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Designing multi-floor arrangements for biodiesel production facilities that utilize empty fruit bunch (EFB) feedstock represents a computationally intensive, large-scale problem that requires the concurrent assessment of cost, hazard mitigation, and building integrity constraints. The present work proposes a Mixed-Integer Nonlinear Programming (MINLP) formulation tailored to multi-level plant layouts, jointly determining optimal equipment materials, vertical floor allocations, sectional positioning, and passive safeguarding features based on explicit safety quantification. Developed within the General Algebraic Modeling System (GAMS) environment, the model is tackled through a staged decomposition consisting of three sequential phases—(i) choice of construction materials together with load-bearing evaluation, (ii) intra-section multi-floor arrangement, and (iii) full-plant sectional coordination—because solving the full monolithic MINLP violates academic solver license restrictions and does not reach convergence under realistic time constraints. In contrast, the sequential procedure consistently delivers solutions featuring small optimality gaps (overall CPU usage: 22.97 min). Applied to a 1,000 t/d EFB processing scenario involving 57 equipment units distributed across seven functional sections, the resulting layout achieves a 28.9% reduction in total capital expenditure, a 51.97% decrease in required land area, and—when separations follow Dow’s Fire and Explosion Index (F&EI) guidelines including credit for installed devices—a 18.8% drop in Maximum Probable Property Damage (MPPD) before protective measures and a 69.0% reduction once protection is accounted for. This hierarchical decomposition technique shows that highly complex facility layout tasks incorporating formal safety limits can be addressed in a tractable and effective manner, supplying a generalizable methodology suitable for diverse multi-objective design problems encountered in the chemical processing and renewable energy domains.

This study addresses the problem of cost-optimal expansion planning for rural radial distribution networks via a mixed-integer nonlinear programming (MINLP) formulation that jointly determines feeder routing and conductor type selection. The developed method was evaluated using standard 9-node and 25-node test networks, with performance benchmarked against minimum spanning tree (MST)-based procedures and two metaheuristic techniques (sine-cosine algorithm and tabu search). The application of the MINLP approach led to significant reductions in overall expenditure. In the 9-node test case, the total cost was reduced from USD 131,819.33 (obtained via MST-TSA) to USD 77,129.34, resulting in savings of USD 54,689.99, equivalent to 41.48%. Energy loss costs alone decreased from USD 111,746.73 to USD 63,764.12, a drop of USD 47,982.61 or 42.94%. In the 25-node network, overall costs fell by more than 65%, from USD 371,516.59 to USD 128,974.72, while energy loss expenses decreased by USD 210,057.16 (61.06%). Although conductor-related capital expenditure increased under the MINLP solution, the strategy generated significant long-run economic benefits by markedly reducing operating expenses. In contrast to conventional strategies that address topology definition and conductor sizing in separate stages, the proposed framework integrates these decisions, thereby ensuring globally optimal configurations. These outcomes highlight the method’s ability to scale and its practical value for strategic, long-horizon planning in sophisticated distribution grids. All numerical experiments were conducted in Julia (v1.10.2), leveraging JuMP (v1.21.1) together with the BONMIN solver.