Minmax regret 1-center problem on a network with a discrete set of scenarios
نویسندگان
چکیده
We consider the minmax regret 1-center problem on a general network with uncertainty on demands. Unlike other papers which considered the problem under interval uncertainty, we assume here that demand uncertainty is modelled by a finite number of discrete scenarios. We develop a solution approach based on the decomposition of the network into basic intervals and present a polynomial algorithm for the problem. Finally, we illustrate our approach with an example.
منابع مشابه
Approximating a two-machine flow shop scheduling under discrete scenario uncertainty
This paper deals with the two machine permutation flow shop problem with uncertain data, whose deterministic counterpart is known to be polynomially solvable. In this paper, it is assumed that job processing times are uncertain and they are specified as a discrete scenario set. For this uncertainty representation, the min-max and min-max regret criteria are adopted. The min-max regret version o...
متن کاملOn the approximability of minmax (regret) network optimization problems
In this paper the minmax (regret) versions of some basic polynomially solvable deterministic network problems are discussed. It is shown that if the number of scenarios is unbounded, then the problems under consideration are not approximable within logK for any ǫ > 0 unless NP ⊆ DTIME(n log ), where K is the number of scenarios.
متن کاملA Linear Approach to Node-restricted Minmax Regret Robust 1-median on a Tree
In this paper, we consider the node-restricted minmax regret 1-median problem on a tree network where node weights are deterministic and edge lengths are subject to uncertainty with unknown symmetric distribution. There have been proposed some complicated and time-consuming algorithms to obtain robust solutions for robust 1-median problem. We formulate the robust regret function as a mixed inte...
متن کامل[11] A. Ben-Tal and A. Nemirovski. Robust solutions of uncertain linear
[4] Igor Averbakh. Minmax regret solutions for minmax optimization problems with uncertainty. [5] Igor Averbakh. On the complexity of a class of combinatorial optimization problems with uncertainty. [7] Igor Averbakh and Oded Berman. Minimax regret p-center location on a network with demand uncertainty. [8] Igor Averbakh and Oded Berman. Minmax p-traveling salesman location problems on a tree.
متن کاملA Polynomial Time Algorithm for Minimax-Regret Evacuation on a Dynamic Path
A dynamic path network is an undirected path with evacuees situated at each vertex. To evacuate the path, evacuees travel towards a designated sink (doorway) to exit. Each edge has a capacity, the number of evacuees that can enter the edge in unit time. Congestion occurs if an evacuee has to wait at a vertex for other evacuees to leave first. The basic problem is to place k sinks on the line, w...
متن کامل