Mahdi Karbasian * & Saeed Abedi ABSTRACT.

Transcription

1 Internatonal Journal of Industral Engneerng & Producton Research December, Volume Number 4 pp ISSN: A Multple Objectve Nonlnear Programmng Model for Ste Selecton of the Facltes Based on the Passve Defense Prncples Mahd Karbasan * & Saeed Abed M. Karbasan, Assstant Professor, Industral Engneerng Dept. Malek Ashtar Unversty S. Abed, Young Researchers Club, Najaf Abad Branch, Islamc Azad Unversty, Najaf Abad, Isfahan, Iran KEYWORDS Passve defense, Ste selecton, Dsperson, Securty Multple objectve decson makng (MODM) ABSTRACT One of the man prncples of the passve defense s the prncple of ste selecton. In ths paper, we propose a multple objectve nonlnear programmng model that consders the prncple of the ste selecton n terms of two qualtatve and quanttatve aspects. The purpose of the proposed model s selecton of the place of facltes of a system n whch not only t observes the dsperson prncple but also reduces the system transportaton costs. Moreover, the proposed model tres to select the stes that can fulfll other elements of ste selecton as well as dsperson n a way that t ncreases the trustworthness of the selected network. IUST Publcaton, IJIEPR, Vol., No. 4, All Rghts Reserved.. Introducton Ste selecton s a knd of spatal plannng durng whch the place of establshment wll be determned. In the usual spatal plannng, frst the features of the zones s determned and then dependng on ther features and specfcatons, the actvty or the actvtes that are sutable for each zone s determned. But n ste selecton, frst the features of a partcular actvty s determned and then the places and zones that are more sutable for the determned actvtes wll be assgned (Drezner, 995). The ndustral ste selecton theores ntend to explan the structure of the ste selecton of the ndustral actvtes based on the factors and varables that are effcent n ste selecton and try to fnd the best stes for establshment of ndustral centers. Most of these theores orgnate from economc thoughts formulated by the economsts. They have tred to create these theores so that they relate the ste varable to the man body of the economc theores. Generally, the * Correspondng author: Mahd Karbasan Emal: mkarbas@mut-es.ac.r Paper frst receved Aug..,, and n revsed form Oct. 4,. ndustral ste selecton theores can be dvded nto three methods (Church and Murray, 9). Mnmum cost method n whch, n the process of ste selecton, the attempt s made to mnmze the producton costs. The analyss of the avalable commercal area n whch the man focus s on the demand and market and also maxmzng the avalable area. Earnng the maxmum advantages that s, n fact, the logcal result of the above methods. The deas made by Lan Hard, Houver and Weber are mostly related to mnmzng the costs. In 89s, Lan Hard tred to show how t s possble to show a optmum ste selecton n smple condtons of two prmary sources and one market n a trangle (Wesolowsk, 993). The begnnng of the ndustral ste electon goes back to 99 when Weber publshed hs book Weber Standortder Industren n ths regard. In ths book, he presented hs paper fndngs on factoral ndustres. He took the fallowng three factors as the nfluental elements n ndustral ste selecton: (Weber, 965) Workforce costs Transportaton costs Assocaton forces or non assocaton of the transportaton costs. In 948, Houver presented hs work on ndustral ste selecton. Comparng wth Weber's theory, he dvded

2 44 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for the costs nto transportaton and producton costs n a more argumentatve manner (Wesolowsk, 993). In recent years, the prncple of ste selecton has been more emphaszed and the scentsts have proposed many theores on ths doman (Hamacher et.al, 4). In most of the above cases, the only mportant factor that s consdered s the system costs. These models can not solely be appled n passve defense ssues because they do not pay attenton to the securty of facltes places, lmtaton of ther dstances, ther dsperson to ncrease the covered areas and reduce ther recognzablty by the enemy and avod mparment of producton network because of beng closeness. If the facltes be placed near each other, they may be attacked n an nroad. One of the defnng objectves n locaton scence s to maxmze dsperson. Facltes can be dspersed for a wde varety of purposes, ncludng keepng compettors of the same franchse system apart, dspersng crmnal rehabltaton facltes from populaton centers, and locatng nuclear power plants n such a way as to maxmze securty (Curtn and Church, 6). Dsperson models can be appled over a