A chance-constraint approach for optimizing social engagement-based services

Social engagement is a novel business model whose goal is transforming final users of a service from passive components into active ones. In this framework, people are contacted by the decision-maker (generally a company) and they are asked to perform tasks in exchange for a reward. This paves the way to the interesting optimization problem of allocating the different types of workforce so as to minimize costs. Despite this problem has been investigated within the operations research community, there is no model that allows to solve it by explicitly and appropriately modeling the behavior of contacted candidates through consolidated concepts from utility theory. This work aims at filling this gap. We propose a stochastic optimization model including a chance constraint that puts in relation, under probabilistic terms, the candidate willingness to accept a task and the reward actually offered by the decision-maker. The proposed model aims at optimally deciding which user to contact, the amount of the reward proposed, and how many employees to use in order to minimize the total expected costs of the operations. A solution approach is proposed to address the formulated stochastic optimization problem and its computational efficiency and effectiveness are investigated through an extensive set of computational experiments