How to cite this paper
Amiri-Aref, M., Javadian, N., Tavakkoli-Moghaddam, R & Aryanezhad, M. (2011). The center location problem with equal weights in the presence of a probabilistic line barrier.International Journal of Industrial Engineering Computations , 2(4), 793-800.
Refrences
Aneja, Y.P., & Parlar, M. (1994). Algorithms for Weber facility location in the presence of forbidden regions and/or barriers to travel. Transportation Science, 28(1), 70–76.
Aupperle, L., & Keil, J. M. (1989) Polynomial algorithms for restricted Euclidean p-centre problems. Discrete Applied Mathematics, 23, 25-31.
Batta, R., Ghose, A., & Palekar, U. (1989). Locating facilities on the Manhattan metric with arbitrarily shaped barriers and convex forbidden regions. Transportation Science, 23(1), 26-36.
Bischoff, M., Fleischmann, T., & Klamroth, K. (2009). The multi-facility location–allocation problem with polyhedral barriers. Computers and Operations Research, 36(5), 1376 –1392.
Bischoff, M., & Klamroth, K. (2007). An efficient solution method for Weber problems with barriers based on genetic algorithms. European Journal of Operational Research. 177(1), 22–41.
Butt, S.E., & Cavalier, T.M. (1996). An efficient algorithm for facility location in the presence of forbidden regions. European Journal of Operational Research, 90(1), 56–70.
Canbolat, M.S, & Wesolowsky, G.O. (2010). The rectilinear distance Weber problem in the presence of a probabilistic line barrier. European Journal of Operational Research, 202(1), 114–121.
Chakrabarty, N. R. & Chaudhuri, P. K. (1990). Geometric solution of a constrained rectilinear distance minimax location problem. Asia-Pacific Journal of Operations Research, 7, 163-171.
Chakrabarty, N. R., & Chaudhuri, P. K. (1992). Geometrical solution to some planar constrained minimax problems involving the weighted rectilinear metric, Asia-Pacific Journal of Operations Research, 9, 135-144.
Charalambous, C. (1982). Extension of the Elzinga-Hearn algorithm to the weighted case. Operations Research, 30, 591-594.
Dearing, P. M., & Segars Jr., R. (2002a). An equivalence result for single facility planar location problems with rectilinear distance and barriers, Annals of Operations Research, 111, 89-110.
Dearing, P. M., & Segars Jr., R. (2002b). Solving rectilinear planar location problems with barriers by a polynomial partitioning. Annals of Operations Research, 111,111-133.
Dearing, P.M., Hamacher, H.W., & Klamroth, K. (2002). Dominating sets for rectilinear center location problems with polyhedral barriers. Naval Research Logistics, 49(7), 647–665.
Dearing, P.M., Klamroth, K., & Segars, R. (2005). Planar location problems with block distance and barriers. Annals of Operations Research, 136(1), 117–143.
Elzinga, D. J., & Hearn, D. W. (1972). Geometrical solutions for some minimax location problems. Transportation Science, 6, 379-394.
Frieß, L., Klamroth, K., & Sprau, M. (2005). A wavefront approach to center location problems with barriers. Annals of Operations Research, 136(1), 35–48.
Hamacher, H.W., & Klamroth, K. (2000). Planar Weber location problems with barriers and block norms. Annals of Operations Research, 96, 191–208.
Hamacher, H.W., & Nickel, S. (1996). Multicriteria planar location problems. European Journal of Operational Research, 94, 66–86.
Hamacher, H.W., & Nickel, S. (1988). Classification of location problems. Location Science, 6, 229–242.
Hansen, P., Peeters, D., & Thisse, J. (1981). On the location of an obnoxious facility. Sistemi Urbani, 3, 299–317.
Hearn, D. W., & Vijay, J. (1982). Efficient algorithms for the (weighted) minimum circle problem. Operations Research, 30, 777-795.
Katz, I.N., & Cooper, L. (1981). Formulation and the case of Euclidean distance with one forbidden circle. European Journal of Operational Research, 6, 166–173.