spectrum of scales: macroscale applcatons nclude such thngs as the locaton of rado transmtters or defense nstallatons over a large geographc regon; mesoscale applcatons nclude the locaton of schools, housng developments, landflls, or ncnerators wthn a smaller, well-defned geographc regon; and mcroscale applcatons of dsperson can nclude such thngs as product shelf locaton and factory or classroom layout studes (Alçada-Almeda et.al, 9, Rakas et.al, 4) By far the most common use of dsperson models s for the locaton of undesrable facltes (see Church and Garfnkel, 978; Drezner and Wesolowsky, 985; Erkut and Neuman, 989; Drezner and Wesolowsky, 996). Ths lterature s further dvded nto the locaton of noxous and obnoxous facltes. Noxous facltes are those that present some health rsk to any populaton that would be exposed to ether the damagng repercussons of an accdent at the faclty or the damagng consequences of long-term exposure to the faclty. Examples of noxous facltes nclude coal-fred power statons, nuclear power plants, hazardous waste storage stes, ol storage tanks, ammunton dumps, landflls, and ncnerators. Obnoxous facltes are not expected to cause health rsks to populatons, but they may have (or be perceved to have) deleterous socal or economc consequences assocated wth ther locaton and operaton. Examples of obnoxous facltes nclude prsons, actvtes that generate excessve nose, socal servce centers, and rehabltaton (e.g., drug treatment) centers (Murray et al. 998). Obnoxousness may result n dsagreements between the faclty operator and the local populaton that are based on deologcal or atttudnal conflct (Sorensen, et.al, 984). Facltes that are consdered undesrable may have attrbutes that are both noxous and obnoxous (Berman and Wang, 8). The Purpose of ths paper s to propose a model that can maxmze the facltes dsperson measure. It can do so by maxmzaton of the set of measured spatal (Eucldean) weghted dstances. It should, also, select the stes that have relablty. Ths relablty refers to the ablty to perform the duty and harmony wth the envronment. Addtonally, we must mnmze the transportaton costs of the facltes. Col. John A. Warden III, a former USAF offcer and theorst of ar power, establshed a theory of strategc attack based on fve levels of system attrbutes. They are: Leadershp Organc/System Essentals Infrastructure Populaton Felded Mltary Forces. Each level of system or "rng" was consdered one of the enemy's centers of gravty. The dea behnd Warden's fve rngs was to attack each of the rngs to paralyze ther forces, an objectve also known as physcal paralyss. (Movahednya, 7) Leadershp Organc/System Essentals Infrastructure Populaton Fg.. Fve Strategc Rngs of Warden Felded Mltary Forces It s worth mentonng that the proposed model s applcable n all the factors n Fve Strategc Rngs of Warden. But, here, we focus more on ts applcaton n the case of Warden's second strategc rng, that s, the producton facltes of key products. The rest of ths paper organzed as follows: In the followng secton, we explan the necessty of ste selecton n the passve defense and then analyze the problem and ts requrements and the way of fulfllng them. We also deal wth the lmtatons of the problem and the reason of ther exstence. In secton 4, we make the hypotheses, nomenclature and present the proposed model. In secton 5, the concluson of the proposed model wll be offered n a unque unt and a numercal example wll be solved. And then, the results and the model capabltes, n comparson wth other models, wll be analyzed. Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

3 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for. Passve Defense and Ste Selecton Necessty In the modern wars, t s nevtable to perform the passve defense steps n order to confront the enemy's attacks and reduce the damages due to ar, land and naval attacks. It s a fundamental ssue that covers all key substructures, crucal, hypersenstve and mportant mltary and non-mltary centers, lke refneres, power plants, ports, arports, large ndustral complexes, mltary and poltc headquarters, telecommuncaton centers, strategc brdges, mltary ndustres, ar bases, mssle pads, populated centers and tactcal quarters, support and defense seats, etc (Movahednya, 7). The paper approach to statstcs and recorded experences n old wars shows that the technology gap between enemy's modern armaments and nsder defensve armaments, vulnerablty of ar defense systems aganst electronc wars, unawareness of these systems aganst fghters and cruse and ballstc mssles, launchng rockets far away the range