Inventory systems with stochastic demand and supply: Properties and approximations

• Published in: European journal of operational research Vol. 206; no. 2; pp. 313 - 328
• Main Authors: Schmitt, Amanda J., Snyder, Lawrence V., Shen, Zuo-Jun Max
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.10.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Approximation; Exact sciences and technology; Inventory; Inventory control, production control. Distribution; Inventory management; Inventory Supply disruptions Risk management Supply chain management; Logistics; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Risk management; Risk theory. Actuarial science; Stochastic models; Studies; Supply chain management; Supply disruptions; Uncertainty; Supply disruptions; Supply chain management; Risk management; Inventory; Costs; Optimal policy; Supply disruption; Risk analysis; Modeling; Exact solution; Production management; Uncertain system; Shortage; Supply demand balance; Retailers; Base stock; Inventory control; Logistics; Discrete event system
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.02.029

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.