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Many operations in daily life, from manufacturing to running a hospital, need to optimise the return on use of resources where volume and value are conditions. Scheduling theory tackles some of the hardest practical optimisation problems, not known to be solvable in reasonable computation time. Strusevich and Kellerer have been able to reformulate practical scheduling challenges as `knapsack problems' - dealing with volume and value constraints - and then design approximation algorithms which can be applied back to the original challenge. The work has attracted EPSRC funding, stimulated a new field of research which is developing fast, been widely published, led to presentations at international conferences including the 2009 Computers and Industrial Engineering conference attended by industry practitioners and is impacting on Combinatorial Optimisation research.
Poor staff rosters are at the heart of socially-unacceptable working patterns, inadequate rest times and increased levels of stress. They lead to poor productivity, low levels of engagement and additional costs associated with high levels of staff turnover and absenteeism. Research undertaken at City University London has harnessed the power of `Optimisation' techniques to assist managers to draw up good quality staff rosters in hospitals, call centres and other large workforce organisations. The state-of-the-art electronic rostering programme improves use of resources, reduces reliance on costly agency staff, reduces the risk of fines for breaching legal requirements such as the European Working Time Directive and leads to significant savings in the health and social care sectors.
Professor Wright has developed practical scheduling implementations for sports fixtures and officials, with regular clients at both professional and amateur level in the UK and abroad, including the England and Wales Cricket Board and the New Zealand Rugby Union. His expertise also supports `what if' exercises, enabling clients to experiment with new ideas and announce changes with confidence that they will work in practice. His work has resulted in financial gains, substantial savings in skilled administrative time and high satisfaction for stakeholders. His research has potential reach across numerous sports, at all levels across the world.
Research on designing mathematical methods for optimisation carried out at the University of Southampton has been fundamental to the development of software solutions for transportation problems and has directly led to the growth and commercial success of the niche software company, Logical Transport. Additional beneficiaries are local councils — who have obtained school bus schedules that typically reduced the number of required vehicles by 10-20% and miles driven by 12-15% and have an information management tool for better decision making — and passengers who have experienced improved service quality.
Research by Gondzio (Maxwell Institute) on algorithms for large-scale optimization has led to major advances in the design of interior point methods (IPMs). The advances include new ways of exploiting centrality (1996-2008) as well as special preconditioning (2004) and warmstarting (2003, 2008) techniques. These techniques make it possible to solve more difficult optimization problems more quickly. Some of these have been implemented by all major commercial providers of optimization software including IBM, Gurobi, Mosek and FICO. The techniques have therefore had an economic impact on these companies and on thousands of their customers worldwide who now benefit from faster, more reliable methods to solve their challenging optimization tasks.
Transport crew scheduling research at Leeds University since 1994 produced optimising algorithms and industry-ready software that led to the spinning out of Tracsis in 2004. The software, including upgrades, is used by over 40 bus and train companies who previously relied on manual processes. A minimum estimate of a £230 million saving in crew costs has been achieved in the UK alone over 2008-31.7.2013. Since 2008, the software has been routinely used by bidders in all UK rail franchise tenders, contributing to cost effective, efficient and reliable rail transport. Success led to the Tracsis floatation in November 2007 (market capitalisation: £46.7 million on 22/5/2013).
This case study demonstrates the benefits achieved when the mathematical and computational aspects of a computational fluid dynamics (CFD) problem were brought together to work on real-world aerodynamic applications. While earlier insight on the solution reconstruction problem was purely based on empirical intuition, research in the School of Mathematics at the University of Birmingham by Dr Natalia Petrovskaya has resulted in the development of the necessary synthetic judgement in which the importance of accurate reconstruction on unstructured grids has been fully recognised by the CFD researchers at the Boeing Company. Boeing has confirmed that the research has led to substantial resultant improvements in their products as well as gains in engineering productivity. For instance, wing body fairing and winglets optimization for the Boeing 787 has been done by means of CFD only. Implementation of CFD in the design of their new aircraft allowed Boeing to reduce the testing time in the wind tunnel for the 787 aircraft by 30% in comparison with testing carried out for Boeing 777. Efficient use of CFD in the design of new aircrafts has helped the Boeing Company to further strengthen their core operations, improve their execution and competitiveness and leverage their international advantage.
Short Term Conflict Alert systems are used by NATS to alert air traffic controllers to the risk of aircraft becoming dangerously close. This research has provided the means to enhance international air traffic safety by automatically optimising STCA systems so as to simultaneously maximise the number of alerts raised in response to truly dangerous situations, while, at the same time, minimising the number of false alerts. This has been achieved by developing multi-objective evolutionary algorithms to automatically locate the Pareto front describing the optimal trade-off between the numbers of true and false positives. The optimiser is described by NATS as "an outstanding improvement to our safety" [KTP-1395, final report].
Inverse kinematics mathematics developed at Surrey for satellite control is being commercialised for motion capture, film animation and for real-time animation in computer games through IKinema, a University of Surrey spin-out company. Ikinema is the most advanced full-body IK solver and has been used in films such as X-men First Class and Wrath of the Titans 2; it is embedded in Luxology's modo-601, and is used by major film studios including 20th Century Fox, Disney, Lucas Film, ILM, and visual effects specialists and game developers such as Framestore, Square Enix, and AudioMotion. IKinema currently employs 6 staff and is profitable, with 80% of sales revenues generated by export.
Novel numerical limit analysis methods developed in the Department of Civil and Structural Engineering have been embedded in commercial software developed by spin-out company LimitState (http://www.limitstate.com). The software is now used by over 100 industrial organisations in more than 30 countries.
The software can model real-world problems far more quickly (up to 50 times faster) than was previously possible, bringing significant productivity and economic benefits to practitioners and their clients, e.g.: