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  1. 1. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166 Facility Layout Selection For The Blood Inventory Using PROMETHEE II Method N.Arunkumar1, S.Godwin Barnabas2, N.Dinesh Kumar2 and T.Kamatchi2 1 Professor,Department of Mechanical Engineering, St.Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai-600 119. 2 Assistant Professor, Department of Mechanical Engineering, Velammal College of Engineering and Technology, Viraganoor, Madurai -625 009Abstract Blood Inventory Management has locations. While applying the PROMETHEE IIattracted significant interest from the Operations method to solve a real time facility locationResearch profession during the last fifteen years. selection problem [1], it is observed that thisThis paper aims to minimize the overall demand method proves its applicability and potentiality tofor the blood in the region is by prioritizing the solve such types of decision-making problems withcollection centre’s as per their shortages, multiple conflicting criteria and alternatives.wastages, issue delays and outages by comparing PROMETHEE II method is compared with thethe results of analytical hierarchy process (AHP) Analytic Hierarchy Process (AHP) to prioritize the 4with PROMETHEE II method blood collection centers in a zone.Keywords: Analytic Hierarchy Process, Literature ReviewPROMETHEE II. In 1973, Jennings [1] was the first to expand this analysis to a regional level instead ofINTRODUCTION single hospital. Using simulation analysis, he The location selection decision may be examines a system with a number of identicalrequired due to various reasons, like change in individual hospital blood banks making decisionsproduction capacity, addition or deletion of based on the same policies. He studies two cases, noproduct line, change in distribution cost or blood sharing between hospitals and bloodchange in customer demand. Wrong selection of transferring between hospitals, and concludes thatlocation may result in inadequate qualified work when blood is shared, shortages and outdates areforce, unavailability of raw materials, insufficient reduced. Thus, managing blood on a regional scaletransportation facility, increased operating with available transfers increases overall efficiency.expenses or even disastrous effect on the This simulation also takes into account theorganization due to political and societal distinction between assigned blood and available,interference. Thus, the decision maker must select unassigned blood. Jennings was the first researcherthe location for a facility that will not only to understand the true importance of this distinction.perform well, but also it will be flexible enough to Cohen and Pierskalla [2] in 1975 attempted to useaccommodate the necessary future changes. simple equations to set optimal inventory levels. Selection of a proper location involves Their analysis uses many variables, such as rates ofconsideration of multiple feasible alternatives. It is demand, the return of unused assigned blood backalso observed that the selection procedure involves into available inventory, and thus the effects of crossseveral objectives and it is often necessary to make matching. Using simulation, they determine ancompromise among the possible conflicting criteria. optimal inventory level based on all significantFor these reasons, multi-criteria decision- making variables and they also analyze various ordering(MCDM) is found to be an effective approach to policies, issuing policies, and cross matchingsolve the location selection problems. In this paper, policies while viewing the supply of blood from athe overall demand for the blood in the region is regional perspective.This work united manyreduced by prioritizing the collection centre’s as per important variables into a single simulation analysistheir shortages, wastages, issue delays and outages and explored the importance and effect of changingby comparing the results of analytical hierarchy specific values such as the shortage rate.process (AHP) with PROMETHEE II method the Randhawa and West [3] proposed apreference ranking organization method for solution approach to facility location selectionenrichment evaluation (PROMETHEE II) is problems while integrating analytical and multi-employed to obtain the best choice from a finite set criteria decision-making models. Houshyar andof alternative facility White [4] developed a mathematical model and 1161 | P a g e
  2. 2. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166heuristics approach that assigns N machines to N Blood distribution schedulesequal-sized locations on a given site such that the During the course of a day the Blood Banktotal adjacency flow between the machines is receives a random number of transfusion requestsmaximized. The proposed model is based on a 0- for each blood type, each request for a random1 integer programming formulation which may number of; units. Once a request for a patient isproduce an optimal, but infeasible solution, received, the appropriate number of units of thatfollowed by the heuristic which begins with the 0- type is removed from free inventory and upon1 integer solution and generates a feasible successful cross matching they are placed on reservesolution. Owen and Daskin [5] provided an inventory for this particular patient. Any of thoseoverview of the methodologies that have been units that are not transfused are returned back to freedeveloped for solving facility location selection inventory. We will define demand to be the numberproblems. of units requested, and usage to be the number of Chu [6] presented a fuzzy TOPSIS units transfused. Any units which are not used(technique for order preference by similarity to within their 2l-day lifetime are considered outdatedideal solution) method-based approach for the plant and are discarded from inventory.location selection problems. The ratings and The problem of managing blood suppliesweights assigned by the decision makers are first can be examined at two levels: the individualnormalized into a comparable scale. The hospital level, or the regional level. At the hospitalmembership function of each normalized rating of level, the objective is to determine decision rules toeach alternative location for each criterion is then be used by the Hospital Blood Banks managementdeveloped. A closeness coefficient is proposed to for the daily operations of the Blood Bank. Suchdetermine the ranking order of the alternatives. decisions would involve quantities to collect orKlose and Drexl [7] reviewed in details the order from the Regional Blood Center, units to issuecontributions to the current state-of-the-art related from inventory against transfusion requests, portionto continuous location models, network location of fresh units to be frozen so that their lifetimes aremodels, mixed-integer programming models and extended, and development of computer informationtheir applications to location selection decision. systems to provide accurate and timely informationYong [8] proposed a new fuzzy TOPSIS method and thus assist with the management of the Bloodwhich deals with the selection of plant location Banks inventory management. At the regional level,decision-making problems in linguistic the objective of a Regional Blood Center is toenvironment, where the ratings of various determine achievable targets of performance withinalternative locations under different criteria and a region, and to set up collection and distributiontheir relative weights are assessed in linguistic schedules that will achieve these desirable targets.terms represented by fuzzy numbers. . Farahani and Asgari [9] presented a Current Blood SituationTOPSIS methodology to find the supportive The current trends in supply and demand ofcenters with the minimum number and maximum blood in the United States present a major problemquality of locations in military logistic systems. that needs to be addressed. The growth rate ofOnut and Soner [10] employed a fuzzy TOPSIS supply is significantly smaller than the growth inbased methodology to solve the solid waste demand. Although total supply of blood (as antransshipment site selection problem, where the aggregate statistic) exceeds total demand in the US,criteria weights are estimated using analytic the disparity between growth rates suggests thathierarchy process (AHP). major shortage situations are imminent. Amiri et al. [11] applied TOPSIS method Understanding the reasons for these growth trendsalong with heuristics based on fuzzy goal should help identify how to address impendingprogramming to select the best location. The shortages. The mismatch of supply and demand asfacility location selection problem is solved in well as the shrinking gap between available supplythree stages, i.e. (a) finding the least number of and demand is a realistic cause for concern in thedistribution centers, (b) locating them in the best future.possible location, and (c) finding the minimumcost of locating the facilities. Although the facility METHEDOLOGYlocation selection problems have already been The Analytic Hierarchy Process (AHP)solved using different MCDM techniques, this The Analytic Hierarchy Process (AHP) is apaper makes a maiden attempt to implement structured technique for dealing with complexanother appropriate MCDM approach, i.e. decisions. Rather than prescribing a "correct"PROMETHEE II method to tackle this complex decision, the AHP helps the decision makers findlocation selection decision-making problem. the one that best suits their needs and their understanding of the problem. The AHP provides a comprehensive and rational framework for 1162 | P a g e
  3. 3. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166structuring a decision problem, for representing and compared over the entire range of the problem. Aquantifying its elements, for relating those elements numerical weight or priority is derived for eachto overall goals, and for evaluating alternative element of the hierarchy, allowing diverse and oftensolutions. incommensurable elements to be compared to one Once the hierarchy is built, the decision another in a rational and consistent way. Thismakers systematically evaluate its various elements capability distinguishes the AHP from otherby comparing them to one another two at a time. In decision making techniques.making the comparisons, the decision makers canuse concrete data about the elements, or they can Steps involved in AHPuse their judgments about the elements relative The AHP converts these evaluations tomeaning and importance. It is the essence of the numerical values that can be processed andAHP that human judgments, and not just the compared over the entire range of the problem. Aunderlying information, can be used in performing numerical weight or priority is derived for eachthe evaluations. element of the hierarchy, allowing diverse and often The outages, shortages for the four incommensurable elements to be compared to onecollection centre’s has been tabulated as follows another in a rational and consistent way. ThisCollection centre1 details; capability distinguishes the AHP from other decision making techniques. In the final step of the Demand making No of process, numerical priorities are calculated for each criteria’s unit/week of the decision alternatives. These numbers Outages 95 represent the alternatives relative ability to achieve Shortages 165 the decision goal, so they allow a straightforward Issued delay 70 consideration of the various courses of action. Wastages 100 Scoring of the equipmentsCollection center 2 details; The values of the previous matrix are Demand making No of obtained by the earlier method, now by using the criteria’s unit/week formula we are going to obtain the weightage for the Outages 100 each issue. Shortages 175 Issued delay 65 Wastages 165 Whereas, r - rating factor; W - weightage factor;Collection center 3 details; The different priority levels reflect the hierarchical relationship between the targets in the objective Demand making No of function where they are arranged in order of criteria’s unit/week decreasing priority (P1>P2>Pm). Outages 90 S.No Demand making No of unit/week Shortages 205 criteria’s Issued delay 85 1 Outages 385 Wastages 165 2 Shortages 765 3 Issued delay 300Collection center 4 details; 4 Wastages 525 Demand making No of These are the data’s of the blood demands criteria’s unit/week in the 4 hospitals in a region for 8 types of blood Outages 110 types now in order to find the priority among these Shortages 220 criteria’s the pair wise comparison is made against Issued delay 80 each of the criteria’s from these values the Wastages 100 inconsistency ratios are obtained .now the scoring of the of the each of the criteria’s is obtained as The use of AHP allows defining a three follows:level hierarchical structure: the top level representsthe goal of the analysis, the second level is relativeto the relevant criteria used, and the third onedefines the possible alternatives. Here the rating factor is obtained by the The AHP converts these evaluations to inconsistency ratios (IR) averages of the each ofnumerical values that can be processed and these criteria’s such as outages, shortages, issue 1163 | P a g e
  4. 4. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166delays, wastages .the weightage factor is obtained the preference and indifference making pair wise comparison is made for each of However, in real time applications, it may bethe criteria’s with one another. From the priorities difficult for the decision maker to specify whichobtained the goal programming is formulated by the specific form of preference function is suitable fordecreasing priority order as follows: each criterion and also to determine the parametersP1>P2>P3….>Pm involved. To avoid this problem, the followingResults of AHP simplified preference function is adopted here:Ranking Demand Priority Priority criteria values1. Issue delay P3 0.2732. Wastages P4 0.255 Step 4: Calculate the aggregated preference3. Shortages P2 0.248 function taking into account the criteria weights.4. Outages P1 0.218 Aggregated preference function,The decreasing priority is of the formP3>P4>P2>P1, the priorities obtained from the AHPresults are compared with the PROMETHEE II where wj is the relative importance (weight) of j thmethod. criterion. Step 5: Determine the leaving and enteringPROMETHEE II method outranking flows as follows: Preference function based outranking Leaving (or positive) flow for ith alternative,method is a special type of MCDM tool that canprovide a ranking ordering of the decision options.The PROMETHEE (preference rankingorganization method for enrichment evaluation)method was developed by Brans and Vincke in 1985 Entering (or negative) flow for ith alternative,[11]. The PROMETHEE I method can provide thepartial ordering of the decision alternatives,whereas, PROMETHEE II method can derive thefull ranking of the alternatives. In this paper, the where n is the number of alternatives.PROMETHEE II method is employed to obtain the Here, each alternative faces (n–1) numberfull ranking of the alternative locations for a given of other alternatives. The leaving flow expressesindustrial application. how much an alternative dominates the otherThe procedural steps as involved in PROMETHEE alternatives, while the entering flow denotes howII method are enlisted as below [11, 12]: much an alternative is dominated by the otherStep 1: Normalize the decision matrix using the alternatives. Based on these outranking flows, thefollowing equation: PROMETHEE I method can provide a partial preorder of the alternatives, whereas, the PROMETHEE II method can give the complete preorder by using a net flow, though it loses much information of preference relations.where Xij is the performance measure of ith Step 6: Calculate the net outranking flow for eachalternative with respect to jth criterion. alternative.For non-beneficial criteria, Eqn. (1) can be rewrittenas follows: Step 7: Determine the ranking of all the considered alternatives depending on the values of ϕ (i).The higher value of ϕ (i), the better is the alternative. Thus, the best alternative is the one having theStep 2: Calculate the evaluative differences of ith highest ϕ (i) value.alternative with respect to other alternatives. This The PROMETHEE method is anstep involves the calculation of differences in interactive multi-criteria decision-making approachcriteria values between different alternatives pair- designed to handle quantitative as well as qualitativewise. criteria with discrete alternatives. In this method,Step 3: Calculate the preference function, Pj (i,i′). pair-wise comparison of the alternatives isThere are mainly six types of generalized preference performed to compute a preference function for eachfunctions as proposed by Brans and Mareschal [12, criterion. Based on this preference function, a13]. But these preference functions require the preference index for alternative i over i′ isdefinition of some preferential parameters, such as determined. This preference index is the measure to 1164 | P a g e
  5. 5. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166support the hypothesis that alternative i is preferredto i′. The PROMETHEE method has significantadvantages over the other MCDM approaches, e.g.multi-attribute utility theory (MAUT) and AHP. ThePROMETHEE method can classify the alternatives Table 2 11-Point Fuzzy Scalewhich are difficult to be compared because of a Linguistic term Crisp scoretrade-off relation of evaluation standards as non Exceptionally low 0.045comparable alternatives. It is quite different fromAHP in that there is no need to perform a pair-wise Extremely low 0.135comparison again when comparative alternatives areadded or deleted. Very low 0.255 Low 0.335ILLUSTRATIVE EXAMPLE: Rao [1] employed the graph theory and Below average 0.410matrix approach (GTMA) for selection of the best Average 0.500facility location for a given industrial application.The same example is considered here to demonstrate Above average 0.590the applicability and effectiveness of PROMETHEEII method as a MCDM tool. This example takes into High 0.665account eight facility location selection criteria and Very high 0.745three alternative facility locations. The objective andsubjective information regarding different location Extremely high 0.865selection criteria are given in Table 1. All thesecriteria, except the cost of labor, are expressed Exceptionally high 0.955subjectively in linguistic terms. The objective valuesfor these criteria are assigned from an 11-point scale,as given in Table 2. The fuzzy judgments average Table 3 Normalized decision matrix(A), above average (AA), high (H) and very high Location CM CR LT MCC(VH), shown in Table 1, are considered equivalent to P1 0.6735 1 0 0good, very good etc. with respect to different criteria. P2 1 0 0 1The 4 selection criteria as considered here to affectthe location selection decision are closeness to P3 0 0 1 0emergency areas (CM), closeness to other blood P4 0.6735 1 0 0bank (CR), low transportation cost (LT), maximumpatient coverage (MC). Now, the preference