Plane Thermoelastic Waves in Infinite Half-Space Caused Decision Making: Applications in Management and Engineering Vol. 5, Issue 1, 2022, pp. 194-207. ISSN: 2560-6018 eISSN: 2620-0104 DOI: https://doi.org/10.31181/dmame0314052022b * Corresponding author. E-mail address: bipradasbairagi79@gmail.com (B. Bairagi) A NOVEL MCDM MODEL FOR WAREHOUSE LOCATION SELECTION IN SUPPLY CHAIN MANAGEMENT Bipradas Bairagi*1 1 Department of Mechanical Engineering, Haldia Institute of Technology, India Received: 1 April 2022; Accepted: 4 May 2022; Available online: 13 May 2022. Original scientific paper Abstract: The present investigation reveals a novel method for the evaluation of warehouse location for leagile supply chain entailing Fuzzy Multi Criteria Analysis (FMCA). An attempt has been made to apply the concept of decision theory for selecting the warehouse under contradictory criteria. Aggregate Modified Weighted Value (MWV) of normalized score of alternative is determined to evaluate Benefit Cost Ratio (BCR) which is considered as the warehouse selection index. The proposed algorithm is illustrated with a suitable numerical example to adjudge its desirable importance in capability and practicability. It also ensured that the achieved result clearly matches with those of previous research works. Finally, sensitivity analysis has been carried out that justify and supports the application of proposed algorithm in finding the most favorable outcome to the selection problem of warehouse location. Key words: Leagile supply chain, Warehouse location selection, FMCDM, Benefit cost ratio. 1. Introduction Supply chain is a system of association concerned with upstream, mid-stream and downstream link in diverse procedure and actions so as to create value in terms of services and products for customer satisfaction (Lee & Billington, 1992). The center of attention of the lean manufacturing has basically been on the diminution or abolition of waste. Lean is concerning doing extra with a smaller amount. The concept of lean work well if demand is predictable and stable and if variety is small (Agarwal et al. (2006). On the other hand for unpredictable demand and additional varieties of customer’s requisite, a higher level of agility is necessary (Lee, 2002). The objective of a supply chain is to exploit the value produced and robustly interrelated through effectiveness of supply chain. The ultimate achievement and profitability of a business depends on proper planning, appropriate design and suitable operation of a supply chain. The effectiveness of a usual supply chain largely A novel MCDM model for warehouse location selection in supply chain management 195 is affected by the transportation, inventory, information and facilities (Chopra & Meindl, 2001), proximity to customers and markets, suppliers’ availability, and even social issues as the potential stability for the warehouse location selection (Heizer & Render, 2004; Stevenson, 2006). Ocampo et al. (2020) applied group TOPSIS for selection of warehouse location considering diverse allocations of expert priority. Ulutas et al. (2021) introduced a novel combined Grey based MCDM approach in selection of ware house location. Micale et al. (2021) advocated an integrated TOPSIS with interval-valued ELECTRE TRI method for appropriate decision making in storage location problem. Kabak and Keskin (2018) used multi-criteria decision making and GIS approach for selection of warehouse for storing hazardous materials. Dey et al. (2017) introduced and applied an MCDM model with group heterogeneity for selection of the best warehouse location. Pang and Chan (2017) employed a data mining based new step by step algorithm foe assignment of storage location in warehouse. Emec and Akkaya (2018) applied stochastic analytical hierarchy process combining with fuzzy VIKOR method for the purpose of right decision making in appropriate warehouse location selection under MCDM environment. The analysis of the gap of the above literature survey exposes that previous researchers have applied MCDM techniques for selection of warehouse location. But this endeavor is not enough for exhaustive and wide decision making regarding proper selection of warehouse location. Thus an attempt in the current investigation is made to suggest a novel method for the evaluation of warehouse location for leagile supply chain entailing Fuzzy Multi Criteria Analysis (FMCA). The current paper has objective of improving the warehouse location selection techniques by using the concept of decision theory. The proposed algorithm has been employed to choose the top warehouse location amongst a set of realistic alternatives. The result of this novel algorithm is compared with works of past researchers on the identical problem. Lastly, an appropriate example is solved to illustrate the proposed algorithm. This investigation proves that the proposed algorithm is compatible for selection of multidimensional warehouse location problem. The current study also enhances the models used for the same. The paper is organized as follows. Section 2 presents a revision on he fuzzy set theory. Section 3 is dedicated for the proposed algorithm. In the section 4, an appropriate example is cited and solved. Sensitivity analysis is conducted in section 5. Section 6 explores the significance of the results of the work and section 7 presents some significant concluding remarks on the proposed model. 