Andreas T. Ernst
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Matheuristics for Synchromodal Logistics
Potential Student Projects

Mine Planning Optimisation

Project Outline: Exploiting and ore body requires extracting the available resource over many years. A good plan for the order in which the resource is to be extracted can have a major impact on the profitabil;ity of a mining project. Typically the ore body is discretised into blocks, so that the aim of creating a good mine plan can be formulated as a very large scale optimisation problem. In this project alterantive integer prgoramming formulations and algorithms will be explored to make this large scale problem tractable. A promising direction for research is iterative aggregation and diaggregation methods that attempt to dynamically adjust the level of detail used in the optimisation.

 

Pre-Requisites: Basic knowledge in programming is essential, knowledge of Linear Programming, scheduling, and heuristic algorithms is highly desirable.

 

References:

The value of this to mining companies can be seen in the recent Phase-X challenge sponsored by BHP with $50,000 in prize money.

For more information on the basic problem see Minelib: http://mansci-web.uai.cl/minelib/
For an example of the effectiveness of iterative disaggregation see:

A Nazari, A Ernst, S Dunstall, B Bryan, J Connor, M Nolan and F Stock. Combined Aggregation and Column Generation for Land-Use Trade-Off Optimisation (2015), IFIP Advances in ICT vol 48, pp 455-466

 

Rostering staff with consideration of fatigue implications

Project Outline: Many organisations have to provide services around the clock and hence roster staff to work at all hours of the day. This can have significant impact on the level of fatigue. The resulting reduction in alertness can have significant implications particularly in health care and emergency services. This project will look at optimisation models and algorithms to generate rosters that are likely to reduce fatigue.

Some real world data is available to allow the student to work with realistic instances of such rostering problems. The project will involve looking at possible models for the fatigue implications of rosters and then develop optimisation methods to generate rosters that are better from this human perspective.

 

Pre-Requisites: Basic knowledge in programming is desirable, knowledge of Linear Programming, scheduling, heuristic algorithms is helpful but not essential

 

References:

Ernst, A. T., Jiang, H., Krishnamoorthy, M. & Sier, D. Staff scheduling and rostering: A review of applications, methods and models. European journal of operational research 153, 3–27 (2004).

Lodree Jr., E. J., Geiger, C. D. & Jiang, X. Taxonomy for integrating scheduling theory and human factors: Review and research opportunities. International Journal of Industrial Ergonomics 39, 39–51 (2009).

 

 

Lagrangian relaxation based decompositions of arbitrary integer programs

Project Outline: Lagrangian relaxation is a technique for removing “difficult” constraints in mathematical programs so that the problem decomposes into smaller subproblems or to ensure the remaining problem has a special structure that can be solved more efficiently. There are often multiple choices for mixed integer linear programs (MIP) of which constraints to relax and how to decompose the problem. This project will look at how to automate this process for arbitrary MIPs.

The decomposition can be shown to be equivalent to a k-partitioning in a hypergraph. Such problems are not easy to solve and this is only a pre-processing step for the computationally demanding task of solving the MIP. Hence efficient heuristic methods for this decomposition are essential. This project will develop a heurist method for this decomposition and evaluate the effectiveness of this approach in obtaining Lagrangian bounds.

 

Pre-Requisites: Basic knowledge in programming is essential, knowledge of Linear Programming, heuristics or graph theory is helpful but not essential.

 

References:

Bergner, M. , A. Caprara, A. Ceselli, F. Furini, M. E. Lübbecke, E. Malaguti, and E. Traversi. Automatic Dantzig–Wolfe reformulation of mixed integer programs. Math. Program. 149, 391–424 (2014).