functions areTable 1 Information for facility location alternatives calculated for all the pairs of alternatives, using[1] Eqns. (3) and (4), and are given in Table 5. Table 6 exhibits the aggregated preference function valuesLocation O S I W for all the paired alternatives, as calculated usingP1 H VH H AA Eqn. (5). The leaving and the entering flows for different location alternatives are now computedP2 VH H H VH using Eqns. (6) and (7) respectively, and are shownP3 A HHHH VH AA in Table 7.P4 H VH A H Table 4 Preference functions for all the pairs of alternativesas shown in Table1, are converted to crisp scores Location pair CM CR LT MCusing the 11-point scale, as given in Table 2. Thetransformed objective data, as given in Table 3, are (P1,P2) 0 1 0 0then normalized using Eqn. (1) or (2) and are given (P1,P3) 0.6735 1 0 0in Table 4. Rao [1] determined the criteria weights (P1,P4) 0 0 0 0for the considered criteria as wO = 0.194, wS =0.387, wI = 0.1518, wW = 0.265, using AHP (P2,P1) 0.3265 0 0 1method and the same criteria weights are used here (P2,P3) 1. 0 0 1for PROMETHEE II method-based analysis. Where (P2,P4) .3 0 0 1wO, wS, wI, wW are the weightages for outages, (P3,P1) 0 0 1 0shortages, issue delay, and wastages. (P3,P2) 0 0 1 0 (P3,P4) 0 0 1 0 1165 | P a g e
  6. 6. N.Arunkumar, S.Godwin Barnabas, N.Dinesh Kumar, T.Kamatchi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1161-1166(P4,P1) 0 0 0 0 region or location by prioritizing the collection centers as per their shortages, outages, issue delay,(P4,P2) 0 1 0 0 and wastages in the collection centers. In future the(P4,P3) 0.6 1 0 0 optimal blood inventory can be developed by using the dynamic programming model, markov chain andTable 5 Aggregated preference function regression model etc.Location P1 P2 P3 P4P1 - 0.387 0.518 0 REFERENCES 1. Jennings, 1968, “An Analysis of HospitalP2 0.329 - 0.46 0.329 Blood Banks Whole Blood Inventory ControlP3 0.1521 0.15211 - 0..1521 Policies Transfusion”, 8(6):335-342. 0 0.387 0,.518 - 2. Cohen and Pierskella, 1975, “Management Policies for a Regional Blood BankTable 6 Leaving and entering flows for different Transfusion”, 11(1):58-67.locations 3. Randhawa S.U and West T.M., 1995, “AnLocation Leaving flow Entering flow Integrated Approach to Facility Location Problem”, Computers and IndustrialP1 0.30166 0.160 Engineering, 29, 261-265.P2 0.372 0.308 4. Houshyar A, and White B, 1997,P3 0.152 0.498 “Comparison of Solution Procedure to theP4 0.301 0.160 Facility Location Problem”, Computers and Industrial Engineering, 32, 77-87.Table 7 Net outranking flow values for different 5. Owen S.H, and Daskin M.S, 1998, “Strategiclocation alternatives Facility Location: A Review”, EuropeanLocation Net outranking flow Rank Journal of Operational Research, 111, 423- 447.P1 0.1413 2 6. Chu T.C, 2002, “Selecting Plant Location viaP2 0.063 3 a Fuzzy TOPSIS Approach”, InternationalP3 -0.346 4 Journal of Advanced ManufacturingP4 0.143 1 Technology, 20, 859-864. 7. Klose A and Drexl A, 2005, “FacilityThe priorities of the collection centers are as follows Location Models for Distribution SystemP4>P1>P2>P3, Design”, European Journal of Operational The net outranking flow values for Research, 162, 4-29.different alternative locations and their relative 8. Yong D, 2006, “Plant Location Selectionrankings are given in Table 8. Now, the alternative Based on Fuzzy TOPSIS”, Internationallocations are arranged in descending order Journal of Advanced Manufacturingaccording to their net outranking flow values. The Technology, 28, choice of location for the given blood inventory 9. Farahani R.Z and Asgari N, 2007,is location 2, which exactly matches with the “Combination of MCDM and Coveringobservations derived. While solving this problem Techniques in a Hierarchical Model forusing graph theory and matrix approach. This Facility Location: A case study”, Europeanproves the applicability and potentiality of the Journal of Operational Research, 176, 1839-PROMETHEE II method for solving complex 1858.decision-making problems in prioritizing the 10. Onut S and Soner S, 2008, “Transshipmentcollection centre. Site Selection using the AHP and TOPSISConclusion: Approaches under Fuzzy Environment”,The comparison of AHP- PROMETHEE II in the Waste Management, 28, 1552-1559.blood inventory has paved the way to minimize the 11. Amiri M, Kazemi A, Sadaghiani J.S,demand for the blood requirement in the hospitals in Yaghoubi A, and Mashatzadegan H, 2009,a particular region by prioritizing shortages, “Developing and Solving a New Model foroutages, issue delay, and wastages in the 4 the Location Problems: Fuzzy-Goalcollection centers. The above said methodology is to Programming Approach”, Journal of Appliedminimize the overall deviations for blood demand Sciences, 9, 1344-1349. 1166 | P a g e