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
Multistage stochastic programs are a viable modeling tool for sequential decisions conditional on information revealed at different points in time (stages). However, as the number of stages increases their applicability is soon halted by the curse of dimensionality. A typical, sometimes forced, alternative is to approximate stages by their expected values thus considering fewer stages … Read more
Emergency care necessitates adequate and timely treatment, which has unfortunately been compromised by crowding in many emergency departments (EDs). To address this issue, we study patient scheduling in EDs so that mandatory targets imposed on each patient’s door-to-provider time and length of stay can be collectively met with the largest probability. Exploiting patient flow data … Read more
In this work we present explicit definitions for the sample complexity associated with the Sample Average Approximation (SAA) Method for instances and classes of multistage stochastic optimization problems. For such, we follow the same notion firstly considered in Kleywegt et al. (2001). We define the complexity for an arbitrary class of problems by considering its … Read more
This paper presents a new formulation for the risk averse stochastic reservoir management problem. Using recent advances in robust optimization and stochastic programming, we propose a dynamic, multi-objective model based on minimization of a multidimensional risk measure associated with floods and droughts for a hydro-electrical complex. We present our model and then identify approximate solutions … Read more
In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal … Read more
In this paper we consider a transportation problem under uncertainty related to gypsum replenishment for a cement producer. The problem is to determine the number of vehicles to book at the beginning of each week to replenish gypsum at all the cement factories of the producer in order to minimize the total cost, given by … Read more
This paper studies a robust maritime inventory routing problem with time windows and stochastic travel times. One of the novelties of the problem is that the length and placement of the time windows are also decision variables. Such problems arise in the design and negotiation of long-term delivery contracts with customers who require on-time deliveries … Read more