Session: Adjustable Robust Optimization: Theories and Algorithms
Chair: Ahmadreza Marandi
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: A semi-infinite Benders’ cut approach for adjustable robust optimization
Speaker: Ayse Nur Arslan
Abstract: In this talk we consider two-stage linear adjustable robust optimization problems with continuous recourse. These problems have been the subject of exact solution algorithms, notably, Benders decomposition and constraint-and-column generation (CCG) approaches. Here, we present an alternative decomposition approach reposing on a novel reformulation of the problem using semi-infinite Benders’ cuts. We argue that this approach will enjoy the same quality of dual bounds as the CCG approach while requiring to solve a smaller number of separation problems. We additionally study the formulation and solution of separation problems under different assumptions on the form of the uncertainty set and the feasibility of the recourse problem. We perform a detailed numerical study that showcases the superior performance of our proposed approach as well as compares the performances of different formulations for the separation problem.
Talk 2: Robust Bilevel Optimization with Wait-and-See Follower: A Column-and-Constraint Generation Approach
Speaker: Henri Lefebvre
Abstract: Bilevel optimization is a classical framework for modeling hierarchical decision-making processes. Typically, it is assumed that all input parameters for both the leader and the follower are known when the leader makes a decision. However, in many real-world applications, the leader must decide without fully anticipating the follower's response due to uncertainties in the follower's problem. In this talk, we address robust bilevel optimization problems in which the follower adopts a ``wait-and-see'' approach. Thus, the leader decides without knowledge of the explicit realization of the uncertainty, then the uncertainty realizes in a worst-case manner, and afterward the follower's decisions are made. For this challenging problem class, we discuss mathematical properties and present a corresponding solution approach based on column-and-constraint generation. The convergence of the proposed algorithm is discussed along with its practical implementation including numerical results. We finally outline potential research directions.
Talk 3: The Value of Flexibility in Robust Supply Chain Network Design
Speaker: Amir Ardestani-Jaafari
Abstract: A supply chain network design problem (SCNDP) involves making long-term and mostly irreversible strategic decisions, requiring the utilization of various sources of flexibility and demand information. The cost efficiency of this process hinges, to a large extent, on how, among other factors, flexibilities from strategic and operational perspectives are tailored and how demand information is leveraged. In this paper, we investigate five distinct policies for our SCNDP, stemming from incorporating new flexibilities at both the strategic and operational levels. We commence with a localized production model where local production satisfies the demand. We then extend the model to cases where the production capacity in one location can be utilized to meet the demand of other nodes (Policy II). Furthermore, the capacity can be shared among open facilities if \textit{capacity-sharing links} have already been arranged (Policy III). In contrast to these policies, where the set capacity in the first stage serves as a surrogate for production amount in the second stage, we allow production decisions to be postponed until after the realization of demand, leading to a make-to-order rather than a make-to-stock production strategy (Policies IV and V). To analyze each of these policies, we develop a two-stage robust optimization framework for which we introduce a novel computationally efficient exact (based on Column-and-Constraint Generation (C\&CG)) and multiple approximation techniques (based on Linear Decision Rules). These techniques effectively solve realistically sized instances of the problem under varying demand uncertainty budgets, enabling us to derive managerial insights that would otherwise be unattainable. We demonstrate, among other results, that (i) the existence of capacity-sharing links among facilities yields (a) the highest percentage of cost-saving due to the pooling effect for all uncertainty budget values (b) significantly reduces shortage probability and (ii) production postponement brings only a marginal improvement in the results, suggesting that upstream supply chain connections (capacity-sharing links among facilities) are more critical than postponing production decisions, especially for moderate budgets of uncertainty. Finally, we apply our most effective policies to a real-world case study to contextualize these concepts, quantify their values, and formulate our design recommendations.
