Asian Research Journal of Mathematics

Efficient allocation of labour is essential for minimising operational costs and improving productivity in cocoa processing. However, conventional assignment models, such as the Hungarian Assignment Method, assume that assignment costs are known precisely; this assumption may not adequately reflect uncertainty associated with worker performance, task difficulty, fatigue, and operational conditions. This study applies fuzzy logic and the Hungarian Assignment Method to determine the most suitable allocation of workers to cocoa-processing activities at Stevefrana Farm. The study considers six processing stages: conditioning, breaking, scalping, middling, purifying, and packaging. Labour costs were initially represented as crisp values obtained from farm records and supervisors' estimates and were subsequently modelled using triangular fuzzy numbers with a symmetric uncertainty spread of 10%. The centroid method was used to defuzzify the fuzzy costs into crisp values, after which the Hungarian Assignment Method was applied to determine the optimal worker-task allocation. In addition, the robustness of the optimal assignment was evaluated using the Robustness Index (RI), Coefficient of Variation of Fuzziness (CVF), and Robustness Degree (RD), while sensitivity analysis was conducted at uncertainty levels of 5%, 10%, 15%, and 20%. The results indicate that the optimal assignment is Worker 1 to Conditioning, Worker 2 to Middling, Worker 3 to Packaging, Worker 4 to Scalping, Worker 5 to Purifying, and Worker 6 to Breaking. This allocation yields a most likely total labour cost of GH¢555 per day, with a fuzzy cost range of GH¢499.50 to GH¢610.50. The robustness analysis produced an RI of 0.20, indicating moderate robustness; a CVF of 10%, indicating uniform relative uncertainty; and an RD of 90%, indicating high reliability. The sensitivity analysis further showed that, although robustness decreases as uncertainty increases, the optimal worker-task assignment remains unchanged across the 5%-20% uncertainty levels. The study demonstrates that integrating fuzzy logic with the Hungarian Assignment Method provides a practical decision-support framework for incorporating uncertainty into labour allocation while maintaining cost efficiency. The proposed model can assist cocoa-processing managers in improving worker-task matching, budgeting for labour-cost variability, and identifying processing stages requiring greater management attention.