Pup Matching: Model Formulations and Solution Approaches

We model Pup Matching, the logistics problem of matching or pairing semitrailers known as pups to cabs that are able to tow one or two of the pups simultaneously, as an AfP-complete version of the Network Loading Problem (NLP). We examine a branch and bound solution approach tailored to the NLP formulation through the use of three families of cutting planes and four heuristic procedures. Theoretically, we specify facet defining conditions for a cut family that we refer to as odd flow inequalities and show that each heuristic yields a 2-approximation. Computationally, the cheapest of the four heuristic values achieved an average error of 1.3% among solved test problems randomly generated from realistic data. Branch and bound solved to optimality 67% of these problems. Application of the cutting plane families reduced the average relative difference between upper and lower bounds prior to branching from 18.8% to 6.4%

Valid Inequalities and Facets of the Capacitated Plant Location Problem

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems.In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure.The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope

Routing in Point-to-Point Delivery Systems

This paper was also printed as a Working Paper at the Yale School of Organization and Management, Series B, No. 103.We develop an optimization-based approach for a point-to-point route planning problem that arises in many large scale delivery systems(for example, less-than-truckload freight, rail, mail and package delivery, communications). In these settings, a firm which must ship goods between many origin and destination pairs on a network needs to specify a route for each origin-destination pair so as to minimize transportation costs and/or transit times. Typically, the cost structure is very complicated. The approach discussed in this paper exploits the structure of the problem to decompose it into two smaller subproblems, each amenable to solution by a combination of optimization and heuristic techniques. One subproblem is an 'assignment' problem with capacity constraints. The other subproblem is a mixed-integer multicommodity flow problem. We propose solution methods based on Lagrangian relaxation for each subproblem. Computational results with these methods and with a heuristic procedure for the multicommodity flow problem on a problem met in practice are encouraging and suggest that mathematical programming methods can be successfully applied to large-scale problems in delivery systems planning and other problems in logistical system design

Facets and Algorithms for Capacitated Lot Sizing

The dynamic economic lot sizing model, which lies at the core of numerous production planning applications, is one of the most highly studied models in all of operations research. And yet, capacitated multi-item versions of this problem remain computationally elusive. We study the polyhedral structure of an integer programming formulation of a single-item capacitated version of this problem, and use these results to develop solution methods for multi-item applications. In particular, we introduce a set of valid inequalities for the problem and show that they define facets of the underlying integer programming polyhedron. Computational results on several single and multiple product examples show that these inequalities can be used quite effectively to develop an efficient cutting plane/branch and bound procedure. Moreover, our results show that in many instances adding certain of these inequalities a priori to the problem formulation, and avoiding the generation of cutting planes, can be equally effective

Sex-specific incidence and temporal trends in solid tumours in young people from Northern England, 1968–2005

<p>Abstract</p> <p>Background</p> <p>This study examined sex-specific patterns and temporal trends in the incidence of solid tumours in the Northern Region of England from 1968 to 2005. This updates earlier analyses from the region where sex was not considered in depth. Sex-specific analyses were carried out to determine whether sex differences might provide clues to aetiology.</p> <p>Methods</p> <p>Details of 3576 cases, aged 0–24 years, were obtained from a specialist population-based cancer registry. There were 1843 males (886 aged 0–14 years and 957 aged 15–24 years) and 1733 females (791 aged 0–14 years and 942 aged 15–24 years). Age-standardized incidence rates (per million population) were calculated. Linear regression was used to analyze temporal trends in incidence and annual percentage changes were estimated. Analyses were stratified by sex and by age-group.</p> <p>Results</p> <p>There were marked differences in incidence patterns and trends between males and females and also between age-groups. For males central nervous system (CNS) tumours formed the largest proportion of under-15 cases and germ cell tumours was the largest group in the 15–24's, whilst for females CNS tumours dominated in the under-15's and carcinomas in the older group. For 0–14 year olds there were male-specific increases in the incidence of rhabdomyosarcoma (2.4% per annum; 95% CI: 0.2%–4.5%) and non-melanotic skin cancer (9.6%; 95% CI: 0.0%–19.2%) and female-specific increases for sympathetic nervous system tumours (2.2%; 95% CI: 0.4%–3.9%), gonadal germ cell tumours (8.6%; 95% CI: 4.3%–12.9%) and non-gonadal germ cell tumours (5.4%; 95% CI: 2.8%–7.9%). For 15–24 year olds, there were male-specific increases in gonadal germ cell tumours (1.9%; 95% CI: 0.3%–3.4%), non-gonadal germ cell tumours (4.4%; 95% CI: 1.1%–7.7%) and non-melanotic skin cancer (4.7%; 95% CI: 0.5%–8.9%) and female-specific increases for osteosarcoma (3.5%; 95% CI: 0.5%–6.5%), thyroid cancer (2.8%; 95% CI: 0.1%–5.6%) and melanoma (4.6%; 95% CI: 2.2%–7.1%).</p> <p>Conclusion</p> <p>This study has highlighted notable differences between the sexes in incidence patterns and trends for solid tumours. Some of these sex-specific differences could have been obscured if males and females had been analysed together. Furthermore, they suggest aetiological differences or differential susceptibility to environmental factors between males and females.</p

