Operations Research Group: Research

THEORY AND METHODOLOGY

Composite Concave Optimization [Sniedovich]
Development of optimization methods and algorithms based on successive first-order linearization of composite concave functions. The methodology unifies a number of well known classes of problems such as fractional, multiplicative and DC programming problems and outlines new approaches to hyper sensitivity analysis and soft constraints.

Dynamic Programming [Sniedovich]
Investigation of theoretical and computational aspects of dynamic programming and its relation to other optimization methods in particular branch and bound and.constraint logic programming. Also, sensitivity analysis of multistage and sequential decision processes.

Integer Programming [Boland; Davey, Mak, Merlot]
Modelling, and development of theory and algorithms for optimization problems in which some, or all, variables must be integral. Techniques applied include cutting planes, branch-and-bound, decomposition and column generation. Problems under investigation include facility location, telecommunications network design, and airline planning.

Interactive Computing and Modelling [Sniedovich]
Investigation of methods, techniques and technologies for building interactive OR models, including the use of machine executable mathematical notation in formulating, modelling and analysis of operations research problems and interactive OR modelling on the Internet.

Multiobjective and Nonsmooth Optimization [Sniedovich]
Investigation of optimization problems where several conflicting objectives must be balanced, or where complicated (nondifferentiable) functions occur in the model. Theoretical questions (describing the optima), and computational algorithms are being studied. Applications include economic models.

APPLICATION AREAS

Airline planning problems [Boland; Mak]:
Schedule crew, determine the aircraft type that should be flown on each leg, and sequence aircraft movements to improve passenger convenience while ensuring maintenance restrictions are met.

Classroom scheduling and timetabling [Boland; Merlot]:
Assign courses to time slots and classrooms so that classroom sizes are appropriate and clashes between courses being taken by the same student are minimised.

Coal mining [Boland, Sniedovich]:
Modelling the dragline operation in open cut coal mining, and writing algorithms and software to compute the fastest schedule for a dragline.

Facility location [Boland]:
Address where facilities should be located so as to achieve the best trade-off between establishment costs and the cost of serving clients or regions.

Inventory control [Sniedovich]:
modelling, analysis and solution of reliability constrained stochastic inventory systems, including reliability constraints and capacity expansion issues.

Interactive Web Pages [Sniedovich]: development of interactive WWW pages using JavaScript, including educational software.

Machine scheduling [Mak]: scheduling of machinery to minimise production time and/or production cost while meeting job completion deadlines and satisfying a variety of other constraints.

Manpower planning [Boland]: set rosters so that every task has a qualified employee assigned to perform the task, so that employees' daily schedules have attributes desired by employees and so that overtime is minimised.

Telecommunications network design [Boland]: determine the most profitable link capacities and tariffs.

Water resources Planning [Sniedovich]:
Modelling, analysis and solution of water resources systems, including reliability constraints and capacity expansion issues.

© The University of Melbourne 1994-2002.
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Created: 1 June 2002
Last modified: 7 June 2002
Authorised by: Moshe Sniedovich, Department of Mathematics and Statistics.