TY  - JOUR
ID  - Nguyen2016
LB  - Nguyen2016
AU  - Nguyen, Kien Trung
AU  - Chi, Nguyen Thi Linh
TI  - A model for the inverse 1-median problem on trees under uncertain costs
ST  - A model for the inverse 1-median problem on trees under uncertain costs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 4
SP  - 513
EP  - 523
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.4.513
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.4.513
AB  - We consider the problem of justifying vertex weights of a tree under uncertain costs so that a prespecified vertex become optimal and the total cost should be optimal in the uncertainty scenario. We propose a model which delivers the information about the optimal cost which respect to each confidence level \(\alpha \in [0,1]\). To obtain this goal, we first define an uncertain variable with respect to the minimum cost in each confidence level. If all costs are independently linear distributed, we present the inverse distribution function of this uncertain variable in \(O(n^{2}\log n)\) time, where \(n\) is the number of vertices in the tree.
KW  - location problem
KW  - uncertain variable
KW  - inverse optimization problem
KW  - tree
SN  - 1232-9274
ER  -