Accelerating Benders' Decomposition: Algorithmic Enhancements and Model Selection Criteria

Not AvailableThis research was supported by the U.S. Department of Transportation under Contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs

Changeover costs (and times) are central to numerous manufacturing operations. These costs arise whenever work centers capable of processing only one product at a time switch from the manufacture of one product to another. Although many researchers have contributed to the solution of scheduling problems that include changeover costs, due to the problem's combinatorial explosiveness, optimization-based methods have met with limited success. In this paper, we develop and apply polyhedral methods from integer programming for a dynamic version of the problem. Computational tests with problems containing one to five products (and up to 225 integer variables) show that polyhedral methods based upon a set of facet inequalities developed in this paper can effectively reduce the gap between the value of an integer program formulation of the problem and its linear programming relaxation (by a factor of 94 to 100 per cent). These results suggest the use of a combined cutting plane/branch and bound procedure as a solution approach. In a test with a five product problem, this procedure, when compared with a standard linear programming-based branch and bound approach, reduced computation time by a factor of seven

A Dual Ascent Procedure for Large Scale Uncapacitated Network Design

The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling.We develop a family of dual ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location,Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints shows that the dual ascent procedure and an associated drop-add heuristic generates solutions that, in almost all cases, are guaranteed to be within 1 to 3 percent of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks,including some models arising in freight transport

On the Price of Anarchy for flows over time

Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is exactly e/(e − 1) ≈ 1.582. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow to determine that the Price of Anarchy in parallel-link networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly e/(e − 1)

Изучение структуры цинктитановых боросиликатных стекол по данным рассеяния рентгеновских лучей под малыми углами

В статті вивчено мікронеоднорідну будову цинктитанових боросилікатних стекол та процесів фазового розділу в них за даним розсіяння нейтронів під малими кутами. Зроблено висновок про характер розподілення часток, що виділяються за розмірами, які змінюються в дослідних стеклах в залежності від вмісту в них TiO₂ та ZnO. Встановлено вплив наявності мікронеоднорідностей після варки на характер їх фазовогорозподілення.In paper the micronon-uniform structure zinc-titanium borosilicate glass and processes of phase separation in them according to diffusing under vanishing angles of neutrons is investigated. It is drawn a In paper the micronon-uniform structure zinc-titanium borosilicate glass and processes of phase separation in them according to diffusing under vanishing angles of neutrons is investigated. It is drawn a leading-out on distribution of depositing corpuscles character on sizes which changes in studied glasses depending on the contents in them TiO₂ and ZnO. Effect of presence micro micronon-uniforms after melting on character of their phase separationis established

Enabling the freight traffic controller for collaborative multi-drop urban logistics: practical and theoretical challenges

There is increasing interest in how horizontal collaboration between parcel carriers might help alleviate problems associated with last-mile logistics in congested urban centers. Through a detailed review of the literature on parcel logistics pertaining to collaboration, along with practical insights from carriers operating in the United Kingdom, this paper examines the challenges that will be faced in optimizing multicarrier, multidrop collection, and delivery schedules. A “freight traffic controller” (FTC) concept is proposed. The FTC would be a trusted third party, assigned to equitably manage the work allocation between collaborating carriers and the passage of vehicles over the last mile when joint benefits to the parties could be achieved. Creating this FTC concept required a combinatorial optimization approach for evaluation of the many combinations of hub locations, network configuration, and routing options for vehicle or walking to find the true value of each potential collaboration. At the same time, the traffic, social, and environmental impacts of these activities had to be considered. Cooperative game theory is a way to investigate the formation of collaborations (or coalitions), and the analysis used in this study identified a significant shortfall in current applications of this theory to last-mile parcel logistics. Application of theory to urban freight logistics has, thus far, failed to account for critical concerns including (a) the mismatch of vehicle parking locations relative to actual delivery addresses; (b) the combination of deliveries with collections, requests for the latter often being received in real time during the round; and (c) the variability in travel times and route options attributable to traffic and road network conditions

Incidence and survival of childhood bone cancer in northern England and the West Midlands, 1981–2002

There is a paucity of population-based studies examining incidence and survival trends in childhood bone tumours. We used high quality data from four population-based registries in England. Incidence patterns and trends were described using Poisson regression. Survival trends were analysed using Cox regression. There were 374 cases of childhood (ages 0–14 years) bone tumours (206 osteosarcomas, 144 Ewing sarcomas, 16 chondrosarcomas, 8 other bone tumours) registered in the period 1981–2002. Overall incidence (per million person years) rates were 2.63 (95% confidence interval (CI) 2.27–2.99) for osteosarcoma, 1.90 (1.58–2.21) for Ewing sarcoma and 0.21 (0.11–0.31) for chondrosarcoma. Incidence of Ewing sarcoma declined at an average rate of 3.1% (95% CI 0.6–5.6) per annum (P=0.04), which may be due to tumour reclassification, but there was no change in osteosarcoma incidence. Survival showed marked improvement over the 20 years (1981–2000) for Ewing sarcoma (hazard ratio (HR) per annum=0.95 95% CI 0.91–0.99; P=0.02). However, no improvement was seen for osteosarcoma patients (HR per annum=1.02 95% CI 0.98–1.05; P=0.35) over this time period. Reasons for failure to improve survival including potential delays in diagnosis, accrual to trials, adherence to therapy and lack of improvement in treatment strategies all need to be considered