+5*x55+*x5+4*x7+38*x+*x73+45*x8+43*x82+ 4*x83+35*x9+*x92+*x93+8*x+*x+7*x2+4*x823+35*x *x82 +5*x824+4*x *x8243+*l+*l4<=58; Constraints related to first objective function c94.. 8*x+75*x2+7*x3+ *x2+9*x3+88*x32+85*x+3*x24+5*x25+4*x2+35*x27+85*x38+2*x39+*x3+5*x 3+75*x42+9*x43+8*x44+5*x55+*x5+4*x7+38*x+*x73+45*x8+43*x82+ 4*x83+35*x9+*x92+*x93+8*x+*x+7*x2+4*x823+35*x *x82 +5*x824+4*x *x *l+352*l<=379; Constraints related to second objective function c95...3*(x+x2+x3)+.3*x2+.*(x3+x32+x)+.5*x24+.5*x25+.7*x2+.*x27+.* x38+.*x39+.4*x3+.4*x3+.2*x42+.5*x43+.*x44+.7*x55+.*x5+.4*(x7 +x+x73)+.2*(x8+x82+x83)+.5*(x9+x92+x93)+.2*x+.3*x+.7*x2 +.*(x823+x8232+x82)+.2*(x824+x8242+x8243)+.29*l+.29*l2<=2.23; Constraints related to third objective function c9.. *(x+x2+x3)+2*x2+5*(x3+x32+x)+8*x24+*x25+8*x2+2*x27+2*x38+ 8*x39+9*x3+9*x3+*x42+2*x43+2*x44+4*x55+4*x5+3*(x7+x+x7 3)+2*(x8+x82+x83)+*(x9+x92+x93)+3*x+*x+8*x2+4*(x823+x8 232+x82)+35*(x824+x8242+x8243)+92*l+92*l3<=77797; Constraints related to λ c97.. l+l<=; c98.. l+l2<=; c99.. l+l3<=; c.. l+l4<=; c.. l+l5<=; c2.. l+l<=; In the above odel λ was used instead of L and - instead of L-L. First, ten scenarios were solved and the results were analyzed. The proble was converted to a ixed integer proble for solving ulti-objective fuzzy proble by using the proposed odel that it can be calculated the results of ain proble by solving it. Mixed integer proble had 2 constraints and variables that these 84

11 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 variables were in three categories such as integer, zero and one and continuous. Based on the odel proposed, solving results of the first ten scenarios are presented in Table 7: Table 7. Solving results of the first scenarios. Scenario S S2 S3 S4 S5 S S7 S8 S9 S Variable Γ=. Γ =.2 Γ =.3 Γ =.4 Γ =.5 Γ =. Γ =.7 Γ =.8 Γ =.9 Γ = x x2 x3 x2 x3 x x x24 x25 x x27 x38 x39 x x3- x4-2 x4-3 x4-4 7 x5-5 x x-7 x- x-73 x-8 x-82 x-83 x-9 x-92 x-93 x7-2 x7-2 x7-22 x8-23 x8-232 x8-2 x8-24 x x

12 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 λ Max Z Total purchase cost cuulative defective rate cuulative lead tie When γ =, the proposed odel was copletely transfored into a haronious collective copensatory odel and When γ =, the proposed odel was copletely transfored into a syetrical non- copensatory odel. It sees that total desirability or the degree of overall satisfaction (the objective function - ) decreased by increasing the aount of γ and proxiity to.5. In fact, this was due to the ain viewpoint about purchasing anageent that had nature of copensatory. As a result, whatever proble found the non-copensatory nature and γ was approaching to, copensatory effect the degree of fuzzy eberships or degree of desirability objective functions and fuzzy constraints will reduce. With regard to specific conditions of this proble and the aount of discounts, the obtained results are equal in the soe scenarios that this can help anagers to ake a final decision and perfor best allocation. Given the iportance of being copensatory criteria, researcher solved the above proble by collective haronic technique and taking into consideration the different weights for objectives and constraints. Different weights is shown in the scenarios fro to that in the scenario with the sae weight, and in the other scenarios proble dissolved with an ephasis on objectives, budget, quality, deand and lead tie and the results are shown in Table 8: Table 8. Solving results of the scenario fro to. Scenario Variable x x2 x3 x2 x3 x32 x x24 x25 x2 x27 Equal weight S 2 5 Iportance of objectives S2 2 5 Iportance of budget S Iportance of quality S4 2 5 Iportance of deand S5 2 5 Iportance of lead tie S 2 5 x38 x39 x3- x3- x4-2 x