of defensve ar armaments, lack of ant mssle arms wll make the crucal ponts as some smple targets for a successful and quck amng by enemy's fghters and armaments. Therefore, t seems necessary and nevtable to observe the prncples of passve defense and execute them n the country. To do so, one of the man prncples s ste selecton. Accordng to the proposed dentfcaton n the passve defense doman, ste selecton s: selectng the best and the most approprate place for establshment n a way that t enables us to hde human force, facltes and actvtes approprately. Thus, f ste selecton s done well, t mnmzes the necessty to use artfcal tools for camouflage (Movahednya, 7). The experence has shown that an approprate and sutable ste selecton can solve many problems related to camouflage and concealment and also reduce the possble threats and vulnerabltes. The advantages of an approprate ste selecton are as follows: The sgnfcant reducton of vulnerablty. Creaton a sutable defensve stuaton. Confrontng the enemy wth problems and lmtatons n hs attacks and dsable t to do any process. The reducton of dependency to defensve armaments. In passve defense, ste selecton ncludes three bases: duty, dsperson and topography (Saham, 7). Duty has the most mportant and hghest role n comparson wth other ste selecton factors. It s possble for a place to be sutable for establshment of a mltary or non mltary unt wth regard to camouflage and concealment but not to be accommodatng for our duty. Dsperson s the dstrbuton and decentralzaton of the forces, facltes, nstallatons or domestc actvtes to reduce ther vulnerablty aganst threats. The man requrement n dsperson prncple s the largeness and extent of a poston. Snce the dsperson of the facltes and nstallaton makes the selected ste vulnerable, t s necessary to dsperse the facltes and nstallatons. Durng ste selecton, we may fnd some places that have an especal form whch dstngushes them from other areas. In these areas, therefore, every change n the form can be an ndcaton of actvty and human exstence. In other words, every knd of new buldng that s not harmonous wth the envronment can help the enemy to recognze and dentfy that area as a crucal pont to focus on. Consderng the above prncples and rules, we must select a ste for facltes and nstallatons so that t can satsfy the requrements of the passve defense. In the same way, we need a model to select the requred ste of the facltes and nstallatons that can formulate all the lmtatons and demands. 3. Analyss of the Problem In ths problem, we deal wth some places whch are placed n one regon. Ther longtudnal and lattudnal dstances (longtudnal and lattudnal coordnates) from a refer pont s determned. These ponts, also, have a feature, named securty coeffcent that depends on some factors, ncludng the ablty of the ponts to help us to do our duty, the harmonousness of the facltes wth the envronment, hdng the facltes from the enemy and other nfluental parameters that enables the enemy to dentfy the facltes. It s calculated by multplyng two above parameters by another one, named crtcalty (gravty). We defne the above parameters as follows: Duty: the ablty to correctly perform the duty based on the facltes n a regon that s dentfed wth a number between zero and one. The more ths number s for a faclty; the more that faclty has the ablty s to perform hs duty n that certan pont. Crtcalty: t shows the ntensty of the effects of enemy's attack on especal faclty on the whole system and the usual crculaton of the people lfe. The value of the crtcalty can be shown by a numercal parameter. The more severe the effects of the attack, the less the value of ths parameter. Recognton: the possblty of the recognton of the ste selected faclty n that place accordng to the nfluental factors n recognton of an faclty by enemy's offensve armaments. The more the measure of recognton, the less the value of ths number. For example, f faclty n a certan pont can perform hs duty wth a probablty of.9, and crtcalty of.5 and recognton of.85, the securty coeffcent of that pont for that faclty wll be calculated as follows: Securty coeffcent= duty crtcalty recognton = =.38 Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

