Dynamic Allocation Optimization of Palm Sap for Palm Sugar and Bioethanol Production Using Pontryagin Maximum Principle
DOI:
https://doi.org/10.30736/voj.v8i2.1366Keywords:
Palm Sap Allocation, Palm Sugar, Bioethanol, Mathematical Modeling, Pontryagin’s Maximum PrincipleAbstract
Palm sap supports renewable bioethanol production for Indonesia’s energy needs while providing nutritious palm sugar with substantial export potential. Large-scale bioethanol production risks palm sugar sustainability, necessitating optimal dynamic allocation balancing energy demand and sugar production. This study models palm sap, sugar, and bioethanol dynamics, formulates optimal control, and analyzes existence, uniqueness, positivity, boundedness, and stability. The objective maximizes cumulative profit, using polynomial regression to forecast prices and profit margins to weight accumulated production. Optimal control uses Pontryagin’s Maximum Principle and fourth-order Runge-Kutta forward-backward sweep computation. ver 24 months, bioethanol allocation exceeds palm sugar’s, fluctuates with forecast prices, and converges to an equal 50–50% distribution. Dynamic allocation increases cumulative profit by 1.17% over static allocation.
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