The recent growth of direct-to-consumer deliveries has stressed the importance of last-mile logistics, becoming one of the critical factors in city planning. One of the key factors lies in the last-mile deliveries, reaching in some cases nearly 50% of the overall parcel delivery cost. Different variants of the the well-known Traveling Salesman Problem (TSP) arise … Read more
In this paper we go one step further in the automatic generation of FPTASes for multi-stage stochastic dynamic programs with scalar state and action spaces, in where the cost-to-go functions have a monotone structure in the state variable. While there exist a few frameworks for automatic generation of FPTASes, so far none of them is … Read more
This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a … Read more
Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and … Read more
In the context of multistage stochastic optimization, it is natural to consider nested risk measures, which originate by repeatedly composing risk measures, conditioned on realized observations. Starting from this discrete time setting, we extend the notion of nested risk measures to continuous time by adapting the risk levels in a time dependent manner. This time … Read more
In a previous work, we have introduced an algorithm, called RaBVItG, used for computing Feedback Nash equilibria of deterministic multiplayers Differential Games. This algorithm is based on a sequence of Game Iterations (i.e., a numerical method to simulate an equilibrium of a Differential Game), combined with Value Iterations (i.e, a numerical method to solve a … Read more
We study new generalizations of the classical capacitated lot-sizing problem with concave production (or transportation), holding, and subcontracting cost functions in which the total production (or transportation) capacity in each time period is the summation of capacities of a subset of n available modules (machines or vehicles) of different capacities. We refer to this problem … Read more
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 study a variant of the multi-period vehicle routing problem, in which a service provider offers a discount to customer in exchange for delivery flexibility. We establish theoretical properties and empirical insights regarding the intricate and complex relation between the benefit from additional delivery flexibility, the discounts offered to customers to gain additional delivery flexibility, … Read more
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more