Integer Labor Allocation to Maximize Coffee Harvest Output: A Branch and Bound Case Study

Labor allocation is an important factor in coffee harvesting because differences in labor productivity, labor costs, working hours, and harvesting capacity can affect the effectiveness of resource utilization. This study aims to formulate and solve a mathematical optimization model for determining the optimal allocation of daily and contract labor to maximize coffee harvesting productivity at Mr Abdur’s coffee plantation. A quantitative mathematical optimization approach with a case study design was employed. Field data were collected through interviews and discussions with the plantation owner and included labor costs, working hours, harvesting capacity, and labor productivity. The problem was formulated as a Linear Programming model and first solved using the Simplex method as a continuous relaxation. Because the resulting decision variable was fractional. The model was subsequently solved as an Integer Linear Programming problem using the Branch and Bound method. The Simplex relaxation produced a continuous solution of approximately and , with an objective value of approximately 450,72 kg. Since the number of workers must be an integer, Branch and Bound was applied and resulted in the optimal integer solution and , yielding a maximum modeled productivity of 450 kf. This allocation requires 120 labor-hours and IDR 900.000 in labor expenditure, while its harvesting capacity reaches 3.120 trees, satisfying the available limits of 240 labor-hours, IDR 1.000.000, and 3.125 trees. The results demonstrate that the Simplex-Branch and Bound approach provides a mathematically feasible and operationally applicable solution for discrete labor allocation in coffee harvesting. The proposed model can support more systematic labor planning and resource allocation in smallholder coffee plantations.