A numerical unhappiness function for allocating cadet engineers to placement positions

All Australian engineering degree programs require students to have exposure to professional practice prior to graduation. At CSU Engineering, this takes the form of a compulsory sequence of four year-long paid cadet placements. The process of ensuring that all cadets are successfully matched with a host organisation (host) has significant complexity due to the diversity of types and locations of hosts, the discipline mix of placements and cadets’ preferences and constraints. The management of ongoing partnerships with the hosts must be balanced with the ability of cadets to proactively and independently seek their own placements. An equitable and fair method of matching cadets to the hosts is required for ethical operation of the placement program.
Purpose: This paper presents the numerical “unhappiness function” that is used to determine the allocation of cadets to placement positions through a competitive marketplace process.
Approach: The competitive marketplace approach attempts to mirror an authentic recruitment process, but the constraints of having to finalise allocations in a timely manner means that compromises are required. The introduction of these additional constraints introduces unhappiness into the system, mostly through either hosts or cadets who do not get their first preferences as a result of the matching. The numerical unhappiness function quantifies five key sources of unhappiness, and weights each of them relative to each other, so that potential allocations of cadets to hosts can be compared impartially, and the optimum matching can be chosen.
Results: Applying the numerical unhappiness function and exhaustively considering alternatives allows the optimum matching of cadets to hosts to be achieved. While all hosts for the first and second cohort of students seem happy up front with the concept of the “numerical unhappiness function” used to ensure the overall optimisation of allocation matching, they become unhappy when the optimised solution does not match their particular preferences. The key benefits of the approach, such as a simultaneous and timely conclusion to the allocation process, securing workplace opportunity for all potential cadets, and the removal of emotion from what is a potentially very high-stakes process, seem largely invisible to many of the participants.
Conclusions: Overall an objective utilitarian method of fairly allocating cadets to placements has been implemented, allowing us to manage the diversity of discipline and location preferences of the cadets without compromising our ability to meet the needs of the hosts. The certainty of general fairness has been a powerful tool in managing ongoing relationships with our partners, even with those who feel specifically disadvantaged by accepting their second or third preferences in a particular allocation round.