Related papers: The Complexity Landscape of Two-Stage Robust Selec…
We study single-stage decision problems in which a subset of items with minimum total cost has to be selected at once from a given set of items, subject to two costs of each item -fixed and uncertain -and cardinality constraints for each…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
In this paper the problem of selecting $p$ out of $n$ available items is discussed, such that their total cost is minimized. We assume that costs are not known exactly, but stem from a set of possible outcomes. Robust recoverable and…
In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
In this work, we study a single-machine scheduling problem that aims at minimizing the total cost of a schedule subject to start-time dependent costs. This framework naturally captures scenarios where costs fluctuate throughout the day,…
This paper considers the resource-constrained project scheduling problem with uncertain activity durations. We assume that activity durations lie in a budgeted uncertainty set, and follow a robust two-stage approach, where a decision maker…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
In this paper the following selection problem is discussed. A set of $n$ items is given and we wish to choose a subset of exactly $p$ items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item…
Two-stage stochastic linear optimization is known to be #P-hard when all involved random variables are independently and uniformly distributed over intervals, even with fixed recourse. We show that this problem is actually #P-hard in the…
In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…
We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…
Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncertainty set without changing…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
This paper deals with a problem of production planning, which is a version of the capacitated single-item lot sizing problem with backordering under demand uncertainty, modeled by uncertain cumulative demands. The well-known interval…
Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…