The evolution of two‐stage production and order equilibrium in a random yield supply chain with demand information updating

The mismatch between production, order, and demand seriously affects supply chain performance. However, most research focus on the mismatch between the retailer's order and customer's demand, which ignores the influence of the supplier's random yield on supply chain members' decision‐making. This paper investigates a two‐stage optimization problem within a two‐echelon supply chain, featuring a supplier with random yield and a retailer updating demand information in real‐time. Faced with a long production lead time, the retailer can either place advance orders at the production season's onset (first‐stage advance order) or opt for instant orders at the beginning of the sales season (second‐stage instant order). To ensure timely order fulfillment, the supplier initially employs a cost‐effective regular production mode with random yield during the production season. If yields are insufficient during sales, a pricier emergency production mode with guaranteed output becomes available. Utilizing a dynamic programming approach, we formulate the two‐stage optimization problem to derive optimal production and order decisions. Our analysis uncovers how realized random yield and stochastic market signals influence emergency production and instant order quantities in the second stage. We compare expected profits in scenarios with perfect and imperfect market signals, probing the members' preferences regarding order strategies. An intriguing finding emerges: as instant wholesale prices rising, the supplier's preferred order strategy diverges from the retailer. By strategic adjustments to the instant wholesale price, we demonstrate the potential for unanimous agreement on preferred order strategies among supply chain members — a quality enhancing the chain's flexibility and performance. Moreover, we extend the model to hybrid order strategies and identify conditions for unanimous preference among the three strategies. To bolster our theoretical findings, we provide numerical examples, lending practical support to our study.