Determining the robust counterpart of uncertain spatial optimization model for water supply allocation problem

Abstract

In this paper we discuss how to get the robust counterpart for the spatial optimization model for water supply allocation (SOMWSA) problem that is proposed by [6]. We employ the robust counterpart methodology that is proposed by Ben-Tal and Nemirovskii [2] also use the new paradigm of robust counterpart methodology of den Hertog et al. [4]. To this end, first we define the uncertain family class of SOMWSA and derive the robust version of the uncertain problem. We assume that there are two uncertain data in SOMWSA problem, ie., the total population and the water demand in a region i at time t. Since the tractability of the problem is very important in Robust Optimization, we discuss three types of uncertainty set, i.e., box, ellipsoidal and polyhedral uncertainty set.