Two-product make-to-stock system: strategic joining and optimal inventory levels

Abstract This paper analyzes a two-product make-to-stock queueing system where a single production facility serves two customer classes with independent Poisson arrivals. Customers make strategic join-or-balk decisions without observing current inventory levels. The analysis establishes the existence and uniqueness of Nash equilibria in customer joining strategies for various inventory scenarios. Optimal base-stock levels are characterized from both profit-maximizing and welfare-maximizing perspectives, with closed-form expressions for key performance measures.