Pareto improvements for a supply chain with price-only contracts based on quick response

Uncertain demand and fierce market competition lead firms to make response as quickly as they can, especially in the manufacturing industry. Quick response manufacturing has become a basic ability of a manufacturer. In this paper, we study how a manufacturer who has quick response abilities and a retailer to make decisions with a price-only contract. We develop our model based on price-only contracts, because the contracts are the simplest and widely used in practice. In our model, the manufacturer decides the initial wholesale price and the reordering wholesale price first, and the retailer decides the initial ordering quantity according the two wholesale prices. Based on our model, we addressed the optimal decisions for the manufacturer and the retailer with two ordering opportunities. Comparing with a single ordering opportunity, we find out the condition of the manufacturer and retailer's performance improvements, respectively. We also find out the condition of Pareto improvements. In the end, we design an unidimensional searching algorithm to address the the condition of Pareto improvements.