Profit-Oriented Tactical Planning of the Palm Oil Biodiesel Supply Chain Under Economies of Scale

The growing demand for sustainable energy alternatives highlights the need for decision support tools in biodiesel supply chains. This study proposes a mixed-integer programming (MIP) model for tactical planning in the palm oil biodiesel supply chain, focusing on refining, blending, and distribution. The model incorporates economies of scale, inventory, and transport constraints and is enhanced with valid inequalities (VI) and a warm-start heuristic procedure (WS) to improve computational efficiency. Computational experiments on simulated instances with up to 6273 variables and 47 million iterations demonstrated robust performance, achieving solutions within 15 min. The model also reduced time-to-first-feasible (TTFF) solutions by 60–75% and CPU times by 17–21% compared to the baseline, confirming its applicability in realistic contexts. The proposed model provides actionable insights for managers by supporting decisions on facility scaling, product allocation, and profitability under supply–demand constraints. Beyond palm oil biodiesel, the formulation and its VI + WS enhancement provide a transferable blueprint for tactical planning in other process industry and renewable energy supply chains, where (i) multi-echelon flow conservation holds and (ii) discrete operating scales couple throughput with fixed/variable cost structures, enabling fast scenario analyses under changing prices, demand, and capacities.