Seminars

Abstract: Many processes in the real-world consist in making choices with probabilities in proportion to the total reward accumulated when making those choices in the past. Universal mathematical models for such processes are the interacting urns with reinforcement on graphs. We will discuss a multiple colour generalisation of the model of graph interacting urns studied by Benaim et. al., Random Struct. Alg., 46: 614-634, 2015. We show that for complete graphs and for a broad class of reinforcement functions governing the addition of balls in the urns, the process of colour proportions at each urn converges almost surely to the fixed points of the reinforcement function. The main tools employed are the stochastic approximation method and Lyapunov functions.

Abstract: With the increasing consumption and depletion of natural resources, the adoption of reverse logistics options has become increasingly necessary for all organizations. Furthermore, reverse logistics represents a source of competitive advantage in business markets. Managing e-commerce returns, waste materials, and other reverse flows in urban areas relies on determining the routes to be performed by a fleet of service vehicles. Specifically, many operational problems in reverse logistics can be studied as variants of the well-known Vehicle Routing Problem (VRP). This talk deals with uncertain reverse logistics VRPs in which some (or all) locations to be serviced are identified as pick-up points. These problems are solved by using stochastic optimization approaches, whereby parts of the input data are modelled as random variables that follow a given probability distribution. Tailored recourse strategies are presented in the solution process.