Kelachankuttu, H., Batta, R., & Nagi, R. (2007). Contour line construction for a new rectangular facility in an existing layout with rectangular departments. European Journal of Operational Research, 180, 149–162.
Klamroth, K. (2001a). A reduction result for location problems with polyhedral barriers. European Journal of Operational Research, 130(3), 486–497.
Klamroth, K. (2001b). Planar Weber location problems with line barriers. Optimization, 49(5-6), 517–527.
Klamroth, K. (2002). Single-facility location problems with barriers. Springer series in operations research.
Klamroth, K. (2004). Algebraic properties of location problems with one circular barrier. European Journal of Operational Research, 154(1), 20–35.
Klamroth, K., & Wiecek, M.M. (2002). A bi-objective median location problem with a line barrier. Operations Research, 50(4), 670–679.
Larson, R.C., & Sadiq, G. (1983). Facility location with the Manhattan metric in the presence of barriers to travel. Operations Research. 31, 652–669.
McGarvey, R.G., & Cavalier, T.M. (2003). A global optimal approach to facility location in the presence of forbidden regions. Computers and Industrial Engineering, 45(1), 1–15.
Nandikonda, P., Batta, R., & Nagi, R. (2003). Locating a 1-center on a Manhattan plane with ‘arbitrarily’ shaped barriers. Annals of Operations Research, 123(1-4), 157–172.
Nickel, S. (1998). Restricted center problems under polyhedral gauges. European Journal of Operational Research, 104, 343-357.
Sarkar, A., Batta, R., & Nagi, R. (2007). Placing a finite size facility with a center objective on a rectangular plane with barriers. European Journal of Operational Research, 179(3), 1160–1176.
Savaş, S., Batta, R., & Nagi, R. (2002). Finite-size facility placement in the presence of barriers to rectilinear travel. Operations Research, 50(6), 1018–1031.
Segars Jr., R. (2000). Location Problems with Barriers Using Rectilinear Distance. Ph.D. thesis, Dept. of Mathematical Sciences, Clemson University, SC.
Sylvester, J. J. (1857). A question in the geometry of situation. Quarterly Journal of Pure and Applied Mathematics, 1, 79-80.
Wang, S.J., Bhadury, J., & Nagi, R. (2002). Supply facility and input/output point locations in the presence of barriers. Computers and Operations Research, 29(6), 685–699.
Aupperle, L., & Keil, J. M. (1989) Polynomial algorithms for restricted Euclidean p-centre problems. Discrete Applied Mathematics, 23, 25-31.
Batta, R., Ghose, A., & Palekar, U. (1989). Locating facilities on the Manhattan metric with arbitrarily shaped barriers and convex forbidden regions. Transportation Science, 23(1), 26-36.
Bischoff, M., Fleischmann, T., & Klamroth, K. (2009). The multi-facility location–allocation problem with polyhedral barriers. Computers and Operations Research, 36(5), 1376 –1392.
Bischoff, M., & Klamroth, K. (2007). An efficient solution method for Weber problems with barriers based on genetic algorithms. European Journal of Operational Research. 177(1), 22–41.
Butt, S.E., & Cavalier, T.M. (1996). An efficient algorithm for facility location in the presence of forbidden regions. European Journal of Operational Research, 90(1), 56–70.
Canbolat, M.S, & Wesolowsky, G.O. (2010). The rectilinear distance Weber problem in the presence of a probabilistic line barrier. European Journal of Operational Research, 202(1), 114–121.
Chakrabarty, N. R. & Chaudhuri, P. K. (1990). Geometric solution of a constrained rectilinear distance minimax location problem. Asia-Pacific Journal of Operations Research, 7, 163-171.
Chakrabarty, N. R., & Chaudhuri, P. K. (1992). Geometrical solution to some planar constrained minimax problems involving the weighted rectilinear metric, Asia-Pacific Journal of Operations Research, 9, 135-144.
Charalambous, C. (1982). Extension of the Elzinga-Hearn algorithm to the weighted case. Operations Research, 30, 591-594.
Dearing, P. M., & Segars Jr., R. (2002a). An equivalence result for single facility planar location problems with rectilinear distance and barriers, Annals of Operations Research, 111, 89-110.
