Stochastic Programming

Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics

  • Margarita P Castro
  • Merve Bodur
  • Yongjia Song
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We introduce a novel aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We present a novel branch-and-cut algorithm integrated … Read more

    Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

  • Johannes Milz
  • Thomas Surowiec
    • Categories Optimization of Systems modeled by PDEs, Stochastic Programming, Systems governed by Differential Equations Optimization Tags , , , , , , ,

    Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more

    A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applications

  • Jonathan Yu-Meng Li
  • Tiantian Mao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by applying the Wasserstein metric to construct a ball centred at the empirical distribution and finding … Read more

    A single cut proximal bundle method for stochastic convex composite optimization

  • Jiaming Liang
  • Vincent Guigues
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , ,

    In this paper, we consider optimization problems where the objective is the sum of a function given by an expectation and a Lipschitz continuous convex function. For such problems, we pro- pose a Stochastic Composite Proximal Bundle (SCPB) method with optimal complexity. The method does not require estimation of parameters involved in the assumptions on … Read more

    Routing and resource allocation in non-profit settings with equity and efficiency measures under demand uncertainty

  • Faisal Alkaabneh
  • Karmel S. Shehadeh
  • Ali Diabat
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    Motivated by food distribution operations for non-profit organizations, we study a variant of the stochastic routing-allocation problem under demand uncertainty, in which one decides the assignment of trucks for demand nodes, the sequence of demand nodes to visit (i.e., truck route), and the allocation of food supply to each demand node. We propose three stochastic … Read more

    A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling under Uncertain Dwell and Running Times

  • Andreas Bärmann
  • Patrick Gemander
  • Alexander Martin
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , , ,

    We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy-efficiency of a timetable. Since deviations from a planned timetable … Read more

    Robust planning of production routing problem in closed-loop supply chain of beverage glass bottles

  • Ali Borumand
  • Ahmadreza Marandi
  • Ali Nookabadi
  • Zümbül Atan
    • Categories Stochastic Programming, Supply Chain Management Tags , , , ,

    Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more

    A Survey on Bilevel Optimization Under Uncertainty

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories Global Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    Bilevel optimization is a very active field of applied mathematics. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision making processes. This ability, however, also makes the resulting problems challenging to solve—both in theory and practice. Fortunately, there have been significant algorithmic advances in the field … Read more

    Planning of Container Crossdocking for an Express Shipment Service Network

  • Anton J. Kleywegt
  • Haotian Wu
    • Categories Applications - OR and Management Sciences, Stochastic Programming, Transportation Tags , , , ,

    In air transportation, container crossdocking refers to a loaded container that is transferred at an airport from an incoming flight to an outgoing flight without handling the freight on the container. It reduces handling time and handling cost relative to unloading the container and sorting the freight, and is an economical alternative if a sufficient … Read more

    Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

  • Maël Forcier
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more