Flock Management for Solar Grazing

Problem Definition: To control vegetation, solar asset owners employ farmers to graze sheep on solar sites. While earning grazing revenue, farmers also provide agricultural value through raising and selling sheep. By accounting for flock dynamics of births, deaths, and sales, we model the operational economics of solar grazing for farmers and focus on key flock management decisions.

Methodology/Results: We model solar grazing operations as a finite-horizon linear program that jointly optimizes initial procurement decisions and subsequent sales decisions, subject to age-structured flock dynamics and a target flock-size constraint. During the flock growth phase, the “breed-versus-buy” decision involves weighing the upfront costs and anticipated revenue from lamb and sheep sales against heightened costs of vegetation management when the flock size is below its target level. By analyzing this trade-off, we demonstrate that the farmer’s total profit function is piecewise-linear and concave in the number of sheep initially purchased externally. Beyond the flock growth phase, we prove that an optimal steady-state solution exhibits a maximum-lifetime structure: ewes are retained up to a maximal age, and sales are restricted to lambs and final-year ewes. Finally, we extend the model to incorporate stochastic births and deaths, showing that a linear programming approach yields a tight bound on achievable performance in the stochastic model for large flocks and long horizons, and provide a practical policy that performs strongly in numerical examples.

Managerial Implications: Our results help small-scale farmers, renewable energy developers, and policymakers understand how solar grazing enhances the environmental benefits of solar farms while preserving agricultural value on land converted to solar use. In partnership with a solar-grazing platform that supports solar grazers and connects them with site owners, a spreadsheet implementation of our model has helped dozens of farmers make procurement decisions, predict cash flows, and even secure financing to purchase a flock.