Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck

Investment and abandonment decisions in the presence of imperfect aggregation of information

The traditional marshallian rule of investing when the value of the investment is greater than its installment cost is modified in the presence of irreversibility and uncertainty, giving rise to an option component. Additionally, the interaction of participants holding each one a right to invest can give rise under imperfect information to situations of deviations from the optimal timing of exercise of the investment and to "herd behavior" or informational cascades given that the agents take into account when deciding not only their private set of information but also the information released to the market by the decisions made by the other agents. In the present paper we develop a model that tries to capture these effects and dynamics by showing revision of conditional expectations of the agents, and with considerations regarding the degree of dispersion of information in the economy and the effect of the number of participants and their effect into their behavior.real options, capital markets, investment, aggregation, information

Real Options and Game Theoretical Approaches to Real Estate Development Projects: Multiple Equilibria and the Implications of Different Tie-Breaking Rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.Game theory and real options, equilibrium selection, real estate development

A posteriori multi-stage optimal trading under transaction costs and a diversification constraint

This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the stage-wise optimal allocation over a time horizon with potential investments in multiple currencies and various assets. Three variants are discussed, including unconstrained trading frequency, a fixed number of total admissable trades, and the waiting of a specific time-period after every executed trade until the next trade. The developed methods are based on efficient graph generation and consequent graph search, and are evaluated quantitatively on real-world data. The fundamental motivation of this work is preparatory labeling of financial time-series data for supervised machine learning.Comment: 25 pages, 4 figures, 6 table

Real Options and Game Theoretical Approaches to Real Estate Development Projects: Multiple Equilibria and the Implications of Different Tie-Breaking Rules

This paper builds on a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the information set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.game theory and real options, equilibrium selection, real estate development