Inventory Management Under Market Size Dynamics

We investigate the situation where a customer experiencing an inventory stockout at a retailer potentially leaves the firm's market. In classical inventory theory, a unit stockout penalty cost has been used as a surrogate to mimic the economic effect of such a departure; in this study, we explicitly represent this aspect of consumer behavior, incorporating the diminishing effect of the consumers leaving the market upon the stochastic demand distribution in a time-dynamic context. The initial model considers a single firm. We allow for consumer forgiveness where customers may flow back to the committed purchasing market from a nonpurchasing “latent” market. The per-period decisions include a marketing mix to attract latent and new consumers to the committed market and the setting of inventory levels. We establish conditions under which the firm optimally operates a base-stock inventory policy. The subsequent two models consider a duopoly where the potential market for a firm is now the committed market of the other firm; each firm decides its own inventory level. In the first model, the only decisions are the stocking decisions and in the second model, a firm may also advertise to attract dissatisfied customers from its competitor's market. In both cases, we establish conditions for a base-stock equilibrium policy. We demonstrate comparative statics in all models