City Research Online

Abstract

In this paper, we develop a stochastic optimization framework for production capacity planning that integrates inventory management and demand backlogging in a discrete-time, dynamic newsvendor-type setting. Our model explicitly accounts for both inventory storage and demand shortage, incorporates revenues and costs within the plant’s cash flow structure, and treats profit as a function of stochastic factors, including commodity prices and demand, with the latter evolving according to a Markov multi-factor process. We contribute to the literature in two key ways. First, we develop a joint capacity and inventory optimization problem to capture the dependence of inventory levels on both the system state and the time-weighted sum of values along the demand path. Second, to efficiently address the resulting path-dependence, we introduce a tree-based method. Subsequently, using empirically calibrated models, we evaluate profitability under different scenarios, with and without inventory management, for varying holding and backlog cost parameters. By recasting the joint problem as a real options model that depends on cumulative demand, we provide a unified and tractable framework that captures both the operational complexity and the financial flexibility involved in capacity investment decisions under uncertainty.

Publication Type:	Article
Additional Information:	© 2026 Springer. This is the accepted manuscript of an article published by Springer. Please refer to the publisher’s terms and conditions for information on re-use.
Publisher Keywords:	Capacity planning, Inventory, Real options, Averaging, Multivariate demand model
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School Bayes Business School > Faculty of Actuarial Science & Insurance Bayes Business School > Faculty of Finance
SWORD Depositor:	Symplectic Administrator

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