13 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 x4-4 x5-5 x x-7 x- x-73 x-8 x-82 x-83 x-9 x-92 x-93 x7-2 x7-2 x7-22 x8-23 x8-232 x8-2 x8-24 x8-242 x8-243 λ Max Z Total purchase cost cuulative defective rate cuulative lead tie As it was shown, different values for objective functions was obtained according to the different weights, as a result the designed odel had high flexibility and considering the iportance of decision criteria in the each specific case and specific projects can be adapted for the intended proble by little changes. Conclusion The ai of this study was presenting the atheatical fuzzy ulti-objective prograing odel to select suppliers and allocating orders in a supply chain. In this study, the proposed odel was presented for allocating orders with regard to the weaknesses points of the older odels. According to the results of the odel that given to purchasing anageent, copatibility between odel results and the reality was approved. In this study, the ulti-sourcing strategies in the odeling of suggested situation was also considered. Modeling for the suggested situation was included three objective functions. One of the was related to cost iniization of total purchase, another was related to iniization of cuulative defective rate and finally, one of the objective functions was related to iniization of cuulative lead tie. Applied constraints were included the budget constraint, 87

14 Turkish. J. Engin. Tech. Vol., 3 (5), 75-88, 2 constraint for perforing the deand, constraint of defective rate, constraints of the variables range, and constraint related to ebership functions. The objectives of different scenarios were defined with regard to the consideration the various degrees of being copensatory or non-copensatory and as well as different weights that each of the scenarios were solved and the results were copared together. It suggested that according to the results, all purchases of organization will be organized in the for of the proposed odel so that best decisions will perfor in organization's purchasing syste and finally will increase organization profit by ore efficient purchasing syste. In order to iprove the present situation, assessent of supplier process perfors supplier's anageent instead of assessent of supplier and is focused on long-ter relationships. By creating long-ter relationships can be used ore discounts. Conflict of interest The authors declare no conflict of interest. References Aid A, Ghodsypour SH, O Brien C, 2. Fuzzy ulti-objective linear odel for supplier selection in a supply chain. International Journal of Production Econoics. 4(2): Ain SH, Razi J, Zhang G, 2. Supplier selection and order allocation based on fuzzy SWOT analysis and fuzzy linear prograing. Expert Systes with Applications. 38(): 4-2. Dickson GW, 9. An analysis of vendor selection systes and decisions. Journal of Purchasing. 2(): 5-7. Erol I, Jr WGF, 23. A ethodology for selection probles with ultiple, conflicting objectives and both qualitative and quantitative criteria. International Journal of Production Econoics. 8(3): Ghodsypour SH, O Brien C, 998. A decision support syste for supplier selection using an integrated analytic hierarchy process and linear prograing. International Journal of Production Econoics. 5 57: Lai YJ, Hwang CL, 993. Possibilistic linear prograing for anaging interest rate risk. Fuzzy Sets and Systes. 54(2): Ozkok BA, Tiryaki F, 2a. A copensatory fuzzy approach to ulti-objective linear supplier selection proble with ultiple-ite. Expert Systes with Applications. 38(9): 3-8. Ozkok BA, Tiryaki F, 2b. A copensatory fuzzy approach to ulti-objective linear supplier selection proble with ultiple-ite. Expert Systes with Applications. 38(9): 3-8. Wang JW, Cheng CH, Huang KC, 29. Fuzzy hierarchical TOPSIS for supplier selection. Applied Soft Coputing. 9(): Weber CA, Current JR, Benton WC, 99. Vendor selection criteria and ethods. European Journal of Operational Research. 59: