We present an exact generic method for solving the pricing problem in a column generation approach, which we call branch-and-bound column search. It searches the space of all feasible columns via a branch-and-bound tree search and returns all columns with a reduced-cost value below a certainthreshold. The approach is based on an idea from Krumke … Read more
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental … Read more
We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two new features: an uncertainty set linearly dependent on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to … Read more
Optimization problems in operations and finance often include a cost that is proportional to the expected amount by which a random variable exceeds some fixed quantity, known as the expected loss function. Representation of this function often leads to computational challenges, depending on the distribution of the random variable of interest. Moreover, in practice, a … Read more
We present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory … Read more
We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the … Read more
Contraflow means lane reversals on networks. In lane reversal reconfiguration, the capacity of arc increases by reorienting arcs towards demand nodes, which maximizes the flow value and reduces the travel time. In this work, we survey the existing pieces of literature on single and multi-commodity contraflow problems with symmetric and asymmetric travel times on parallel … Read more
Motivated by the worldwide Covid-19 vaccine procurement, we study an inventory problem with an advance purchase contract which requires all ordering decisions to be committed at once. In reality, not only the demand is uncertain, but its distribution can also be ambiguous. Hence, we assume that only the mean and the variance are known and … Read more
Optimal capacity expansion requires complex decision-making, often influenced by technology learning, which represents the reduction in expansion cost due to factors such as cumulative installed capacity. However, having perfect foresight over the technology cost reduction is highly unlikely. In this work, we develop a multistage stochastic programming framework to model capacity planning problems with endogenous … Read more
While useful probability bounds for \(n\) pairwise independent Bernoulli random variables adding up to at least an integer \(k\) have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when \(k = 1\), the tightest upper bound on the probability … Read more