# Allocating Students to Industry Placements Using Integer Programming and Ant Colony Optimisation
## 1 Introduction  
There is an increasing emphasis on _Work Integrated Learning_ (WIL) in universities and other tertiary education providers [1] As a result, the number of students undertaking WIL is growing rapidly, and the need to effectively manage the processes involved is increasingly important. The Australian National Strategy of Work Integrated Learning ([[http://cdn1.acen.edu.au/wp-content/uploads/2015/03/National-WIL-Strategy-in-university-education-032015.pdf](http://cdn1.acen.edu.au/wp-content/uploads/2015/03/National-WIL-Strategy-in-university-education-032015.pdf)]([http://cdn1.acen.edu.au/wp-content/uploads/2015/03/National-WIL-Strategy-in-university-education-032015.pdf](http://cdn1.acen.edu.au/wp-content/uploads/2015/03/National-WIL-Strategy-in-university-education-032015.pdf)), accessed 21 July 2021) proposes actions in eight key areas, including: (1) developing university resources, processes and systems to grow WIL and engage business and community partners and (2) addressing equity and access issues to enable students to participate in WIL. The problem of allocating students to industry placements is of significant interest. Several factors need to be considered in order to achieve an acceptable allocation. In particular, we consider the Industry Based Learning (IBL) allocation problem where students are allocated to industry placements. The aim is to provide an excellent educational experience to students whilst maximising industry partner satisfaction (and thus engagement). In addition, the allocation aims to provide gender diversity within placements and ensures that students allocated consecutive placements experience a diversity of sectors. Constraintsarising from inclusive practices are increasingly important. For example, ref. [2] discusses this in the context of resettlement of refugees and comments that 'the remaining question is how to design mechanisms that cater to diversity objectives while still satisfying desirable properties'. We have considered real problem instances, but it is notable that the number of student placements have been increasing overtime. Moreover, in certain university departments (e.g., nursing), the number of placements to be filled can involve a very large number of students and placements (\(>\)2000). A recent survey [3] of the placement of students in nurse practitioner programs in the United States found that only 12% of facilities used electronic means for placing students. They comment that 'an investment in these platforms could reduce faculty time for securing clinical placements'. Discussing a related problem of assigning students to medical schools, ref. [4] investigate the need to improve efficiency and reduce costs while ensuring that the pairing of students to medical schools is fair and ensures that students are allocated to suitable schools. Integer programming (IP) is an effective approach to solving optimisation problems [5]. The IBL problem is one that can be modeled effectively as an IP, particularly because the underlying structure is that of the assignment or bi-partite matching problem [6], which can be solved efficiently by commercial solvers. It is known that a linear assignment problem (LAP) can be solved in a polynomial time, and an IP problem is categorised as an NP-complete problem from a complexity point of view [7]. However, when problem instances are large and consist of a very large number of variables and/or complicating constraints, the IP can struggle to find feasible solutions, let alone prove optimality. In such cases, meta-heuristics [8] provide an alternative way of generating good solutions in reasonable time-frames (note that metaheuristics on their own have limitations; in particular, they cannot provide guarantees of solutions they find and they often struggle with problems which consist of nontrivial hard constraints) and in this study ant colony optimisation (ACO) [9] is the meta-heuristic of choice.