Increasing speed scheduling and Flow scheduling

Network flows and scheduling have been studied intensely, but separately. In many applications a joint optimization model for routing and scheduling is desireable. Therefore, we study flows over time with a demand split into jobs. The objective is to minimize the weighted sum of completion times of these jobs. This is closely related to preemptive scheduling on a single machine with a processing speed increasing over time. For both, flow scheduling and increasing speed scheduling, we provide an EPTAS. Without release dates we can proof a tight approximation factor of (sqrt{3}+1)/2 for Smith's rule, by fully characterizing the worst case instances. We give exact algorithms for some special cases and a dynamic program for speed functions with a constant number of speeds. We can proof a competitive ratio of 2 for the online version. We also study the class of blind algorithms, i.e., those which schedule without knowledge of the speed function. For both online, and blind algorithm we provide a lower bound

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Optimization of transportation requirements in the deployment of military units

Cataloged from PDF version of article.We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which no analytical models are existent. In this study, we define the problem in detail and analyze it with respect to the academic literature. We propose three mixed integer programming models with the objectives of cost, lateness (the difference between the arrival time of a unit and its earliest allowable arrival time at its destination), and tardiness (the difference between the arrival time of a unit and its latest arrival time at its destination) minimization to solve the problem. The cost-minimization model minimizes total transportation cost of a deployment and is of use for investment decisions in transportation resources during peacetime and for deployment planning in cases where the operation is not imminent and there is enough time to do deliberate planning that takes costs into account. The lateness and tardiness minimization models are of min-max type and are of use when quick deployment is of utmost concern. The lateness minimization model is for cases when the given fleet of transportation assets is sufficient to deploy units within their allowable time windows and the tardiness minimization model is for cases when the given fleet is not sufficient. We propose a solution methodology for solving all three models. The solution methodology involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branchand-bound. The solution times for intermediate sized problems are around one hour at maximum for cost and lateness minimization models and around two hours for the tardiness minimization model. Producing a suboptimal feasible solution based on trial and error methods for a problem of the same size takes about a week in the current practice in the Turkish Armed Forces. We also propose a heuristic that is essentially based on solving the models incrementally rather than at one step. Computational results show that the heuristic can be used to find good feasible solutions for the models. We conclude the study with comments on how to use the models in the realworld.Akgün, İbrahimPh.D

A MATHEMATICAL FRAMEWORK FOR OPTIMIZING DISASTER RELIEF LOGISTICS

In today's society that disasters seem to be striking all corners of the globe, the importance of emergency management is undeniable. Much human loss and unnecessary destruction of infrastructure can be avoided with better planning and foresight. When a disaster strikes, various aid organizations often face significant problems of transporting large amounts of many different commodities including food, clothing, medicine, medical supplies, machinery, and personnel from several points of origin to a number of destinations in the disaster areas. The transportation of supplies and relief personnel must be done quickly and efficiently to maximize the survival rate of the affected population. The goal of this research is to develop a comprehensive model that describes the integrated logistics operations in response to natural disasters at the operational level. The proposed mathematical model integrates three main components. First, it controls the flow of several relief commodities from sources through the supply chain until they are delivered to the hands of recipients. Second, it considers a large-scale unconventional vehicle routing problem with mixed pickup and delivery schedules for multiple transportation modes. And third, following FEMA's complex logistics structure, a special facility location problem is considered that involves four layers of temporary facilities at the federal and state levels. Such integrated model provides the opportunity for a centralized operation plan that can effectively eliminate delays and assign the limited resources in a way that is optimal for the entire system. The proposed model is a large-scale mixed integer program. To solve the model, two sets of heuristic algorithms are proposed. For solving the multi-echelon facility location problem, four heuristic approaches are proposed. Also four heuristic algorithms are proposed to solve the general integer vehicle routing problem. Overall, the proposed heuristics could efficiently find optimal or near optimal solution in minutes of CPU time where solving the same problems with a commercial solver needed hours of computation time. Numerical case studies and extensive sensitivity analysis are conducted to evaluate the properties of the model and solution algorithms. The numerical analysis indicated the capabilities of the model to handle large-scale relief operations with adequate details. Solution algorithms were tested for several random generated cases and showed robustness in solution quality as well as computation time

