A Mixed Integer Linear Programming Model for Livestock Planning

Abstract

In this work, we propose a mixed integer linear programming formulation for the strategic planning of a livestock operation over a multi‑period horizon. The model aims to optimize the overall revenue of the operation while explicitly accounting for the complex biological, operational, and economic constraints inherent to livestock breeding systems. These constraints include herd dynamics, breeding and replacement decisions, capacity limitations, resource availability, and time‑dependent production factors. The proposed formulation provides a structured and transparent decision‑support framework that captures the dependencies between planning periods and supports long‑term strategic decision‑making. To assess the effectiveness and robustness of the model, extensive computational experiments are conducted across multiple scenarios and parameter settings that reflect realistic operational conditions. The results are benchmarked against a contesting model that represents the heuristic‑based decision rules currently applied by company managers. The numerical results demonstrate that the model consistently adapts to diverse scenarios, outperforming the existing heuristics in terms of revenue and resource utilization. Moreover, the solutions obtained are interpretable and aligned with managerial intuition, which facilitates their practical adoption. Overall, the proposed approach shows strong potential as a systematic tool to support and improve livestock operation planning and management decisions