Inverse single facility location problem on a tree with balancing on the distance of server to clients

Abstract

<p style='text-indent:20px;'>We introduce a case of inverse single facility location problem on a tree where by minimum modifying in the length of edges, the difference of distances between the farthest and nearest clients to a given facility is minimized. Two cases are considered: bounded and unbounded nonnegative edge lengths. In the unbounded case, we show the problem can be reduced to solve the problem on a star graph. Then an <inline-formula><tex-math id="M1">\begin{document}$ O(nlogn) $\end{document}</tex-math></inline-formula> algorithm is developed to find the optimal solution. For the bounded edge lengths case an algorithm with time complexity <inline-formula><tex-math id="M2">\begin{document}$ O(n^2) $\end{document}</tex-math></inline-formula> is presented.</p>

The inverse minisum circle location problem

“…Alizadeh et al [1] and Alizadeh and Etemad [4] presented some combinatorial algorithms for inverse obnoxious median and center problems, respectively. Omidi et al [22] and [21] developed algorithms for solving some cases of the inverse balanced facility location models. Recently, Gholami and Fathali [14] proposed mathematical models for the inverse minimax circle location problem with variable weights.…”