Integrated Bayesian Networks and Linear Programming for Decision Optimization

This paper proposes a universal method for optimizing decisions under complex structured uncertainty based on the integration of Bayesian networks (BN) and linear programming (LP). The method allows formalizing and taking into account not only individual probabilities of events, but also their complex cause-and-effect relationships, which is especially important for management tasks in the agro-industrial complex, logistics, energy, and other areas. The use of BNs provides automatic inference of joint probabilities of complex scenarios, while the use of LP allows finding optimal management decisions taking into account all relevant constraints and risks. The effectiveness and advantages of the method are demonstrated by a case study of farm planning, which shows that the integration of BN and LP provides more realistic, flexible, and adaptive optimization compared to classical stochastic and robust approaches. A comparative analysis with traditional methods is conducted, and issues of computational complexity, scalability, and prospects for further development of the methodology are discussed.