Multi-Uncertainty Problems (MUP) with applications to managing risk in resource-constrained project scheduling

Optimization problems under uncertainty have received considerable attention in recent years due to their practical implications. In real-world applications, a problem is usually confronted with multiple types of uncertainties that are incommensurable with each other. Decision makers in the real-world do not trade-off objectives alone, but also and more importantly trade-off different uncertainties. The contemporary optimization techniques that deal with uncertainty generally treat different types of uncertainties by aggregating them into a single form. In this paper, we introduce a new type of optimization problems which are characterized by multiple conflicting uncertainties. We term them as multi-uncertainty optimization problems. Modeling multiple conflicting uncertainties as an optimization problem can provide analysts a powerful tool to search non-dominated solutions in a risk space in addition to the objective space. This is particularly useful since sources of uncertainties are usually uncontrollable and cannot be optimized as objectives. The concept of a risk operating curve is introduced which provides a unique perspective of the problem to the decision makers allowing them to opt for solutions based on their risk attitude toward different sources of uncertainties. The application of these concepts is demonstrated through a test problem in the resource-constrained project scheduling domain.