Managing Self-Replicating Innovative Goods
研究了自我复制创新产品制造商的最优生产和销售策略，重点分析了“保留或销售”权衡，并区分了强复制和弱复制两种情境下的不同最优政策。
Inspired by self-replicating three-dimensional printers and innovative agricultural and husbandry goods, we study optimal production and sales policies for a manufacturer of self-replicating innovative goods with a focus on the unique “keep-or-sell” trade-off—namely, whether a newly produced unit should be sold to satisfy demand and stimulate future demand or added to inventory to increase production capacity. We adopt the continuous-time optimal control framework and marry a self-replication model on the production side to the canonical innovation-diffusion model on the demand side. By analyzing the model, we identify a condition that differentiates Strong and Weak Replicability regimes, wherein production and sales, respectively, take priority over the other and fully characterize their distinct optimal policies. These insights prove robust and helpful in several extensions, including backlogged demand, liquidity constraints, stochastic innovation diffusion, launch inventory decision, and exogenous demand. We also find that social marketing strategies are particularly well suited for self-replicating innovative goods under Strong Replication. This paper was accepted by Victor Martínez de Albéniz, operations management.