4 46 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for These places have some dstances too that are dfferent from ther spatal dstances. The yare the same dstances that must be traversed by the land forces who are busy wth the system so that they can move from one place to another. In ths ssue, there are two knds of nteracton between the facltes that are defned as follows: Repulson nteracton (dsagreement): t s dentfed by a number between zero and one. The less ths number s, the more dsagreement wll be between those two facltes. Ths nteracton shows that whether these two facltes should be placed far from each other or no. Ths coeffcent s mposed on the system by the essence two facltes applcaton, offcal polces and other nfluental factors. The nteracton of the synergetc relatonshp between two facltes: t s also dentfed by a number between zero and one that shows the relaton weght between two facltes. The greater the value of ths coeffcent, there are more transportatons between these two facltes and thus, the cost of the dstance between two facltes. Because of some spatal lmtatons and some other factors, we should determne the maxmum ar dstance between dfferent knds of facltes. These dstances are even defned for smlar facltes. Our objectves n ths model are: a) We can acheve the maxmum dsperson wth a focus on maxmzaton of the sum of weghted dstances by repulson coeffcents. Ths purpose seeks to make the created network by ste selected facltes, provde the dsperson prncple n the passve defense and also be dspersed through the entre network. b) Mnmzaton the system transportaton cost whch dentfed by synergetc relatonshp coeffcent. c) Achevng the maxmum created securty by the network f t maxmze the securty coeffcent of the selected stes. Thus, ths paper goal s to locatng facltes based on the passve defense goals wth subject to the lmtatons of locaton theory and passve defense requrements. Model Hypotheses It s supposed that the number of the facltes s less or equal to the number of all the stes. The land dstances can not be less than ar dstances. The presented repulson coeffcents are taken from the system specalsts and experts. The synergetc relatonshp coeffcent shows the comng and gong cost accordng to the dstance between two facltes. These comng and gong can be due to non-producton relatonshps too. The facltes that are n the process of ste selecton must be kept n a certan dstance from each other. Because they may have posonous and flammable materal. The reference pont s not a part of selected stes, but t s located at the below and left of all the stes. Except the faclty ste determnaton varable, other features and parameters related to the stes, facltes, costs and coeffcents are known parts of the ssue. All the dstances are specfed n a center to center mode. Defntons The set of selected ponts ( features for ste selecton: P ) has the followng Longtudnal coordnate that shows the stes dstance from the reference pont on the X axs n the coordnate system. Lattudnal coordnate that shows the stes dstance from the reference pont on the Y axs n the coordnate system. Each two places have a dstance from each other that must be traversed on the land. The total number of the selected stes s clean cut. The set of dfferent knd of facltes n ste selecton (t ) has the followng features: The repulson coeffcent between facltes s based on ther knd not ther places. The weght coeffcent, also, s changed based on the knd of facltes and not ther places. In ste selecton, the number of every knd of faclty s certan. Notaton: In order to defne the consdered model, we use the followng symbols: N : The total number of the selected stes. n : The number of the knd of facltes. X : The longtudnal coordnate of the selected ste. Y : The lattudnal coordnate of the selected ste. D j : The dstance between two selected stes, and j, that ranges from to N. R kl : The repulson coeffcent between k and l facltes that ranges from tot. C kl : The cost of communcaton between k and l facltes that ranges accordng to the dstance unt. H k : The requred number of k faclty. MD kl : The mnmum dstance between the k and l facltes. S : The securty coeffcent of the place for the k faclty k that ranges from zero to one. α : The functonal weght of the th objectve functon n the fnal objectve functon. Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

