Research On Optimal Allocation of Hu Sheep Breeding Based on Stochastic Difference Equations

Abstract

This study addresses the dynamic resource allocation problem in large-scale Hu sheep farming by establishing a production cycle model based on stochastic difference equations. Through systematic analysis of seven production stages (mating period, pregnancy confirmation, etc.), we develop a population dynamic system incorporating multi-dimensional state variables. Three critical stochastic factors—conception success rate, gestation duration variance, and lambing number variation—are innovatively integrated using composite probability models for stochastic process characterization. An improved Genetic Algorithm (GA) is employed to optimize multiple parameters including ram-to-ewe ratio, lactation duration, and sheep pen allocation, constructing a nonlinear programming model with dynamic pen utilization cost functions and production constraints. Simulation experiments demonstrate that optimized key production parameters significantly reduce spatial utilization costs while maintaining annual yield targets, validating the model's effectiveness in balancing production efficiency and cost control. This research provides a decision-making framework for large-scale breeding operations through synergistic optimization of stochastic process modeling and intelligent algorithms, offering substantial practical guidance value.