Pricing, Production, and Channel Coordination with Stochastic Learning

We study a two-period supply chain in which a manufacturer produces a product, learns to reduce cost, and sells it through a retailer with a price-dependent demand. The manufacturer's second-period production cost declines linearly in the first-period production with a random learning rate. The manufacturer may or may not have the option to carry inventory. We investigate the impact of mean learning rate and learning rate variability on the manufacturer's production and pricing decisions, as well as on the retailer's procurement and pricing decisions. We demonstrate that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We provide revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Lastly, we demonstrate the robustness of our results by examining a model in which learning takes place continuously