Optimizing flow rates in a queueing network with side constraints

Network Analysis;operations research

A two-stage stochastic transportation problem with fixed handling costs and a priori selection of the distribution channels

In this paper, a transportation problem comprising stochastic demands, fixed handling costs at the origins, and fixed costs associated with the links is addressed. It is assumed that uncertainty is adequately captured via a finite set of scenarios. The problem is formulated as a two-stage stochastic program. The goal is to minimize the total cost associated with the selected links plus the expected transportation and fixed handling costs. A prototype problem is initially presented which is then progressively extended to accommodate capacities at the origins and multiple commodities. The results of an extensive set of computational tests are reported and discussed

Optimizing Emergency Transportation through Multicommodity Quickest Paths

In transportation networks with limited capacities and travel times on the arcs, a class of problems attracting a growing scientific interest is represented by the optimal routing and scheduling of given amounts of flow to be transshipped from the origin points to the specific destinations in minimum time. Such problems are of particular concern to emergency transportation where evacuation plans seek to minimize the time evacuees need to clear the affected area and reach the safe zones. Flows over time approaches are among the most suitable mathematical tools to provide a modelling representation of these problems from a macroscopic point of view. Among them, the Quickest Path Problem (QPP), requires an origin-destination flow to be routed on a single path while taking into account inflow limits on the arcs and minimizing the makespan, namely, the time instant when the last unit of flow reaches its destination. In the context of emergency transport, the QPP represents a relevant modelling tool, since its solutions are based on unsplittable dynamic flows that can support the development of evacuation plans which are very easy to be correctly implemented, assigning one single evacuation path to a whole population. This way it is possible to prevent interferences, turbulence, and congestions that may affect the transportation process, worsening the overall clearing time. Nevertheless, the current state-of-the-art presents a lack of studies on multicommodity generalizations of the QPP, where network flows refer to various populations, possibly with different origins and destinations. In this paper we provide a contribution to fill this gap, by considering the Multicommodity Quickest Path Problem (MCQPP), where multiple commodities, each with its own origin, destination and demand, must be routed on a capacitated network with travel times on the arcs, while minimizing the overall makespan and allowing the flow associated to each commodity to be routed on a single path. For this optimization problem, we provide the first mathematical formulation in the scientific literature, based on mixed integer programming and encompassing specific features aimed at empowering the suitability of the arising solutions in real emergency transportation plans. A computational experience performed on a set of benchmark instances is then presented to provide a proof-of-concept for our original model and to evaluate the quality and suitability of the provided solutions together with the required computational effort. Most of the instances are solved at the optimum by a commercial MIP solver, fed with a lower bound deriving from the optimal makespan of a splittable-flow relaxation of the MCQPP

Multi-period whole system optimisation of an integrated carbon dioxide capture, transportation and storage supply chain

Carbon dioxide capture and storage (CCS) is an essential part of the portfolio of technologies to achieve climate mitigation targets. Cost efficient and large scale deployment of CCS necessitates that all three elements of the supply chain (capture, transportation and storage) are coordinated and planned in an optimum manner both spatially and across time. However, there is relatively little experience in combining CO2 capture, transport and storage into a fully integrated CCS system and the existing research and system planning tools are limited. In particular, earlier research has focused on one component of the chain or they are deterministic steady-state supply chain optimisation models. The very few multi-period models are unable to simultaneously make design and operational decisions for the three components of the chain. The major contribution of this thesis is the development for the first time of a multi-period spatially explicit least cost optimization model of an integrated CO2 capture, transportation and storage infrastructure under both a deterministic and a stochastic modelling framework. The model can be used to design an optimum CCS system and model its long term evolution subject to realistic constraints and uncertainties. The model and its different variations are validated through a number of case studies analysing the evolution of the CCS system in the UK. These case studies indicate that significant cost savings can be achieved through a multi-period and integrated system planning approach. Moreover, the stochastic formulation of the model allows analysing the impact of a number of uncertainties, such as carbon pricing or plant decommissioning schedule, on the evolution of the CSS system. In conclusion, the model and the results presented in this thesis can be used for system planning purposes as well as for policy analysis and commercial appraisal of individual elements of the CCS network.Open Acces

Network Routing Using the Network Tasking Order, a Chron Approach

This thesis promotes the use of the network tasking order (NTO), in collaboration with the air tasking order (ATO), to optimize routing in Mobile Ad hoc Networks (MANET). The network topology created by airborne platforms is determined ahead of time and network transitions are calculated offline prior to mission execution. This information is used to run maximum multi-commodity flow algorithms offline to optimize network flow and schedule route changes for each network node. These calculations and timely route modifications increases network efficiency. This increased performance is critical to command and control decision making in the battlefield. One test scenario demonstrates near a 100% success rate when route scheduling and splitting network traffic over an emulated MANET compared to Open Shortest Path First (OSPF) which only achieved around a 71% success rate, and Mesh Made Easy (MME) which achieved about 50% success. Another test scenario demonstrates that the NTO can experience degradation due to schedule delay. Overall, if executed and planned properly, the NTO can significantly improve network Quality of Service (QoS)

