In this paper, we study a new variant of orienteering problem (OP) where each vertex in the OP tour is a facility within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple objective function such as maximizing a linear sum of score of selected vertices, we introduce a complicated non-linear objective function that necessitate the selection of locations to maximize a profit value such as expected customer demand or revenue. In our study, routing constraints included in the form of the OP is handled by Constraint Programming (CP), and the non-linear objective function, resulting from the utilization of random utilities, is tackled by two types of valid cuts, namely, outer-approximation and submodular cuts. These lead to the development of an exact solution methods: Cutting Plane, where these valid cuts are iteratively added to a master problem. Extensive experiments are conducted on problem instances of varying sizes, demonstrating that our approach excels in terms of solution quality and computation time when compared to other baseline approach.