2. The Fuzzy Set Theory Decision makers usually have a preference subjective to objective assessment of fuzzy information. Theory of fuzzy set is used to convert these subjective data into numerical (objective) values (Chiou, 2005). A number of important definitions on fuzzy set are presented in the following subsection 2.1. 2.1. Some Important Fuzzy Definitions Definition 1: A fuzzy set A ~ is defined in a universe of discourse denoted by X specified by  x A ~ , called membership function, which connects every member x (a Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 196 real number) in X in a interval where x belong to [0, 1]. (Zadeh, 1965, Dubois and Prade, 1978). Definition 2: A Triangular Fuzzy Number (TFN) q is defined as a triplet  1 2 3, ,q q q . Membership function is characterized as follows (Chu, 2002; Keufmann & Gupta, 1991).   1 1 1 2 2 1 3 2 3 2 3 3 0, , , 0, . q x q x q q x q q q x x q q x q q q x q                  (1) Membership function of a TFN  1 2 3, ,q q q q is graphically shown in Fig. 1. Figure1. Membership function of a TFN  1 2 3, ,q q q q Definition 3: Let  1 2 3, ,q q q q and  1 2 3, ,r r r r be two TFNs, then the distance between the two fuzzy numbers can be calculated as        1 2 22 1 2 2 3 3 1 , 3 d q r q r q r q r            This method of calculating distance between two fuzzy numbers is termed as vertex method (Klir & Yuan, 1995). 2.2. Fuzzy Operations Let   321 ,, ~ qqqq  and  1 2 3, ,r r r r are two triangular fuzzy numbers. (a) Addition:  1 1 2 2 3 3, ,q r q r q r q r     (b) Multiplication of a fuzzy number  1 2 3, ,q q q q with a real number k  1 2 3, ,k q kq kq kq  where Rkk  &0 (c) Multiplication commutative property k q q k   where Rkk  &0 . (d) Division of a fuzzy number   321 ,, ~ qqqq  with a real number k 1 0 q1 q3 q2 x A novel MCDM model for warehouse location selection in supply chain management 197 31 2( ) , , qq q q k k k k         Where Rkk  &0 (Dubois, & Prade, 1978). 3. Proposed Algorithm A multi-criteria decision-making procedure has been applied for the evaluation of the most excellent warehouse location among various suitable alternatives. A quantitative approach of decision theory has been utilized in order to improve the selection procedure of warehouse location. The steps of the process of the newly proposed algorithm have been furnished below. Step 1: Formation of decision making committee: The committee unanimously chooses effective criteria and selects the alternatives preliminarily. Let, D1, D2...Dp are the decision-makers; C1, C2… Cn are the selected criteria; where number of benefit criteria is ‘b’ and that of cost criteria is ‘c’such that   .ncb  and A1, A2… Am are initially selected warehouse locations. Step 2: Formation of decision matrix: The committee makes a short list of alternative warehouses for further assessment on the basis of the selection criteria. Each alternative warehouse is given a score by the committee (or each member of the committee) with respect to each attribute; this score is termed as performance rating or simply rating. Performance ratings under objective criteria are expressed in crisp (specific) values and under subjective criteria are expressed in linguistic terms due to vagueness, imprecision, and ambiguity. The words or phrases like ‘good’, ‘very good’, ‘medium’, ‘poor’, ‘very poor’ etc. are called linguistic variables which are measured by human perception, feelings, experience etc. A decision matrix with m number of alternatives, 1 ... ... T i mA A A   , 1 j n(C C C ) where n is criteria number.   1 11 1 11 1i m 1 ... ... A A A j n k jk nk m n i k ijk ink m k mjk mnk C C C x x x DM x x x x x x                    (2) ijk x is performance rating in linguistic variable which is converted into fuzzy number ijk x where,  , ,ijk ijk ijk ijkx a b c or  , , ,ijk ijk ijk ijk ijkx a b c d is the performance rating of ith candidate (alternative) for j th factor (criterion) given by kth decision maker. Step 3a: Formation of weight matrix: the committee members give diverse importance to the criteria in linguistic variables according to their knowledge and experience. Each linguistic variable is changed into corresponding TFN. The weight matrix is presented in Eq. (3). Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 198 1 11 1 11 1 1 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... j n k p j j jk jp n n nk np C C C w w wC W C w w w C w w w                   (3) Here  jkjkjkjkw  ,, or  jkjkjkjkjkw  ,,, is the importance weight of jth (factor) criterion awarded by the k th (experts) decision maker in fuzzy numbers (triangular or trapezoidal) respectively Step 3b: Defuzzification and average weight: For decision-making committee, the defuzzified average weight of the criteria is considered. Defuzzified average weight of each criterion is calculated by using Eq. 4(a) for triangular fuzzy number or Eq. 4 (b) for trapezoidal fuzzy number. )( 3 1 1 jkjk P k jkj P w     4(a) )( 4 1 1 jkjkjk P k jkj P w     , j = 1, 2… n. 4(b) Step 3c: Normalization of weight: Normalization process of defuzzified average importance weight of each criterion is accomplished by Eq. 4(c).    n j j jN j w w w 1 , j = 1, 2, 3,… ,n. 4(c) Step 4a: Defuzzification and average rating: Determination of defuzzified average performance rating of every alternative for every subjective criterion by following Eq. (5a) for triangular fuzzy number or Eq. (5b) for trapezoidal fuzzy number. Average ratings for the objective criteria are calculated by the Eq. 5(c).     p k ijkijkijkij cba P x 1 3 1 5(a)     p k ijkijkijkijkij dcba P x 1 4 1 5(b)     p k ijkij x P x 1 1 5(c) Step 4b: Normalization of rating: Average rating of each alternative is normalized using Eq. (6).    m i ij ijN ij x x x 1 (6) Step 5: Calculation of modified weighted values: In this method, modified weighted normalized rating is advocated for the assessment of alternative for each benefit and non-benefit criterion. Performance weight replaces both interest factor as well as time A novel MCDM model for warehouse location selection in supply chain management 199 period under consideration. The benefit of using importance weight in its place of both interest rate and time period is that the computed coefficient of normalized rating provides a modified weight which depends upon corresponding weight. Modified- weighted benefit and non benefit criteria value is calculated using Eq. (7) and Eq. (8) respectively.   N jwN j N ij B ij wxmwv  1/ (7) N jw N j N ij C ij wxmwv        1/ (8)  B ijmwv Modified weighted value of normalized rating of alternative i under benefit criterion j, Cijmwv Modified weighted value of normalized rating of alternative i under cost criterion j, Nijx Corresponding normalized rating of alternative i under criterion j, Njw Corresponding importance weight of jth criterion. Weight of criteria has been modified using the Eq. (7) and Eq. (8) respectively. Here importance weight ( Njw ) is simultaneously an analogue to the interest rate and number of periods of cash flows in finding the future value in engineering economy. So, the weight of criteria successfully replaces discounted rate (or interest rate) and time period. The value so obtained will be termed as modified weighted value throughout the paper. This modified weighted value is multiplied with normalized rating in order to obtain the modified normalized rating which gives the measurement of benefit or cost. Step 6: Aggregate modified weighted value: Modified weighted values of ratings under benefit criteria and cost criteria are separately added for calculating aggregate modified-weighted value. Aggregate modified-weighted Value under benefit criteria and cost criteria reflect the assessment of total beneficial scores and cost scores respectively. Aggregate modified-weighted Values are calculated using the following simple Eq. (9) and Eq.(10) respectively.   1 / 1 N j b w B N N i ij j j AMWV x w    (9)   1 / 1 N j c w C N N i ij j j AMWV x w    (10) B iAMWV  Aggregate modified weighted value of alternative i for all benefit criteria. CiAMWV  Aggregate modified weighted value of alternative Ai for all cost criteria. Step 7: Benefit-Cost Ratio (BCR): In this paper, benefit-cost ratio is proposed to consider warehouse selection index. Benefit-cost ratio of an alternative is expressed by the ratio of aggregate modified weighted value of ratings under benefit criterion to that of the cost criterion. The higher value of Benefit Cost Ratio is desirable. The following Eq. (11) is used for calculating Benefit Cost Ratio (BCR) of ith alternative.  iBCR =  CiBi MWVMWV / (11) The higher the benefit cost ratio is, the better the alternative is. Step 8: Selection: The alternative warehouses are arranged in order of decreasing benefit cost ratio. Higher benefit-ratio is desirable. The best warehouse is one which Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 200 has the highest benefit cost ratio. Similarly the worst warehouse is one which is which attains the least benefit cost ratio. The above algorithm is applied to solve a warehouse location selection problem and to demonstrate implementation of the paradigm. 