Gemischt-autonome Flotten in der urbanen Logistik

We consider a city logistics application in which a service provider seeks a repeatable plan to transport commodities from distribution centers to satellites. The service provider uses a mixed autonomous fleet that is composed of autonomous vehicles and manually operated vehicles. The autonomous vehicles are only able to travel independently on feasible streets of the heterogeneous infrastructure but elsewhere need to be pulled by manually operated vehicles in platoons. We introduce the service network design problem with mixed autonomous fleets to determine a tactical plan that minimizes the total costs over a medium-term time horizon. The tactical plan determines the size and mix of the fleet, schedules transportation services, and decides on the routing or outsourcing of commodities. We model this problem as an integer program on a time-expanded network and study the impact of different problem characteristics on the solutions. To precisely depict the synchronization requirements of the problem, the time-expanded networks need to consider narrow time intervals. Thus, we develop an exact solution approach based on the dynamic discretization discovery scheme that refines partially time-expanded networks containing only a fraction of the nodes and arcs of the fully time-expanded network. Further methodological contributions of this work include the introduction of valid inequalities, two enhancements that exploit linear relaxations, and a heuristic search space restriction. Computational experiments show that all evaluated variants of the solution approach outperform a commercial solver. For transferring a tactical plan to an operational solution that minimizes the transshipment effort on a given day, we present a post-processing technique that specifically assigns commodities to vehicles and vehicles to platoons. Finally, we solve a case study on a real-world based network resembling the city of Braunschweig, Germany. Analyzing the tactical and operational solutions, we assess the value of using a mixed autonomous fleet and derive practical implications.Wir betrachten eine Anwendung der urbanen Logistik, bei der ein Dienstleister einen wiederholbaren Plan für den Gütertransport von Distributionszentren zu Satelliten anstrebt. Dafür setzt der Dienstleister eine gemischt-autonome Flotte ein, die sich aus autonomen Fahrzeugen und manuell gesteuerten Fahrzeugen zusammensetzt. Die autonomen Fahrzeuge können nur auf bestimmten Straßen der heterogenen Infrastruktur selbstständig fahren, außerhalb dieser müssen sie von manuell gesteuerten Fahrzeugen mittels Platooning gezogen werden. Wir führen das „service network design problem with mixed autonomous fleets“ ein, um einen taktischen Plan zu ermitteln, der die Gesamtkosten über einen mittelfristigen Zeithorizont minimiert. Der taktische Plan bestimmt die Größe und Zusammensetzung der Flotte, legt die Transportdienste fest und entscheidet über das Routing oder das Outsourcing von Gütern. Wir modellieren dieses Problem als ganzzahliges Programm auf einem zeiterweiterten Netzwerk und untersuchen die Auswirkungen verschiedener Problemeigenschaften auf die Lösungen. Um die Synchronisationsanforderungen des Problems präzise darzustellen, müssen die zeiterweiterten Netzwerke kleine Zeitintervalle berücksichtigen. Daher entwickeln wir einen exakten Lösungsansatz, der auf dem Schema des „dynamic discretization discovery“ basiert und partiell zeiterweiterte Netzwerke entwickelt, die nur einen Teil der Knoten und Kanten des vollständig zeiterweiterten Netzwerks enthalten. Weitere methodische Beiträge dieser Dissertation umfassen die Einführung von Valid Inequalities, zweier Erweiterungen, die lineare Relaxationen verwenden, und einer heuristischen Suchraumbegrenzung. Experimente zeigen, dass alle evaluierten Varianten des Lösungsansatzes einen kommerziellen Solver übertreffen. Um einen taktischen Plan in eine operative Lösung zu überführen, die die Umladevorgänge an einem bestimmten Tag minimiert, stellen wir eine Post-Processing-Methode vor, mit der Güter zu Fahrzeugen und Fahrzeuge zu Platoons eindeutig zugeordnet werden. Schließlich lösen wir eine Fallstudie auf einem realitätsnahen Netzwerk, das der Stadt Braunschweig nachempfunden ist. Anhand der taktischen und operativen Lösungen bewerten wir den Nutzen einer gemischt-autonomen Flotte und leiten Implikationen für die Praxis ab

Freight transport industry in New Zealand

This paper focuses on the domestic freight industry in New Zealand. It reviews the geographical basis and historical development of freight transport. The supply and demand factors of the freight industry are then discussed. The individual rail, road, coastal shipping, and domestic air modes are also reviewed. Competition between these modes is covered. The paper concludes with an overview of some of the major policy issues facing the freight transport industry in New Zealand. These policy issues relate to the environment, safety, road pricing, marine transport taxation and labour relations

Selfish versus coordinated routing in network games

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 159-170) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems. More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion.(cont.) As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm. In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.by Nicolás E. Stier-Moses.Ph.D

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Multi-Period Natural Gas Market Modeling - Applications, Stochastic Extensions and Solution Approaches

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in shorter solution times relative to solving the extensive-forms. Larger problems, up to 117,481 variables, were solved in extensive-form, but not when applying BD due to numerical issues. It is discussed how BD could significantly reduce the solution time of large-scale stochastic models, but various challenges remain and more research is needed to assess the potential of Benders decomposition for solving large-scale stochastic MCP