Value of operational flexibility in co-production systems with yield and demand uncertainty

We study the production decisions of a firm that operates a co-production system (single input but multiple simultaneous outputs) with random yield and demand. The firm uses its outputs to meet multiple end-market demands with different quality requirements. Outputs serving a market segment may be a result of a blending process of different quality products of the co-production system. After the realisation of yield and before the realisation of demand, the firm has the option to upgrade the quality of outputs in order to better position itself to meet market demands. With the goal of maximising expected profits, we formulate a three stage stochastic programming problem, to investigate the value of intermediate upgrading flexibility. Using a stylised model of two products and two markets with different quality requirements, we characterise the optimal decisions and show that the quality upgrading policy is of a single-threshold type. Although upgrading is costly, it creates value for the firm through reducing total production cost and better managing the yield uncertainty. Positive correlation between demands of the end-markets decreases the value of upgrading. The more general model formulation offers the blueprint of a stochastic programming model that can be solved for realistic applications.