4. Illustrative Example Demonstrating Proposed Algorithm The proposed algorithm has been illustrated with an example. This has been presented dividing it into two sub-sections: Warehouse location selection problem definition, calculation and discussions. 4.1 Warehouse Location Selection Problem Definition The proposed algorithm has been demonstrated with an example on warehouse location selection. The objective is to develop a process for the combination of different criteria pertinent to selection of warehouse location with a view to obtain a comprehensive ranking order of the alternative warehouses. The example on warehouse location selection has been cited from Chen et al. (2006). In the present example, a homogeneous decision-making committee is composed of three decision- makers or experts namely D1, D2 and D3. Each members of the homogeneous decision making committee has equal importance weight. Through a screening test, the committee preliminarily takes three alternatives warehouse locations A1, A2 and A3 under consideration of further assessment. The committee also considers five subjective decision criteria viz. Cost (C1), Possibility of expansion (C2), Availability of required material (C3), Human resource (C4) and Proximity to market (C5). 4.2 Calculation and Discussions Owing to subjective, vague and imprecise, the performance ratings of the alternatives are with respect to all the five criteria are estimated by linguistic variables. Linguistic variables are easy use and understand. Linguistic variables requires less efforts and less time with compared to other mode of expression. That is why decision makers prefer linguistic variables to objective measurement. In the current problems decision makers uses seven degrees of linguistic variables to express their assessment and perception regarding the alternative warehouse locations towards the criteria. The seven degrees of linguistic variables used for expressing performance ratings, their respective acronyms and the corresponding triangular fuzzy numbers have been accommodated in Table 1. The degree of importance weights of various criteria in decision making on proper selection of warehouse location varies from criterion to criterion and decision maker to decision makers. The decision makers involved in the decision making process are inspired to use a common set of seven degrees of linguistic variables for measuring importance weights of the criteria. A novel MCDM model for warehouse location selection in supply chain management 201 The seven degrees of linguistic variables used for expressing importance weights, their respective acronyms and the corresponding triangular fuzzy numbers have been arranged in Table 2. The decision makers estimate the weights of criteria in linguistic variables and are represented in Table 3. Since the criteria have different dimensions, they are normalized in order to convert into dimensionless quantity so as to compare one another. Defuzzified average values of weight are calculated using Eq. 4(a). Normalized weights are calculated using Eq. 4(c). Defuzzified and normalized values of weights are shown in Table 4. Performance rating of each warehouse is estimated by the each decision makers with respect to each criterion which are estimated by the knowledgeable decision makers. Cost criteria are expressed in numerical values. And the remaining four Table 1. Linguistic variables with fuzzy numbers for ratings Linguistic variables Acronym Fuzzy numbers Extremely Poor V P ( 0, 0, 1 ) Poor P ( 0, 1, 3 ) Slightly Poor M P ( 1, 3, 5 ) Fair F ( 3, 5, 7 ) Medium Good M G ( 5, 7, 9 ) Good G ( 7, 9, 10 ) Extremely Good V G ( 9, 10, 10 ) (Source: Chen et al. 2006) Table 2. Linguistic variables, Acronyms and TFN for the estimation of weight Linguistic variables Acronym Fuzzy Numbers Very low VL ( 0, 0, 0.1 ) Low L ( 0, 0.1, 0.3 ) Medium Low ML (0.1, 0.3, 0.5) Medium M ( 0.3, 0.5, 0.7 ) Medium High MH (0.5, 0.7, 0.9 ) High H ( 0.7, 0.9, 1.0 ) Very high VH ( 0.9, 1.0, 1.0 ) (Source: Chen et al. 2006) Table 3. The linguistic weight of the criteria. Criteria D1 D2 D3 C1 H VH VH C2 H H H C3 MH H MH C4 MH MH MH C5 H H H (Source: Chen et al. 2006) Table 4. Defuzzified and normalized weight of the criteria Values C1 C2 C3 C4 C5 Defuzzified values 0.93 0.87 0.75 0.70 0.87 Normalized values 0.226 0.21 0.182 0.17 0.211 Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 202 criteria are evaluated by prescribed linguistic variables in specified degrees. It can be easily observed that the performance ratings of the warehouse A1, A2, and A3 with respect to criterion C1 by the decision maker D1 are 6, 3, 4 