A Two-Stage Stochastic Linear Programming Model for Tactical Planning in the Soybean Supply Chain

Abstract

Background: The soybean market is representative of the world. Brazil is the largest producer and exporter of this crop and has low production costs but high logistical costs, which are influenced mainly by transport costs. Added to these characteristics, the disputed grain supply, the possibility of crop failure, and the randomness of some parameters that influence the soybean supply chain make decisions even more challenging. Methods: To mathematically model this problem, we carried out an analysis of the scientific production related to grain supply chain and the models used to address the problem, as well as a document analysis and a case study. Results: This paper proposes a new two-stage stochastic linear programming model with fixed recourse for tactical planning in the soybean supply chain from the perspective of the shipper under take or pay contracts over a one-year time horizon. The first-stage variables are the grain purchasing decisions and the volumes of rail and road transportation hired in advance. The model addresses 243 scenarios derived from four uncertainty sources: the purchase and sale prices of raw agricultural products on the spot market, the probability of crop failure, and the external demand. Conclusions: The model is successfully applied to a soybean trade firm in Brazil with expected gain of US$4,299,720 when using the stochastic model instead of the deterministic model. The stochastic model protected the firm from take or pay fines and crop failures, contracting a smaller volume of rail transport than what the company does.