INNOVATIVE STRATEGIES TO OPTIMIZE WATER RESOURCES

The focus on the rationalisation of the industrial consumption of energy and water has become central worldwide in the academic, governmental and industrial debate over the last 30 years. It is clear that water scarcity will become more and more critical worldwide, and that the increasing energy demand involved by the industrialisation of developing countries will provide a substantial contribution to this phenomena. However, Industry does not make many efforts to reduce freshwater demand, mainly for the low profitability of water optimisation projects, but also for practical issues that the operators may face when pursuing the water optimisation goal in existing factories not originally designed with this target in mind. The rationalisation of freshwater supply to industrial complexes involves the integrated application of different methodologies in the areas of Data Validation and Reconciliation, Pinch Techniques and Optimisation Methods. This study aims at testing the effectiveness of State of the Art methodologies for actual industrial cases to propose solutions to the potential technological gaps and limitations which might hinder their application. To pursue this goal, three practical exercises focused on actual industrial cases have been studied, the first two concerning a retrofit case and the last one a new design case: \u2022 The first exercise covers an existing industrial complex in the food industry (maize milling factory producing starch, sugars and co-products), where the problem of flowrates data reconciliation have been deepened. In this context, the issues related to the lack of measurements and fluctuating water (unavailability of direct analysis of water content in feedstock and product streams) have been addressed. A suitably modified data reconciliation approach, able to fit these specific requirements have been developed. \u2022 The second exercise consists in a Water Pinch Study aimed at targeting the potential freshwater saving in the base case and assuming the Reverse Osmosis treatment of a portion of the streams currently fed to the wastewater treatment facilities. \u2022 The third exercise covers the new design of a Reverse Osmosis Network (RON), where the problem related to the identification of the optimal arrangements of RO modules considering the goals of the treatment, the economics and the specific technical constraints of the system and RO modules have been studied. In this context, a numerical modelling algorithm suitably modified to reach robust and reliable solutions have been developed. The meaningful results obtained during the research activity can be summarized as follows: \u2022 the inclusion of statistical fluctuations in the composition of water in products, obtained by modifying the usual reconciliation algorithms; \u2022 the estimate the water savings obtainable, through the application of a well-established water pinch methodology; \u2022 the identification of the optimal arrangement of a RON (Process Synthesis problem) which involved the use of a modified Simulated Annealing algorithm

The 1st International Electronic Conference on Algorithms

This book presents 22 of the accepted presentations at the 1st International Electronic Conference on Algorithms which was held completely online from September 27 to October 10, 2021. It contains 16 proceeding papers as well as 6 extended abstracts. The works presented in the book cover a wide range of fields dealing with the development of algorithms. Many of contributions are related to machine learning, in particular deep learning. Another main focus among the contributions is on problems dealing with graphs and networks, e.g., in connection with evacuation planning problems

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

Mixed Integer Programming Approaches to Novel Vehicle Routing Problems

This thesis explores two main topics. The first is how to incorporate data on meteorological forecasts, traffic patterns, and road network topology to utilize deicing resources more efficiently. Many municipalities throughout the United States find themselves unable to treat their road networks fully during winter snow events. Further, as the global climate continues to change, it is expected that both the number and severity of extreme winter weather events will increase for large portions of the US.We propose to use network flows, resource allocation, and vehicle routing mixed integer programming approaches to be able to incorporate all of these data in a winter road maintenance framework. We also show that solution approaches which have proved useful in network flows and vehicle routing problems can be adapted to construct high-quality solutions to this new problem quickly. These approaches are validated on both random and real-world instances using data from Knoxville, TN.In addition to showing that these approaches can be used to allocate resources effectively given a certain deicing budget, we also show that these same approaches can be used to help determine a resource budget given some allocation utility score. As before, we validate these approaches using random and real-world instances in Knoxville, TN.The second topic considered is formulating mixed integer programming models which can be used to route automated electric shuttles. We show that these models can also be used to determine fleet composition and optimal vehicle characteristics to accommodate various demand scenarios. We adapt popular vehicle routing solution techniques to these models, showing that these strategies continue to be relevant and robust. Lastly, we validate these techniques by looking at a case study in Greenville, SC, which recently received a grant from the Federal Highway Administration to deploy a fleet of automated electric shuttles in three neighborhoods