Minimizing the stabbing number of matchings, trees, and triangulations

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the original 30 outstanding open problems in computational geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide is negative for a number of minimum stabbing problems by showing them NP-hard by means of a general proof technique. It implies non-trivial lower bounds on the approximability. On the positive side we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. We obtain lower bounds (in polynomial time) from the corresponding linear programming relaxations, and show that an optimal fractional solution always contains an edge of at least constant weight. This result constitutes a crucial step towards a constant-factor approximation via an iterated rounding scheme. In computational experiments we demonstrate that our approach allows for actually solving problems with up to several hundred points optimally or near-optimally.Comment: 25 pages, 12 figures, Latex. To appear in "Discrete and Computational Geometry". Previous version (extended abstract) appears in SODA 2004, pp. 430-43

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

Waste processing facility location problem by stochastic programming: Models and solutions

The paper deals with the so-called waste processing facility location problem (FLP), which asks for establishing a set of operational waste processing units, optimal against the total expected cost. We minimize the waste management (WM) expenditure of the waste producers, which is derived from the related waste processing, transportation, and investment costs. We use a stochastic programming approach in recognition of the inherent uncertainties in this area. Two relevant models are presented and discussed in the paper. Initially, we extend the common transportation network flow model with on-and-off waste-processing capacities in selected nodes, representing the facility location. Subsequently, we model the randomly-varying production of waste by a scenario-based two-stage stochastic integer linear program. Finally, we employ selected pricing ideas from revenue management to model the behavior of the waste producers, who we assume to be environmentally friendly. The modeling ideas are illustrated on an example of limited size solved in GAMS. Computations on larger instances were realized with traditional and heuristic algorithms, implemented within MATLAB. © Springer Nature Switzerland AG 2019

Registration of cancer in girls remains lower than expected in countries with low/middle incomes and low female education rates.

BACKGROUND: A decade ago it was reported that childhood cancer incidence was higher in boys than girls in many countries, particularly those with low gross domestic product (GDP) and high infant mortality rate. Research suggests that socio-economic and cultural factors are likely to be responsible. This study aimed to investigate the association between cancer registration rate sex ratios and economic, social and healthcare-related factors using recent data (1998-2002). METHODS: For 62 countries, childhood (0-15 years) cancer registration rate sex ratios were calculated from Cancer Incidence in Five Continents Vol IX, and economic, social and healthcare indicator data were collated. RESULTS: Increased age standardised cancer registration rate sex ratio (M:F) was significantly associated with decreasing life expectancy (P=0.05), physician density (P=0.05), per capita health expenditure (P=0.05), GDP (P=0.01), education sex ratios (primary school enrolment sex ratio (P<0.01); secondary school enrolment sex ratio (P<0.01); adult literacy sex ratio (P<0.01)) and increasing proportion living on less than Int$1 per day (P=0.03). CONCLUSION: The previously described cancer registration sex disparity remains, particularly, in countries with poor health system indicators and low female education rates. We suggest that girls with cancer continue to go undiagnosed and that incidence data, particularly in low- and middle-income countries, should continue to be interpreted with caution