Distributionally robust production and pricing for risk-averse contract-farming supply chains with uncertain demand and yield

Abstract

Contract farming is a common and emerging practice in agricultural supply chains in both developing and developed countries, yet it has not received much attention in prior studies. This paper addresses this gap by examining a risk- and ambiguity-averse contract farming supply chain consisting of a risk-neutral agribusiness manufacturer and a risk-averse smallholder farmer, under conditions of demand and yield randomness with limited distributional information. A distributionally robust Stackelberg game model is developed to tackle this challenging manufacturer-farmer ambiguity problem. The model enables us to determine the risk-averse farmer’s robust production quantity under the conditional value-at-risk criterion, as well as the agribusiness manufacturer’s robust procurement price, which follows a simple threshold policy. Our analysis reveals that there exists a threshold level of risk aversion beyond which the farmer would decline the contract and cease production altogether. Furthermore, we find that the farmer’s risk-averse behavior adversely impacts both parties, even in the worst-case scenario, resulting in lower profits and reduced production quantities for both. Surprisingly, our comparative analysis shows that higher demand variability benefits the risk-averse farmer, creating a win-lose outcome for the farmer and the manufacturer. In contrast, higher yield uncertainty leads to a lose-lose outcome for both parties.