Integer programming based solution approaches for the train dispatching problem

Railroads face the challenge of competing with the trucking industry in a fastpaced environment. In this respect, they are working toward running freight trains on schedule and reducing travel times. The planned train schedules consist of departure and arrival times at main stations on the rail network. A detailed timetable, on the other hand, consists of the departure and arrival times of each train in each track section of its route. The train dispatching problem aims to determine detailed timetables over a rail network in order to minimize deviations from the planned schedule. We provide a new integer programming formulation for this problem based on a spacetime network; we propose heuristic algorithms to solve it and present computational results of these algorithms. Our approach includes some realistic constraints that have not been previously considered as well as all the assumptions and practical issues considered by the earlier works

Exact and Heuristic Methods for the Weapon Target Assignment Problem

The Weapon Target Assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimum. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There do not exist any exact methods for the WTA problem which can solve even small size problems (for example, with 20 weapons and 20 targets). Though several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem. We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms which indicate that we can solve moderately large size instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few second

Network Flows

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Faster algorithms for the shortest path problem

We investigate efficient implementations of Dijkstra\u27s shortest path algorithm. We propose a new data structure, called the redistributive heap, for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C, a one-level form of redistributive heap gives a time bound for Dijkstra\u27s algorithm of O(m + nlogC). A two-level form of redistributive heap gives a bound of O(m + nlogC/loglogC). A combination of a redistributive heap and a previously known data structure called a Fibonacci heap gives a bound of O(m+ nsqrt{log C}). The best previously known bounds are O(m + nlogn) using Fibonacci heaps alone and O(mloglogC) using the priority queue structure of Van Emde Boas, Kaas, and Zijlstra

Some Recent Advances in Network Flows

The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of activity on the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several techniques have proven to be very successful in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of algorithms, especially amortized average case performance and the use of potential functions; and (iii) enhanced data structures. In this survey, we illustrate some of these techniques and their usefulness in developing faster network flow algorithms. Our discussion focuses on the design of faster algorithms from the worst case perspective and we limit our discussion to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. We consider several representative algorithms from each problem class including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem

Behavioural disorders amongst children of a rural community of Lucknow, India

Background: Behavioural disturbances are notable child health problem, the importance of which is increasingly recognized in most countries. A behaviour problem is nothing but a deviation from the accepted pattern of behavior on the part of the child when he is exposed to an inconsistent social and cultural environment. Aims & Objectives: To assess the prevalence of behavioural disorders in children of a rural community. Material & Methods: This was a village based cross-sectional study done among the children for the assessing the behavioural disorders. Results: Of the total 1157 children studied, 195 (16.9%) showed one or the other behavioural disorders. Various disorders elicited were bed wetting (11.6%), thumb sucking (3.1%), nail biting (1.6%) and food fad (0.5%). The disorders were more common in preschool children (34.2%) compared to school going age children (11.0%). Behavioural disorders were more frequent in children at extremes of birth orders (birth orders I & V) compared to others. The prevalence of disorders did not differ much in boys (16.2%) and girls (17.6%). Conclusions: The present study has reported a relatively higher prevalence of behavior disorders (16.9%) in children in a rural setting. The pattern of behavior problems was studied in terms of age, sex and birth order. In such children, there is a need for health education and counseling by psychiatrist/psychiatric social worker at the primary care level and must be worked ou

Structure and function in flow networks

Peer reviewedPublisher PD

A grounded theory study of the narrative behind Indian physiotherapists global migration

It is estimated that an additional 6.4 million allied health professionals are required to address India's health challenges. Physiotherapy is amongst the largest of these professions. Over the last decade, thousands of Indian physiotherapists have sought to study and work overseas. In this study, 19 physiotherapists from across India were interviewed. Data were collected and analysed using construct+ivist grounded theory methods. The findings indicate that the Indian physiotherapy profession faces many political and clinical hierarchical challenges within the Indian healthcare infrastructure. The profession's education provision has developed, and the private clinical sector has grown, but there are significant disparities in quality and standards across the sector. The profession in India has variable autonomy, is not nationally regulated, is poorly paid, and the leadership has been divided. The political, educational, and clinical context in Indian physiotherapy impacts upon physiotherapists' ability to practise effectively to their professional satisfaction. Individual physiotherapists are frustrated by their workplace and travel overseas where they hear that the physiotherapy profession and practice is different. Whilst the disjunctures influencing these factors continue, and overseas physiotherapy practice is perceived as different and superior, Indian physiotherapists will continue to seek to migrate overseas, and facilitating their return will be challenging

Competitive Equilibrium and Trading Networks: A Network Flow Approach

Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks, and is equivalent (after a restriction to equilibrium trades) to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient outcome as a generalized submodular flow problem on a suitable network. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability