Quickest Flows Over Time

Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Traditionally, flows over time are solved in time‐expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time‐expanded network. We present several approaches for coping with this difficulty. First, inspired by the work of Ford and Fulkerson on maximal s‐t‐flows over time (or “maximal dynamic s‐t‐flows”), we show that static length‐bounded flows lead to provably good multicommodity flows over time. Second, we investigate “condensed” time‐expanded networks which rely on a rougher discretization of time. We prove that a solution of arbitrary precision can be computed in polynomial time through an appropriate discretization leading to a condensed time‐expanded network of polynomial size. In particular, our approach yields fully polynomial‐time approximation schemes for the NP‐hard quickest min‐cost and multicommodity flow problems. For single commodity problems, we show that storage of flow at intermediate nodes is unnecessary, and our approximation schemes do not use any

An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times

Given a network with capacities and transit times on the arcs, the quickest flow problem asks for a "flow over time" that satisfies given demands within minimal time. In the setting of flows over time, flow on arcs may vary over time and the transit time of an arc is the time it takes for flow to travel through this arc. In most real-world applications (such as, e.g., road traffic, communication networks, production systems, etc.), transit times are not fixed but depend on the current flow situation in the network. We consider the model where the transit time of an arc is given as a non-decreasing function of the rate of inflow into the arc. We prove that the quickest s-t-flow problem is NP-hard in this setting and give various approximation results, including a fully polynomial time approximation scheme (FPTAS) for the quickest multicommodity flow problem with bounded cos

Distributed Storage Control Algorithms for Dynamic Networks

Recent technological advances have rendered storage a readily available resource, yet there exist few examples that use it for enhancing network performance. We revisit in-network storage and we evaluate its usage as an additional degree of freedom in network optimization. We consider the network design problem of maximizing the volume of end-to-end transferred data and we derive storage allocation (placement) solutions. We show that different storage placements have different impact on the performance of the network and we introduce a systematic methodology for the derivation of the optimal one. Accordingly, we provide a framework for the joint optimization of routing and storage control (usage) in dynamic networks for the case of a single commodity transfer. The derived policies are based on time-expanded graphs and ensure maximum performance improvement with minimum possible storage usage. We also study the respective multiple commodity problem, where the network link capacities and node storage resources are shared by the different commodities. A key advantage of our methodology is that it employs algorithms that are applicable to both centralized as well as to distributed execution in an asynchronous fashion, and thus, no tight synchronization is required among the various involved storage and routing devices in an operational network. We also present an extensive performance evaluation study using the backbone topology and actual traffic traces from a large European Internet Service Provider, and a number of synthetic network topologies. Our results show that indeed our approach offers significant improvements in terms of delivery time and transferred traffic volume.EC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNetEC/FP7/628441/EU/Improving Performance and Cost of Content Delivery in a Hyperconnected World/CDN-

Design of an optimality-based decomposition procedure for an air freight scheduled planning

M.S.Ronald L. Rardi

OPTIMIZATION OF RAILWAY TRANSPORTATION HAZMATS AND REGULAR COMMODITIES

Transportation of dangerous goods has been receiving more attention in the realm of academic and scientific research during the last few decades as countries have been increasingly becoming industrialized throughout the world, thereby making Hazmats an integral part of our life style. However, the number of scholarly articles in this field is not as many as those of other areas in SCM. Considering the low-probability-and-high-consequence (LPHC) essence of transportation of Hazmats, on the one hand, and immense volume of shipments accounting for more than hundred tons in North America and Europe, on the other, we can safely state that the number of scholarly articles and dissertations have not been proportional to the significance of the subject of interest. On this ground, we conducted our research to contribute towards further developing the domain of Hazmats transportation, and sustainable supply chain management (SSCM), in general terms. Transportation of Hazmats, from logistical standpoint, may include all modes of transport via air, marine, road and rail, as well as intermodal transportation systems. Although road shipment is predominant in most of the literature, railway transportation of Hazmats has proven to be a potentially significant means of transporting dangerous goods with respect to both economies of scale and risk of transportation; these factors, have not just given rise to more thoroughly investigation of intermodal transportation of Hazmats using road and rail networks, but has encouraged the competition between rail and road companies which may indeed have some inherent advantages compared to the other medium due to their infrastructural and technological backgrounds. Truck shipment has ostensibly proven to be providing more flexibility; trains, per contra, provide more reliability in terms of transport risk for conveying Hazmats in bulks. In this thesis, in consonance with the aforementioned motivation, we provide an introduction into the hazardous commodities shipment through rail network in the first chapter of the thesis. Providing relevant statistics on the volume of Hazmat goods, number of accidents, rate of incidents, and rate of fatalities and injuries due to the incidents involving Hazmats, will shed light onto the significance of the topic under study. As well, we review the most pertinent articles while putting more emphasis on the state-of-the-art papers, in chapter two. Following the discussion in chapter 3 and looking at the problem from carrier company’s perspective, a mixed integer quadratically constraint problem (MIQCP) is developed which seeks for the minimization of transportation cost under a set of constraints including those associating with Hazmats. Due to the complexity of the problem, the risk function has been piecewise linearized using a set of auxiliary variables, thereby resulting in an MIP problem. Further, considering the interests of both carrier companies and regulatory agencies, which are minimization of cost and risk, respectively, a multiobjective MINLP model is developed, which has been reduced to an MILP through piecewise linearization of the risk term in the objective function. For both single-objective and multiobjective formulations, model variants with bifurcated and nonbifurcated flows have been presented. Then, in chapter 4, we carry out experiments considering two main cases where the first case presents smaller instances of the problem and the second case focuses on a larger instance of the problem. Eventually, in chapter five, we conclude the dissertation with a summary of the overall discussion as well as presenting some comments on avenues of future work