Prof. Alexander Teytelboym (University of Oxford): "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects"
We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents’ substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability—which is a strictly weaker condition than gross substitutability—is sufficient for the existence of competitive equilibrium. We also extend the “demand types” classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.
Ramin Barzanji (AdONE, TUM): "Decomposition Algorithms for Capacitated Location-Routing Problems"
Last-mile delivery in urban areas remains a central challenge in today’s logistics networks. Here, using micro-hubs to allow for sustainable last-mile solutions, e.g., to split the last mile into two phases that allow for the usage of cargo bikes, has recently been vividly discussed by researchers and practitioners. In this context, we encounter a new use case for the capacitated location-routing problem and its variants in the context of micro hub network design. Here, logistics service providers need to determine optimal micro-hub locations in a recurring fashion for day or week-ahead planning.
From an academic perspective work on the capacitated location-routing problem has mainly been focusing on metaheuristic solution approaches, whereas existing exact algorithms are still limited to solving small-scale instances. For large instances, few algorithms exist that primarily improve on lower bounds in order to prove optimality for benchmark solutions. However, these algorithms cannot be used for frequently changing real-world instances where benchmark solutions are not known. Against this background, we study a new Benders’ decomposition approach to solve large-scale problems that arise in this context.
This is ongoing work with Stefan Minner and Maximilian Schiffer.
Date: Monday 13th of July 2020, starting at 2 p.m.
The seminar will take place online.