Optimizing inventory and sales decisions in a two-stage supply chain with imperfect production and backorders

• An integrated inventory model with price-sensitive demand is developed.
• An imperfect product and backorder are considered.
• The results indicate coordination improves the total expected profit of the system.
• Allowing backorders increases the total expected profit of the supply chain.
• Backorders become more beneficial as price sensitivity of demand increases.

This paper develops a model of an integrated vendor–buyer supply chain with imperfect production and shortages. We assume that market demand is sensitive to the buyer’s selling price and thus study combined operations and pricing decisions in the supply chain. We first derive the expected profit per unit of time using the well-known renewal-reward theorem, and then maximize profit for the cases of independent and joint optimization. Numerical examples and a sensitivity analysis are provided to illustrate the proposed models. The results indicate that coordination and backordering improve the total expected profit of the system, and that both measures become more important for the supply chain as the price sensitivity of demand increases. Furthermore, the coordinated supply chain often prefers to perform inspection at the vendor, who is more familiar with the product and its deficiencies than the buyer in many cases.