Question

Consider single-facility rectilinear minisum location problem. Four existing facilities are located at (7,4), (4,6), (9,10), (12,6). The weights are 30, 40, 55, and 80 respectively.

Write the mathematical formulation of the problem in open form.

Answer 1

The mathematical formulation of the single-facility rectilinear minisum location problem in open form involves minimizing the weighted sum of distances between the facility to be located and the existing facilities.

Step-by-step explanation:

The mathematical formulation of the single-facility rectilinear minisum location problem in open form can be expressed as follows:

Let x and y be the coordinates of the facility to be located. The objective is to minimize the weighted sum of distances between the facility and the existing facilities. Let (xi, yi) be the coordinates of the i-th existing facility and wi be its weight. The problem can be formulated as the following mathematical program:

minimize ∑iwi(|x-xi| + |y-yi|)