OPTIMAL FACILITY LOCATION FOR NORMALLY AND EXPONENTIALLY DISTRIBUTED POINTS

被引:13
作者
KATZ, IN
COOPER, L
机构
[1] WASHINGTON UNIV, DEPT SYST SCI & MATH, ST LOUIS, MO 63130 USA
[2] SO METHODIST UNIV, DEPT IND ENG & OPERATION RES, DALLAS, TX 75275 USA
来源
JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES | 1976年 / 80卷 / 01期
关键词
D O I
10.6028/jres.080B.010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
N destinations in the plane left brace P //j: j equals 1,. . . , N right brace are given as independent random variables with specified probability densities, and the problem is to find the location of the point P which minimizes the expected sum of the Euclidean distances PP//j. In this paper, upper bounds for the minimizing sum of distances are found in terms of solutions to corresponding deterministic problems and the first and second moments of the probability densities. Three commonly occurring classes of bivariate probability densities, normal, exponential, and symmetric exponential, are then considered. Numerical tests are presented which show that in all cases, Steffensen's iteration is effective in accelerating convergence. Finally it is shown that in constrastto the deterministic case, P need not be in the convex hull of the means of P//j and a sufficient condition is given for P to be in this convex hull.
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页码:53 / 73
页数:21
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