Who should invest in cost reduction in supply chains?

We have observed four modes of cost reduction in supply chains from practice. In particular, considering a supply chain with one manufacturer and one retailer, we identify four modes: the manufacturer solely invests, the retailer solely invests, or both firms collaboratively or independently invest to reduce the manufacturer's production cost. A question that arises naturally is which one is preferred by the manufacturer, the retailer, and the chain. With iso-elastic demand being sensitive to retail price and sales effort, we define channel powers (in addition to cost factors) for both firms to characterize the firms' investments and identify the best mode. We show that both firms are better off by investing collaboratively rather than independently if and only if the two firms have comparable channel powers and comparable cost factors. Moreover, a firm prefers to invest by itself solely rather than invest by its partner or both firms collaboratively if and only if its cost factor is sufficiently smaller than its partner's. We apply our results to supplier development and get some new insights. As a byproduct, the retailer may get less from the chain profit, which contradicts the retailer-dominant property in the literature under consignment contracts with revenue sharing. Finally, we show that our results are robust to different contract forms and whether the two firms have symmetric or asymmetric impacts on cost reduction.