OPTIMISATION MODELLING OF A STUDENT’S DAILY ROUTINE: FORMALISATION AND EMPIRICAL JUSTIFICATION

Abstract

Introduction. Time is a limited resource identical for every individual: a day comprises 24 hours and a week 168, so the decisive factor in a student’s academic performance and quality of life is not the available amount of time but the rationality of its allocation among major activities. Empirical studies confirm the link between time management, academic performance and well-being, yet formalising the individual time-allocation problem by mathematical programming remains insufficiently researched.

Purpose. The purpose of the study is to construct, solve and comparatively analyse linear and nonlinear models of a student’s optimal daily time allocation, and to empirically justify the form of the utility function underlying the nonlinear model.

Materials and methods. The materials comprised the input parameters of a student’s daily time allocation (duration limits of seven activities and their importance weights) and the results of a survey of 50 students from years 1–6 on the subjective utility of different study durations. Linear programming (the simplex method, MS Excel) was used for the baseline model, nonlinear programming (the GRG Nonlinear method) for the diminishing-marginal-utility model, and the specification methodology to approximate the empirical relationship by six functional forms via least squares, evaluated by the coefficient of determination, standard error and the F-statistic.

Results. An optimization model of a student's daily time allocation among seven types of activity is developed and examined by means of linear programming. The effect of corner solutions is identified, whereby the linear model concentrates time on the activities with the highest weight coefficients and crowds out the others regardless of their importance. A nonlinear model with diminishing marginal utility is proposed; the form of its utility function is justified empirically on the basis of a student survey using the model-specification methodology (by the coefficient of determination and a set of quality indicators). It is shown that the nonlinear model provides a balanced time allocation and eliminates the shortcoming of the linear formulation.

Prospects. Prospects for further research lie in moving towards a utility function with internal saturation that more accurately reflects the observed decline in utility under excessive study duration, refining the weight coefficients on a larger sample, and extending the model to a weekly planning horizon accounting for deadlines and uneven workload.