Product portfolio depth in competitive manufacturing systems with inventory and production complexity

We study the problem of defining product-variety portfolios in competitive manufacturing environments, focusing on the trade-off between revenue gains from increased variety and the resulting inventory, production, and operational complexity costs. This trade-off is central to logistics system design, yet becomes computationally challenging in competitive settings. To deal with the high complexity we propose a framework that assumes firms compete in terms of their number of varieties or portfolio depth. Moreover, this assumption fits the competition dynamics of many product families in practice. Based on this framework, we derive analytical results for duopolies (simultaneous decisions or leader/follower structure). We prove that the product portfolio depth of a monopolist constitutes a limit to the proliferation of product varieties, providing a tractable benchmark for managing product variety in logistics systems. Through numerical experiments, we relax the assumption of competition solely in portfolio depth and show that limiting product portfolio length is effective across demand preference distributions or entails low profit loss, implying that simplified variety decisions can be effective for inventory and production planning. We also observe the monopoly as a limit when we extend our analysis to markets that consist of more firms and to settings of incomplete information. Moreover, we demonstrate that a firm can benefit from disclosing its actual -or even a more cost-efficient- inventory management or manufacturing technology when its competitor is uncertain about the technology employed by the firm.