Objective function evaluation methods for the orienteering problem with stochastic travel and service times

In this paper, a variant of the orienteering problem in which the travel and service times are stochastic, is examined. Given a set of potential customers, a subset of them has to be selected to be serviced by the end of the day. Every time a delivery to a selected customer is fulfilled before the end of the day, a reward is received, otherwise, if the delivery is not completed, a penalty is incurred. The target is to maximise the expected income (rewards-penalties) of the company. The focus of this paper is to evaluate faster ways to approximate the objective function and compare them to an analytical way previously proposed in the literature. K