Adjustable robust counterpart optimization model for internet shopping online problem

Abstract

In this paper, a discussion on deriving the Adjustable Robust Counterpart for Internet Shopping Online (ARC-ISO) is discussed. The problem on Internet Shopping Online is considered as an application of Robust Maximum Flow Problem (RMFP) with circular demand. The decision variables which considered as the adjustable variable is the maximum flow from a destination node in a flow network which back to the source node. In this paper, when the source nodes is multiple, then it is possible to add a dummy node as a single source node. For the multiple destinations, the same design is done. The main challenge is when and how we assume the data can be uncertain and assumed to be lies within a box, an ellipsoidal or polyhedral uncertainty set. In this paper, the uncertain delivering time is assumed to be lied in a polyhedral uncertainty set.