5 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for 47 The decson varable of the followng model s defned as follows: k = : = : If the faclty of type k s placed n. Otherwse N N n n = Mn Dj k jlckl () = j= k = l= 3 = Max Mn S k (3) Formulaton of the Model Because the mentoned purposes can not be explaned wth a sngle objectve functon and n some cases have contradctory wth each other, we just can represent the ssue as a mult-objectve model. Therefore, we formulate the problem as follows: N N n n = Max ( X X j ) + ( Y Yj ) k jlr () kl = j= k= l= ( X X ) + ( Y Y ) j j k jl MD kl Consderng the followng restrctons: n k= N = =,..., N, + k, l =,..., n, k =,..., N k = Hk k =,..., n k = j N (6) (4) (5) The objectve functon () s to maxmzng the sum of weghted Eucldean dstances by the repulson coeffcent. The objectve functon () s to mnmzng weghted dstances by the weght of nteractonal relatonshps. The objectve functon (3) s to maxmzng the mnmum securty coeffcent of the selected ponts that s the same as maxmzaton of the total securty coeffcent of the selected network. The restrctons (4) are to have confdence that there s only one faclty n each place. The restrctons (5) are to have confdence that all knds of facltes are located and the restrctons (6) observng the ar dstance lmtatons between the facltes. Usng ths form t makes the calculatons smple and the problem of ste selecton n passve defense wll change the qualtatve form of problem to a quanttatve form that the understandng of ths form s much easer than qualtatve form. 4. The Proposed Method Many solutons have been made for the multobjectve questons n the lterature. We use the followng soluton (see Roy, 996, Branke et.al, 8). Frst, solve each objectve functon separately accordng to the lmtatons. We call the obtaned answer. In these cases, we calculate other measures of objectve functon and call the worst of every objectve functon and then to equalze the unt of the objectve functons to each other, we dvde the objectve functon by the measure of the dfference of these two obtaned measure for t n the prevous step. Then, we multply t by a coeffcent that s presented by the group of system experts and decson makers for each objectve functon. Thereafter, we change all the objectve functons as a one objectve functon. Here, because the second objectve functon seeks to mnmze, we mpose t n the fnal objectve functon wth a mnus mark. By dvson of the functons by ther measure of effcency, not only we equalze ther unt, but also we avod them to extravagate from ther effcency measure. The fnal objectve functon s formulated as follows: 3 Max α + α opt opt 3 (7) 3 4 = α opt Now that the model has been changed to a model wth a unque objectve functon, we can solve t by some software desgned for solvng the plannng ssue, lke Lngo and GAMS. It s worth mentonng that the presented model need more tme to solve the problems by the above softwares f the measure of N and t becomes greater ( N =, t = 5 ). In order to solve these hgh measures, we advce usng the Heurstc and Meta- Heurstc algorthms. For example, f N = 3 and t = 6, the number of the lmtatons of the ssue s equal to Numercal Example: Consder a stuaton whch there s 4 facltes to be located n 6 stes. The envronmental features of the selected stes are as follows: the frst and the thrd stes are located n the slope of a great mountan that prevents the offensve armaments to see and attack to them. The second ste s located n a mountan slope but the mountan s not very hgh and t s also located n a way that s easy to be dentfed by the enemy. The fourth and ffth stes are located n the deserts near the cty. The sxth and the seventh stes also are located n the around deserts but at a longer dstance wth the cty. All the numercal measures related to the stes and facltes are ncluded n the followng tables. Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

6 48 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for Tab.. Cost of communcaton between facltes ( ) C kl Avaton Industres Avaton Industres Tab.. Type and Requred Numbers for each faclty ( N, n, ) Type Requred numbers H k Avaton Industres Table 3: Parameters for facltes securty coeffcent Avaton Industres Ste recognton Crtcalty Duty recognton Crtcalty Duty recognton Crtcalty Duty recognton Crtcalty Duty Ste No Ste No Ste No Ste No Ste No Ste No Ste No ١ Avaton Industres Tab. 4. Repulson Coeffcents ( R kl ) Avaton Industres Tab. 5. Securty coeffcent n each place for facltes ( ) S k Stes Ste No. Ste No. Ste No. 3 Ste No. 4 Ste No. 5 Ste No Avaton Industres Ste No Stes Coordnate longtudnal coordnate( ) X lattudnal coordnate( Y ) Tab. 6. Coordnates of canddate stes Ste No. Ste No. Ste No. 3 Ste No. 4 Ste No Ste No. 6 6 Ste No Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