million respectively. The linguistic variables for the alter natives A1, A2, and A3 estimated by decision maker D1 with respect to criterion C2 are expressed as G, EG, and MG respectively. The linguistic variables for the alter natives A1, A2, and A3 estimated by decision maker D2 with respect to criterion C2 are expressed as EG, EG, and G respectively. The remaining performance rating of the three alternative warehouses with respect to the criteria as assessed by the decision makers are provided in the following table 5. Average and normalized values of rating of objective criteria as well as defuzzified and normalized values of rating of alternatives under subjective criteria are shown in Table 6. The normalized decision matrix is represented in Table 7. Modified weighted normalized rating is calculated. For example, modified weighted value of alternative A1 for benefit criterion C2 (expansion possibility) is computed as   3206.021.01/3052.0 21.012  B mwv . Modified weighted value of alternative A1 for cost criterion C1 (investment cost) is computed as   4636.0226.01/4375.0 226.011  C mwv . Aggregate modified weighted ratings are determined. For alternative A1 for benefit criteria (C2, C3, C4, C5) , the calculation process is    1 12 13 14 15 0.3206 0.3145 0.3442 0.2491 1.228B B B B BAMWV mwv mwv mwv mwv         Table 5. Performance ratings of the warehouses by the decision makers Criteria Alternative D1 D2 D3 C1 A1 A2 A3 6 (million) 3 (million) 4 (million) 8 (million) 4 (million) 5 (million) 7 (million) 5 (million) 6 (million) C2 A1 A2 A3 G E G M G E G E G G F E G E G C3 A1 A2 A3 F G G G G S G G G E G C4 A1 A2 A3 EG G G G G E G G G E G C5 A1 A2 A3 F G G F F G F G G (Source: Chen et al. 2006) Table 6. Average normalized rating of objective criteria and defuzzified normalized rating of subjective criteria C1 C2 C3 C4 C5 Alternative AV NV D V N V D V N V D V N V D V NV A1 7 0.4375 8.0 0.3052 7.44 0.3032 9.00 0.3335 5.00 0.237 A2 4 0.25 9.66 0.3686 8.66 0.3529 8.66 0.3209 7.44 0.3526 A3 5 0.3125 8.55 0.3262 8.44 0.3439 9.33 0.3457 8.66 0.4104 AV= Average value, DV =Defuzzified Values, NV =Normalized values A novel MCDM model for warehouse location selection in supply chain management 203 The modified weighted values and aggregate modified weighted values are determined and presented in Table 8. Benefit-Cost Ratio (BCR) is calculated by using Eq. (11)., BCR for alternative A1 is calculated as  1BCR =  1 1/B CAMWV AMWV =  4636.0/228.1 .6488.2 Benefit-cost ratios and the ranking order of the alternative warehouse locations are accommodated in Table 9. The final ranking of the alternatives is decided on the basis of benefit cost ratio vs. alternatives. The ranking orders of the warehouse locations under consideration are graphically depicted in Figure 2, for achieving higher visibility and clarity. Figure 2. Benefit cost ratio of alternatives warehouse locations The graphical representation clearly shows that the ranking order of the warehouse locations as per the proposed method is A2>A3>A1. The best warehouse location is A2. A comparison of the results obtained by the proposed approach with those of past researches available in the open journals has been made and shown in Table 10. 0 1 2 3 4 5 6 B e n e fi t- C o s t R a ti o A1 A2 A3 Alternatives Table 7. Normalized decision matrix C1 C2 C3 C4 C5 Weight 0.226 0.21 0.182 0.17 0.211 A1 0.4375 0.3052 0.3032 0.3335 0.237 A2 0.25 0.3686 0.3529 0.3209 0.3526 A3 0.3125 0.3262 0.3439 0.3457 0.4104 Table 8. Modified weighted values, Aggregate modified weighted values Modified weighted values Aggregate modified weighted values Alternatives C imwv 1 B imwv 2 B imwv 3 B imwv 4 B imwv 5 C iAMWV B iAMWV A1 0.4636 0.3206 0.3145 0.3442 0.2491 0.4636 1.228 A2 0.2649 0.3873 0.3660 0.3312 0.3706 0.2649 1.455 A3 0.3311 0.3427 0.3671 0.3568 0.4314 0.3311 1.498 Table 9. Benefit–cost ratio and ranking order of the alternatives Alternatives Benefit-Cost ratio Ranking order A1 2.6488 3 A2 5.4926 1 A3 4.5243 2 Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 204 5. Sensitivity Analysis A sensitivity analysis of the problem of warehouse location selection has been carried out and the result has been depicted in Figure 3. The sensitivity analysis is the graphical representation of benefit cost ratio of warehouses with respect to variable decision making attitude. The following Eq. (12) governs the warehouse selection index in sensitivity analysis.   ** 1 Ci B ii MWVMWVWSI   (12) Figure 3. Sensitivity analysis of selection index with respect to coefficient of attitude *B iMWV and *C iMWV are aggregate normalized value and Modified Weighted value of alternative i for benefit and cost criteria respectively.  = Coefficient of decision making attitude in the range 10  .The sensitivity plot clearly shows that warehouse location 2 has the maximum BCR in the range of 87.00   .The result of the sensitivity plot in the range of 87.00   is also in line with the ranking order of warehouse locations. But warehouse location 3 has the highest benefit cost ratio while 187.0  which is shown in Table 11. The sensitivity analysis gives a readymade and prompt solution to the current problem under unpredictable coefficient of decision attitude. 0.5714 0.8197 1 0.9712 0.8 1 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Coef f icient of Attitude W a re h o u s e S e le c ti o n I n d e x Warehouse A1 Warehouse A2 Warehouse A3 Table 10. Comparison of results (Ranking) among various papers Alternatives Chen T.C.(2006) Proposed method A 1 3 3 A 2 1 1 A 3 2 2 (α) A novel MCDM model for warehouse location selection in supply chain management 205 6. Discussions The concept of lean is well applicable where demand is comparatively steady and predictable with low variety. On the other hand, for unstable demand and varieties of customer’s need, to a large extent of higher level “agility” is necessary. The leagile supply chain integrates the lean and agile paradigms contained by a total supply chain approach by placing the decoupling point for the best suit of the need. The decision making in the leagile supply chain is very intricate in nature. The approach proposed in the paper is an aid to the managers for correct decision for the leagile supply chain. The proposed algorithm recommends the benefit cost ratios as the selection criteria of warehouse location. Accordingly, the warehouse locations are ranked as follows: A2 > A3 > A1 It is observed that A2 is the best warehouse location. It has also been revealed that the ranks of warehouse locations found by applying the proposed algorithm that employs the proposed methodology produces the similar result obtained by past researchers using different method as shown in Table 9. The method validates the judgment behind the approach which complies with the technique adopted by the researchers as demonstrated in literature survey. The proposed algorithm has a number of significant features as follows: a. The modification of weight in the proposed algorithm is exclusive in nature. b. It is able of managing fuzziness of the decision making environment. c. The method is capable of considering subjective and objective criteria to select the best warehouse location. d. The algorithm is simple, easier and straightforward. 7. Conclusions Lean supply chain is capable of maximizing profit through waste reduction whereas agile supply chain maximizes profit by delighting the customers. Leagility in the supply chain makes the upstream cost effective whereas the downstream becomes more service oriented. In this paper, the algorithm has incorporated the concept of modified weighted value into the decision theory for the selection of warehouse in a supply chain which may be very handy for the decision makers. This paper gives a revised version of weight avoiding direct use by employing engineering economy. This modification of weight has not yet been reported in any research work. The consistency of results of the cited problem with those of other works strongly justifies the concept of modification of weight. Benefit cost ratio is considered as the key selection parameter for warehouse location selection. The importance weight of criteria play a great role in the evaluation process as it simultaneously act as the interest rate and number of periods of cash flows. Table 11. Sensitivity analysis Option Range of coefficient of attitude(α) Selection of Warehouse 1. 0 ≤ α < 0.87 Select 2A 2. 0.87 < α ≤ 1 Select 3A 3. α = 0.87 Indifferent towards 2 A & 3A Bairagi/Decis. Mak. Appl. Manag. Eng. 5 (1) (2022) 194-207 206 This algorithm is simple, easier and capable of considering fuzziness. This new method may be thought of an extended version of simple additive weighting (SAW) method with modified weight applying engineering economy or financial management. This approach is appropriate for implementation in other managerial decision making problems. By transforming it into computerized algorithm, a large number of criteria, alternatives, and decision makers’ view can be considered. Author Contributions: Conceptualization, B.B.; methodology, B.B.; validation, B.B.; formal analysis, B.B.; investigation, B.B.; resources, B.B.; writing—original draft preparation, B.B.; writing—review and editing, B.B.; visualization, B.B.; supervision, B.B.; The author has read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Agarwal, A., Shankar, R. & Tiwari, M.K. (2006). Modeling the metrics of lean, agile, and leagile supply chain: An ANP-based approach. European Journal of Operational Research, 173, 211-225. 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