A decomposition algorithm for two-stage stochastic programs with nonconvex recourse

In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variable. Due to the failure of the Clarke regularity of the resulting nonconvex recourse function, classical decomposition approaches such as Benders … Read more

Theoretical Insights and a New Class of Valid Inequalities for the Temporal Bin Packing Problem with Fire-Ups

The temporal bin packing problem with fire-ups (TBPP-FU) is a two-dimensional packing problem where one geometric dimension is replaced by a time horizon. The given items (jobs) are characterized by a resource consumption, that occurs exclusively during an activity interval, and they have to be placed on servers so that the capacity constraint is respected … Read more

A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the objective is sparse. We use a graphical representation of the support of Q, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This … Read more

Differential Privacy in Multi-Party Resource Sharing

This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of … Read more

A decomposition approach for integrated locomotive scheduling and driver rostering in rail freight transport

In this work, we consider the integrated problem of locomotive scheduling and driver rostering in rail freight companies. Our aim is to compute an optimal simultaneous assignment of locomotives and drivers to the trains listed in a given order book. Mathematically, this leads to the combination of a set-packing problem with compatibility constraints and a … Read more

A novel decomposition approach for holistic airline optimization

Airlines face many different planning processes until the day of operation. These include Fleet Assignment, Tail Assignment and the associated control of ground processes between consecutive flights, called Turnaround Handling. All of these planning problems have in common that they often need to be reoptimized on the day of execution due to unplanned events. In … Read more

Decomposition strategies for vehicle routing heuristics

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterisation of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: we discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight … Read more

A Parallel Hub-and-Spoke System for Large-Scale Scenario-Based Optimization Under Uncertainty

Efficient solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We describe the overall architecture and provide computational examples and results showing scalability to the largest instances that we know of for the … Read more

A Novel Solution Methodology for Wasserstein-based Data-Driven Distributionally Robust Problems

Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for their sound mathematical properties. For right-hand-sided uncertainty, however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, … Read more

Risk-Averse Multistage Stochastic Programs with Expected Conditional Risk Measures

We study decomposition algorithms for risk-averse multistage stochastic programs with expected conditional risk measures (ECRMs). ECRMs are attractive because they are time-consistent, which means that a plan made today will not be changed in the future if the problem is re-solved given a realization of the random variables. We show that solving risk-averse problems based … Read more