On Deriving and Solving the Generalized Bivariate, Linear Location Problems.

摘要

The generalized, bivariate, linear location problem concerns the locating of a linear facility, x sub 2 = (sub o +(sub 1(X sub 1) in a two-dimensional Euclidean space such that the p-norm distance taken to the q power is minimized of a serving n existing fixed facilities whose location in the two-dimensional Euclidean space is given by (ail,ai2) with i=1,...,n. The solution of a the generalized, bivariate linear location problem consists of two subproblems. The first subproblem involves the determination of the point on any linear facility that minimizes the p-norm distance to an individual existing facility. The second subproblem consists of determining the optical linear facility that minimizes the sum of a the q multiple of the p-norm distance from all the existing facilities to the point on the linear facility determined by the previous step. The lack of convexity of the generalized, bivariate linear location problem prohibits a universal solution technical for all combinations of possible values for p and q. For certain combinations of p's and q's. however, an exact solution can be determined.