We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader’s problem. Both bounding problems are equivalent to explicit mixed-integer linear programs … Read more
We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely … Read more
Two approaches to time consistency of risk averse multistage stochastic problems were dis- cussed in the recent literature. In one approach certain properties of the corresponding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to … Read more
With greater penetration of renewable generation, the uncertainty faced in electricity markets has increased substantially. Conventionally, generators are assigned a pre-dispatch quantity in advance of real time, based on estimates of uncertain quantities. Expensive real time adjustments then need to be made to ensure demand is met, as uncertainty takes on a realization. We propose … Read more
Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more
We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly all existing exact methods for … Read more
This paper proposes a multi-stage stochastic programming formulation for the reservoir management problem. Our problem specifically consists in minimizing the risk of floods over a fixed time horizon for a multi-dimensional hydro-electrical complex. We consider well-studied linear time series model and enhance the approach to consider heteroscedasticity. Using these stochastic processes under very general distributional … Read more
Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves upon these bounds by re-enforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into ‘groups’. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve … Read more
We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. We propose a hierarchy of bounds based on partitions of the scenario set into subsets of (nearly) equal cardinality. These expected partition (EP) bounds coincide with EGSO bounds provided by Sandikci et al. … Read more
Building on the work of Gendreau, Laporte, and Seguin (1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems (SVRP). The numerous variants of the problem that have been studied in the literature are described and categorized. Also a thorough review of solution methods applied to the SVRP is included … Read more