A two-period sourcing model with demand and supply risks

In this paper, we study the problem of sourcing a product when the demand and supply may be uncertain. We consider a two-period model where the supplier’s production quantity in the second period is dependent on the amount produced in the first period. This is a common situation in industries where the production capacity cannot be changed in a short period of time such as in the almond industry. In this industry usually a two-year contract between the supplier (farmer) and buyer (handler) is preferred. The buyer can sign two sets of contracts: a production contract where she is responsible for the uncertainty of yield or a purchasing contract where the provided quantity is guaranteed by the supplier at a higher cost. The buyer has to decide about the quantities to buy through the production and purchasing contracts. The buyer has the option to carry excess inventory from the first period to the second. We establish some analytical properties of our proposed model and perform comparative static analysis to study the buyers decisions. In particular, we show under which conditions the buyer may benefit from purchasing contracts. In addition, we shed some light the debate of the merits of inventory carry-over in mitigating the yield risk in the almond industry. To gain some practical insights, we also apply our model to some real data from the California almond industry. Finally, we extend the model to investigate two cases: when the prices in the primary and the secondary markets are functions of yield and when the amount of carry-over is a decision variable.