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- Title
Adjustable Robust Maximum Flow Problem with Parametric Ellipsoidal and Polyhedral Uncertainty Set.
- Authors
Chaerani, Diah; Agustini, Rahmah Arie; Rusyaman, Endang
- Abstract
In this paper the Adjustable Robust Maximum Flow Problem (ARMFP) is discussed. The problem is considered as a two-stage optimization problem with two kinds of variables, i.e., adjustable and non-adjustable variables. There is also an assumption that the input parameter, i.e. arc capacities, lie within an uncertainty set. The main challenge in Adjustable Robust Optimization (ARO) is to find whether the robust counterpart of ARMFP be can be formulated into a computationally tractable optimization problem. To this end, a convex continue set is assumed to be the set of the adjustable variables and or the uncertain arc capacities. In this paper it is considered the parametric ellipsoidal and polyhedral uncertainty set. The ARMFP is constructed by defining the maximum flow for the whole network represented by a flow xts that connect the destination node t back to the source node s. This xts is assumed to be the adjustable variable. In the case of parametric ellipsoidal uncertainty, the characteristic of ARMFP is analysed using the Theorem of Max-Flow and Min- Cut. In the case of polyhedral uncertainty set, the counterpart is obtained as a linear programming problem. Some examples are presented.
- Subjects
ROBUST optimization; UNCERTAINTY; LINEAR programming; CONVEX sets
- Publication
IAENG International Journal of Applied Mathematics, 2021, Vol 51, Issue 1, p82
- ISSN
1992-9978
- Publication type
Article