Multi-Stage Network Optimization Model and Decomposition Algorithm for Improving the Efficiency of Enterprise Production System under the Background of Digital Economy

Driven by the digital economy, enterprise production systems feature multi-stage networking with deeply embedded data elements, posing challenges for traditional optimization methods in modeling coupling relationships and efficiency improvement. To address this, this paper constructs a multi-stage network optimization model (MSN-OPT) that integrates digital elements, abstracting the production system as a resource- and information-flow-driven directed network. The model maximizes overall system efficiency through collaborative optimization of resource allocation and data input, incorporating stage weights and digital input costs. Using Benders Decomposition and column generation, the high-dimensional coupling problem is transformed into an iterative master-subproblem framework, significantly reducing computational complexity. Numerical experiments on a 100-200 node production network show that the proposed method reduces computation time by 55%-67% while maintaining optimal solution consistency. Under various disturbance scenarios, system efficiency stabilizes within 12%-18%. Sensitivity analysis reveals that when digital element disturbances are controlled within ±10%, efficiency fluctuations remain below 3%, confirming the model's robustness and stability. This paper provides a computable modeling approach and efficient algorithmic support for production system optimization in the digital economy context.