Adjustable robust minimization problems in which the adjustable variables appear in a convex way are difficult to solve. For example, if we substitute linear decision rules for the adjustable variables, then the model becomes convex in the uncertain parameters, whereas for computational tractability we need concavity in the uncertain parameters. In this paper we reformulate … Read more
We study the robust resource constrained shortest path problem (RCSPP) under uncertainty in cost and multiple resource consumption. Contrary to the deterministic RCSPP where the cost and the consumption of resources on an arc are known and fixed, the robust RCSPP models the case where both the cost and the resource consumption are random, and … Read more
We focus on a problem of locating recharging stations in one-way station based electric car sharing systems which operate under demand uncertainty. We model this problem as a mixed integer stochastic program and develop a Benders decomposition algorithm based on this formulation. We integrate a stabilization procedure to our algorithm and conduct a large-scale experimental … Read more
We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods … Read more
In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more
We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more
In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more
Markov decision processes (MDPs) have found success in many application areas that involve sequential decision making under uncertainty, including the evaluation and design of treatment and screening protocols for medical decision making. However, the usefulness of these models is only as good as the data used to parameterize them, and multiple competing data sources are … Read more
A chance constrained optimization problem involves constraints with random data which can be violated with probability bounded above by a prespecified small risk parameter. Such constraints are used to model reliability requirements in a variety of application areas such as finance, energy, service and manufacturing. Except under very special conditions, chance constrained problems are extremely … Read more
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although the connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied by … Read more