Dearing, P. M., & Segars Jr., R. (2002b). Solving rectilinear planar location problems with barriers by a polynomial partitioning. Annals of Operations Research, 111,111-133.
Dearing, P.M., Hamacher, H.W., & Klamroth, K. (2002). Dominating sets for rectilinear center location problems with polyhedral barriers. Naval Research Logistics, 49(7), 647–665.
Dearing, P.M., Klamroth, K., & Segars, R. (2005). Planar location problems with block distance and barriers. Annals of Operations Research, 136(1), 117–143.
Elzinga, D. J., & Hearn, D. W. (1972). Geometrical solutions for some minimax location problems. Transportation Science, 6, 379-394.
Frieß, L., Klamroth, K., & Sprau, M. (2005). A wavefront approach to center location problems with barriers. Annals of Operations Research, 136(1), 35–48.
Hamacher, H.W., & Klamroth, K. (2000). Planar Weber location problems with barriers and block norms. Annals of Operations Research, 96, 191–208.
Hamacher, H.W., & Nickel, S. (1996). Multicriteria planar location problems. European Journal of Operational Research, 94, 66–86.
Hamacher, H.W., & Nickel, S. (1988). Classification of location problems. Location Science, 6, 229–242.
Hansen, P., Peeters, D., & Thisse, J. (1981). On the location of an obnoxious facility. Sistemi Urbani, 3, 299–317.
Hearn, D. W., & Vijay, J. (1982). Efficient algorithms for the (weighted) minimum circle problem. Operations Research, 30, 777-795.
Katz, I.N., & Cooper, L. (1981). Formulation and the case of Euclidean distance with one forbidden circle. European Journal of Operational Research, 6, 166–173.
Kelachankuttu, H., Batta, R., & Nagi, R. (2007). Contour line construction for a new rectangular facility in an existing layout with rectangular departments. European Journal of Operational Research, 180, 149–162.
Klamroth, K. (2001a). A reduction result for location problems with polyhedral barriers. European Journal of Operational Research, 130(3), 486–497.
Klamroth, K. (2001b). Planar Weber location problems with line barriers. Optimization, 49(5-6), 517–527.
Klamroth, K. (2002). Single-facility location problems with barriers. Springer series in operations research.
Klamroth, K. (2004). Algebraic properties of location problems with one circular barrier. European Journal of Operational Research, 154(1), 20–35.
Klamroth, K., & Wiecek, M.M. (2002). A bi-objective median location problem with a line barrier. Operations Research, 50(4), 670–679.
Larson, R.C., & Sadiq, G. (1983). Facility location with the Manhattan metric in the presence of barriers to travel. Operations Research. 31, 652–669.
McGarvey, R.G., & Cavalier, T.M. (2003). A global optimal approach to facility location in the presence of forbidden regions. Computers and Industrial Engineering, 45(1), 1–15.
Nandikonda, P., Batta, R., & Nagi, R. (2003). Locating a 1-center on a Manhattan plane with ‘arbitrarily’ shaped barriers. Annals of Operations Research, 123(1-4), 157–172.
Nickel, S. (1998). Restricted center problems under polyhedral gauges. European Journal of Operational Research, 104, 343-357.
Sarkar, A., Batta, R., & Nagi, R. (2007). Placing a finite size facility with a center objective on a rectangular plane with barriers. European Journal of Operational Research, 179(3), 1160–1176.
Savaş, S., Batta, R., & Nagi, R. (2002). Finite-size facility placement in the presence of barriers to rectilinear travel. Operations Research, 50(6), 1018–1031.
Segars Jr., R. (2000). Location Problems with Barriers Using Rectilinear Distance. Ph.D. thesis, Dept. of Mathematical Sciences, Clemson University, SC.
Sylvester, J. J. (1857). A question in the geometry of situation. Quarterly Journal of Pure and Applied Mathematics, 1, 79-80.
Wang, S.J., Bhadury, J., & Nagi, R. (2002). Supply facility and input/output point locations in the presence of barriers. Computers and Operations Research, 29(6), 685–699.