Trustworthy and insightful algorithms for industrial decision making

Some of the most critical decision-making challenges in industry take the form of mathematical optimisation problems, which seek to efficiently determine optimal decisions from a huge number of choices.

Often these problems have difficult and conflicting constraints that make even finding an acceptable solution challenging, let alone a provably optimal one. Complicating matters further, there are often several conflicting goals that must be considered to trade-off or balance economic, social and environmental outcomes.

Efficient algorithms for complex personnel scheduling problems are critical for ensuring organisations can provide a suitably qualified workforce at minimal cost while satisfying a wide variety of strict regulations meeting occupational health and safety requirements, as well as employee preferences. Likewise, efficient algorithms for complex logistics and transportation problems, such as optimal packing of container ships and delivery vehicles, are also critical to ensure supply chain efficiencies.

This research project will focus on two particular instances of these critical industrial optimisation problems:

• nurse rostering, where nurses must be optimally allocated to work shifts in a manner that ensures their specialised expertise is available when required to support scheduled surgeries and other activities, while satisfying rules about shift lengths, leave days, and accommodating as much as possible their individual preferences.
• cutting and packing, where raw materials must be optimally cut to form manufacturing components with minimal wastage and minimal energy use from cutting, and the related problem of optimal packing of items of different sizes and shapes into a container to maximise the value of packed goods.

Industry needs support from academic experts in optimisation to cast their industrial decision-making challenges onto a mathematical optimisation framework and to access state-of-the-art optimisation technologies in the form of mathematical models and algorithms to find optimal solutions. However, it is critically important that the algorithms developed for one industry partner’s problem are rigorously stress-tested to:

1. Establish the bounds of trust
2. Understand robustness under future uncertainty
3. Understand strengths and weaknesses of an algorithm under various conditions
4. Gain insights into new algorithm ideas suited to particular conditions

By rigorously stress-testing any algorithm, well beyond showing trust and reliability on the initial motivating industrial case study, there is an opportunity to develop innovative algorithms that generalise well to suit a broader range of industry partners and to achieve further impact

The University of Melbourne has strong expertise in tackling related scheduling problems but will benefit enormously from the specific expertise of the KU Leuven team developed over several decades in advancing models and algorithms for nurse rostering and cutting and packing problems.

The partnership will enable new collaborative links with Melbourne based hospitals to be forged to support this project, via the new ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications (OPTIMA).

The KU Leuven team will also benefit from the application of the University of Melbourne’s Instance Space Analysis methodology to gain deep insights into the strengths and weaknesses of nurse rostering and cutting and packing algorithms, and ensure that the project’s newly developed algorithmic advances are rigorously “stress-tested” to understand their robustness and reliability for a wide range of hospital industrial settings in both Australia and Belgium.