New PDF release: The Discrete Ordered Median Problem: Models and Solution

New PDF release: The Discrete Ordered Median Problem: Models and Solution

By Patricia Dominguez-Marin

This is the 1st ebook concerning the discrete ordered median challenge (DOMP), which unifies many classical and new facility situation difficulties. a number of distinct and heuristic methods are built during this booklet so as to clear up the DOMP.

Audience: The e-book is appropriate for researchers in position concept, and graduate scholars in combinatorial optimization.

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Extra resources for The Discrete Ordered Median Problem: Models and Solution Methods

Sample text

2 Strengthening the Form_II_1_a_ti_on_s____________________4_7 Again, to apply this definition, we require IXI = N. Therefore, the name is justified, since (x, y, s, w) must indeed be a feasible solution to (LDOMP2)' The following example illustrates the construction of an (LDOMP2 )-feasible point induced by X. e. A = (0,0,1,1,0). The optimal solution is formed by the facilities X = (1,4) and the assoczated cost vector is c(X) = (0,2,5,0,1). Therefore, by Definition 2, X induces a feasible point to (LDOMP2) as follows: o Let x be defined by x = (1,0,0,1,0).

E. kJ +k2-trimmed mean problems, and T6). Therefore, their description of the feasible regions is very similar. But after strengthening these linearisations the results are clearly different. ype Tl. e. N-median problems.

E the relationship between the feasible regions described by formulations (LDOMP;) and (LDOMP;). 2. Therefore, the result presented in Theorem 5 can be reformulated for these two improved linearisations of (DOMP), as it is shown in the following theorem. Theorem 9 There exists a surjective function, 7f, which assigns each feasible solution (x,y,s,w) of the linear programming relaxation of (LDOMPi), denoted by (LDOMPi)LP, to a feasible solution (x, y, s, w') of (LDOMP;)-LP. Proof. First, we have to prove that 7f is well defined.

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