Managing Self-Replicating Innovative Goods
Inspired by self-replicating 3D 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.
Keywords: Innovation Diffusion, Bass Model, Optimal Control, Production Planning, Inventory Management