Robust grain supply chain design considering post-harvest loss and harvest timing equilibrium

•Robust bi-level models for processing/storage facility locations in a grain supply chain.•Post-harvest loss and harvest time equilibrium among independent farmers.•Risk-averse and risk-seeking investment strategies in light of crop yield uncertainty.•Application to Illinois and Brazil cases for managerial insights.

This paper presents a bi-level robust optimization model, where a food company maximizes its profit and minimizes post-harvest loss by optimally deploying grain processing/storage facilities and determining grain purchase price, while a group of spatially distributed non-cooperative farmers determine harvest time, shipment, storage, and market decisions under yield uncertainty and market equilibrium. The non-cooperative behavior of the food company and the farmers is represented by a bi-level Stackelberg leader follower’s game model with mixed-integer decision variables. The proposed model and solution approach are applied to case studies for Illinois and Brazil.