We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint … Read more
We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification … Read more
This paper studies the economic desirability of UAV parcel delivery and its e ect on e-retailer distribution network while taking into account technological limitations, government regulations, and customer behavior. We consider an e-retailer o ering multiple same day delivery services including a fast UAV service and develop a distribution network design formulation under service based competition where … Read more
Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvatal-Gomory inequalities obtained by strengthening Chvatal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvatal-Gomory inequalities is … Read more
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often, e.g. due to contractual constraints, such flexible and adaptive policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of … Read more
In this paper we extend a game theoretic meta-model used to assess the future of Paris agreement to the time horizon 2100 and we include in the strategic decisions of the negotiating coalitions the use of Carbon Dioxyde Removal (CDR) technologies. The meta-game model is calibrated through statistical emulation of GEMINI-E3, a world computable general … Read more
Wasserstein distributionally robust optimization (DRO) estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify model parameters (or) decision choices that are … Read more
We study tactical models for the design of same-day delivery (SDD) systems. Same-day fulfillment in e-commerce has seen substantial growth in recent years, and the underlying management of such services is complex. While the literature includes operational models to study SDD, they tend to be detailed, complex, and computationally difficult to solve, and thus may … Read more
Some popular heuristics for combinatorial optimisation start by constructing a feasible solution to a dual of the problem. We show that such dual-based heuristics can exhibit highly counter-intuitive behaviour. In particular, for some problem classes, solving the dual exactly invariably leads to much worse primal solutions than solving the dual with a simple greedy heuristic. … Read more
This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more