University Staff Teaching Allocation: Formulating and Optimising a Many-Objective Problem

Abstract

The allocation of university staff to teaching exhibits a range of often competing objectives. We illustrate the use of an augmented version of NSGA-III to undertake the seven-objective optimisation of this problem, to fi nd a trade-off front for a university department using real world data. We highlight its use in decision-making, and compare solutions identi fied to an actual allocation made prior to the availability of the optimisation tool. The criteria we consider include minimising the imbalance in workload distribution among staff; minimising the average load; minimising the maximum peak load; minimising the staff per module; minimising staff dissatisfaction with teaching allocations; and minimising the variation from the previous year’s allocation (allocation churn). We derive mathematical forms for these various criteria, and show we can determine the maximum possible values for all criteria and the minimum values for most exactly (with lower bounds on the remaining criteria). For many of the objectives, when considered in isolation, an optimal solution may be obtained rapidly. We demonstrate the advantage of utilising such extreme solutions to drastically improve the optimisation effi ciency in this many-objective optimisation problem. We also identify issues that NSGA-III can experience due to selection between generations.