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

• We study the problem of defining the product-variety portfolio of a firm in a competitive environment. • We consider competitive environments that can be modeled based on some empirical regularities. • We prove that in this type of competitive environments, the optimal monopolist product-variety portfolio length constitutes a barrier to the proliferation of product varieties. • We also prove that the monopolistic barrier is valid for markets with incomplete information. • The monopolistic barrier gives a heuristic with low loss for general preferences settings. 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.