In 2001, info-gap decision theory re-invented the then 40-year old model of local robustness, known universally as radius of stability (circa 1960). Since then, this model of local robustness has been promoted by info-gap scholars as a reliable tool for the management of a severe uncertainty that is characterized by a vast (e.g. unbounded) uncertainty … Read more
In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more
This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more
Scarf’s min-max order formula for the distribution-free risk-neutral newsvendor problem is a classical result in the field of inventory management. The min-max order formula provides, in closed-form, the order quantity that maximizes the worst-case expected profit associated with the demand of a single product when only the mean and variance of the product’s demand distribution, … Read more
Eliciting the utility of a decision maker is difficult. In this paper, we develop a flexible decision making framework, which uses the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. The ideas are developed by giving a probabilistic interpretation to utility and marginal utility functions. Boundary and additional … Read more
This paper deals with the problem of determining the optimal size of a residential grid-connected photovoltaic system to meet a certain CO2 reduction target at a minimum cost. Ren et al. proposed a novel approach using a simple linear programming that minimizes the total energy costs for residential buildings in Japan. However, their approach is … Read more
This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. … Read more
Power grid vulnerability analysis is often performed through solving a bi-level optimization problem, which, if solved to optimality, yields the most destructive interdiction plan with the worst loss. As one of the most effective operations to mitigate deliberate outages or attacks, transmission line switching recently has been included and modeled by a binary variable in … Read more
In this paper, we consider a linear two-stage robust optimization model with a mixed integer recourse problem. Currently, this type of two-stage robust optimization model does not have any exact solution algorithm available. We first present a set of sufficient conditions under which the existence of an optimal solution is guaranteed. Then, we present a … Read more
Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few … Read more