Two-Product Make-to-Stock System: Strategic Joining and Optimal Inventory Levels

TL;DR

This paper studies a two-product make-to-stock system with strategic customer behavior, deriving equilibrium strategies and optimal inventory levels to maximize profit and welfare.

Contribution

It introduces a novel analysis of customer strategic decisions and optimal inventory policies in a two-product queueing system with no prior work on this specific setup.

Findings

Existence and uniqueness of Nash equilibria established.

Closed-form expressions for optimal base-stock levels derived.

Performance measures characterized for profit and welfare maximization.

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.