7 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for 49 Tab. 7. Mnmum requred Eucldean dstances between facltes ( ) MD kl Falty Avaton Industres ٠ Avaton Industres Tab. 8. Dstances between canddate stes ( D j ) Stes Stes Ste No. Ste No. Ste No. 47 Ste No. 3 7 Ste No. 4 9 Ste No. 5 Ste No. 6 7 Ste No Ste No Ste No Ste No Ste No Ste No Ste No After solvng the presented model, we assume that the weght of the frst and thrd objectve functon show the securty mportance of the consttuted network by the system and the weght of the second objectve functon shows the mportance of the network costs whch all are determned by the government. Snce the government polcy s n a way that the securty of the system has a more mportance to t than the costs, we consdered the weghts n a way that shows ths polcy. Then, usng LINGO software, we solved some examples of dfferent weght measures for objectve functons. The results are as follows: Tab. 9. Results for objectve functons by usng dfferent Weght measures Weght of objectve functons Suggested Stes Values of each objectve functon 3 Type No. Type No. Type No. 3 Type No. 4 3 ( opt ) 7, opt ( ) 5, ( opt 3 ) 5, , , , Concluson Snce one of the man prncples of passve defense s faclty ste selecton n a manner that the possblty of the total network beng damaged by the enemy be reduced, we presented a model n ths paper that can select the ste n a manner that not only the created network can perform ts duty wth maxmum securty coeffcent but also the possblty of Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4

8 5 M. Karbasan & S. Abed A Multple Objectve Nonlnear Programmng Model for dentfcaton by the enemy be reduced to a mnmum. At the same tme, the proposed model helps the system to acheve to ts maxmum relablty when attacked by the enemy. What s mportant n ths model s achevement to the above purposes wth a sgnfcant reducton n the costs that s one of the man purposes of the passve defense. Ths paper formulates the problem of ste selecton n passve defense and t consders all objectves of ste selecton n passve defense that s the unque model n ths ssue. Because ths model just deals wth the second Warden's Strategc Rng, t s suggested that ths model be elaborated for other rngs too. Also, the model s appled for ndustral ste selecton, partcularly ar ndustres. Because so far there was no research n ths aspect, we hope that the results of ths research use n future researches and the problems n the passve defense ste selecton feld had solved. References [] Alçada-Almeda, L., Coutnho-Rodrgues, J., Current, J., A Multobjectve Modelng Approach to Locatng Incnerators, Soco-Economc Plannng Scences, Vol. 43, Issue, 9, pp.-. [] Berman, O., Wang, Q., Locatng a Sem-Obnoxous wth Expropraton, Computers & Operatons Research, Vol. 35, 8, pp [3] Branke, J., Deb, K., Mettnen, Słow nsk, R., Multobjectve Optmzaton Interactve and Evolutonary Approaches, Frst Edton, Sprnger, Verlag Berln Hedelberg. 8. [] Drezner,., Hamacher, W.H., Locaton: Applcatons and Theory, Frst Edton, Sprnger, Verlage Berln Hedelberg, 4. [] Movahednya, J., The Prncples and Bass of Passve Defense, Frst Edton, Malk Ashtar Unversty of Tech., Tehran(n Persan), 7. [3] Murray, A.T., Church, R.L., Gerrard, R.A. Tsu, W.S., Impact Models for Stng Undesrable Facltes, Papers n Regonal Scence, Vol. 77(), 998, pp [4] Rakas, J., Teodorov'c, D.S., Km, T., Mult-Objectve Modelng for Determnng Locaton of Undesrable Facltes, Transportaton Research, Part D, Vol. 9, Issue, 4, pp [5] Roy, B., Multcrtera Methodology for Decson Adng, Frst Edton, Sprnger, The Netherlands: Kluwer, 996. [6] Saham, H., Logstcs and Ste Selecton, Frst Edton, Malk Ashtar Unversty of Tech., Tehran(n Persan), 7. [7] Sorensen, J.H., Soderstrom, J., Carnes, S.A., Sweet for the Sour: Incentves n Envronmental Medaton, Envronmental Management, Vol. 8(4), 984, pp [8] Weber, A., Theory of the Locaton of Industres, Frst Edton, Edtor: Fredrch, C.J., Unversty of Chcago Press, Chcago, 965. [9] Wesolowsk, G., The Weber Problem: Hstory and Perspectve, Locaton Scence, Vol., 993, pp [4] Church, R.L., Murray, T., Busness Ste Selecton Locaton Analyss and GIS, Canada, John Wley & Sons, 9. [5] Church, R.L., Garfnkel, R., Locatng an Obnoxous on a Network, Transportaton Scence, Vol., 9, pp [6] Curtn, K.M., Church, R.L., A Famly of Locaton Models for Multple-Type Dscrete Dsperson, Geographcal Analyss, Vol.38, 6, pp [7] Drezner,., Locaton: A Survey of Applcatons and Methods, Frst Edton, Sprnger, New York Berln Hedelberg, 995. [8] Drezner,., Wesolowsky, G.O., Obnoxous Locaton n the Interor of a Planar Network, Journal of Regonal Scence, Vol. 35(4), 996, pp [9] Drezner,., Wesolowsky, G.O., Locaton of Multple Obnoxous Facltes, Transportaton Scence Vol. 9(3), 985, pp. 93. [] Erkut, E., Neuman, S., Analytcal Models for Locatng Undesrable Facltes, European Journal of Operatonal Research, Vol. 4, 989, pp Internatonal Journal of Industral Engneerng & Producton Research, December, Vol., No. 4