Robust Optimization Model Using Ellipsoidal And Polyhedral Uncertainty Sets For Spatial Land-Use Allocation Problem

Land-use planning becomes an important thing to do because some land-use types can impact the environment and life quality. Land-use planning is generally an activity that involves the allocation of activities in a particular land. Spatial Optimization can be applied in land-use planning activity. The optimization model for the land-use allocation problem aims to determine the percentage of land-use changes that can maximize the comprehensive index and compactness index. In land-use planning, there are several uncertainty factors. In this paper, the robust optimization model for the land-use allocation problem is discussed as a multi-objective function. There are two objective functions to maximize the comprehensive index and to maximize the density index. The uncertainties are assumed are in benefit and acquisition cost when a land planning is changed to another land-use type. In order to get a robust counterpart (RC) formulation, the uncertain parameter is assumed to lie within an ellipsoidal and a polyhedral uncertainties set. A study for the numerical experiment is done for Jatinangor District in Kabupaten Sumedang, Indonesia, as an educational area. In this case study, two scenarios are discussed, i.e., the first scenario allows a policy for changing all types of land to be other land types. The second scenario preserves a condition that a type of land cannot be changed to another type. To handle the multi-objective optimization function, the lexicographic method is employed. It is shown that the computational tractability of the RC is gained with ellipsoidal and polyhedral uncertainty set. Thus, the robust optimal solutions are achieved.