Multichannel distribution strategy: Selling to a competing buyer with limited supplier capacity

We study the optimal distribution strategy of a supplier with limited capacity. The supplier may adopt the supplier-only role, be the solo seller in the market, or use the dual-channel strategy and compete with its downstream buyer. In comparison to the case of unlimited capacity, we show that the supplier, the buyer, and consumers may all benefit from the supplier's limited capacity at the same time, leading to a "win-winwin" outcome. We also find that, under limited capacity, the downstream buyer may order the supplier's entire capacity and strategically withhold some supply from being sold to the market even if there is no underlying supply-side or demand-side uncertainty. Our result points to a new form of strategic purchasing behavior by the buyer in the face of upstream and downstream competition. Interestingly, we show that while buyer withholding is always beneficial for the supplier, it can reduce the buyer's profit under certain cases, although total supply chain profit is the first-best outcome. Also, counter to conventional antitrust concerns, buyer withholding at times may benefit consumers in spite of reduced downstream competition. Finally, in contrast to intuition, we find that the supplier's benefit from investing in direct selling capability is highest when its capacity size is moderate and not large.