Modified Hungarian Method based binary integer goal programming model for optimum allocation and assignment lecturers to courses considering areas of Mathematics

The assignment problem involves determining optimal assignments when assigning n subjects to m jobs under varying degrees of efficiencies. Specifically, lecturer-to-course assignment in Mathematics is a complex problem as lecturers possess different competency, preferences, level of experience and expertise. Existing studies have never considered integrating the optimization of preferences, competency and lecturers’ training costs for upskilling as multiple objective functions when solving lecturers to courses allocation and assignment problem. In addition, incorporating the areas of Mathematics (AOM) and analyzing the training needs for Mathematics lecturers upskilling were lacking in these past studies. Thus, this study proposes the enhanced Modified Hungarian Method (MHM) model based mathematical programming model to identify lecturers’ AOM and clustering the courses involved accordingly. Subsequently, multi-objective Binary Integer Goal Programming (BIGP) models with three variants were formulated, where the first one is CT-BIGP model (Variant 1 or V1) that maximizes the total competency scores of lecturers for coursed assigned and minimizes the total training costs for lecturers’ upskilling. Next is CCPT-BIGP (V2) which maximizes the combined competency and preference scores of lecturers for the assigned courses and minimizes total training costs for lecturers’ upskilling. Meanwhile, the third variant is CPT-BIGP (V3) which maximizes the competency scores of lecturers for the assigned courses, maximizes the preference scores of lecturers for the courses assigned and minimizes the total training costs for lecturers’ upskilling, in this order. Data were collected through surveys and interviews with Mathematics lecturers and academic administrators at Universiti Teknologi MARA (UiTM) Shah Alam and UiTM Seremban. The BIGP models were solved using a preemptive goal programming approach via MATLAB intlinprog Solver. Results revealed that the CCPT-BIGP (V2) model was most effective for UiTM Shah Alam, while CPT-BIGP (V3) model performed best for UiTM Seremban. The findings offer optimal workload distribution strategies, identify lecturers requiring upskilling and contribute to improving teaching quality and lecturer well-being within Mathematics departments.