Optimization of Coffee Production and Distribution under Multi-Demand Scenarios: A Linear Programming and Dual Analysis Approach

Abstract

Efficient production and distribution planning is essential for improving profitability and operational performance in coffee supply chains. This study develops a linear programming model to optimize coffee production and distribution decisions under multiple demand scenarios. The model considers three coffee products, namely Robusta, Arabica, and Blend coffee, distributed to four regional markets. The objective is to maximize total net profit while satisfying production capacity, demand, distribution capacity, service-level, and minimum production constraints. Three demand scenarios—low, medium, and high demand—were evaluated to examine the impact of varying market conditions on optimal production and distribution strategies. The results indicate that the optimal profit increased from Rp 56.585 million under the low-demand scenario to Rp 80.375 million under the medium-demand scenario and Rp 94.350 million under the high-demand scenario. The optimization model consistently prioritized Arabica and Blend products because of their higher profitability, while Robusta was utilized primarily to satisfy capacity and demand requirements under higher-demand conditions. Shadow price analysis identified Arabica production capacity and regional distribution capacities as the most critical resources affecting profitability. In addition, reduced cost analysis revealed distribution routes that were not economically competitive under current operating conditions. The findings demonstrate that the proposed linear programming framework provides an effective decision-support tool for optimizing coffee production and distribution planning. The integration of scenario analysis and dual analysis offers valuable managerial insights for improving resource allocation, operational efficiency, and profitability in coffee-based food enterprises.