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Inventory planning under supplier uncertainty in a two-level supply chain

Noura Yassine (Beirut Arab University, Beirut, Lebanon)

The International Journal of Logistics Management

ISSN: 0957-4093

Article publication date: 15 March 2022

Issue publication date: 14 March 2023




Due to uncertainty in supply chains caused by the coronavirus disease 2019 (COVID-19), organizations are adjusting their supply chain design to address challenges faced during the pandemic. To safeguard their operations against disruption in order quantities, supply chain members have been looking for alternate suppliers. This paper considers a two-level supply chain consisting of a manufacturer and two suppliers of a certain type of components required for the production of a finished product. The primary supplier (supplier A) is unreliable, in the sense that the quantity delivered is usually less than the ordered quantity. The proportion of the ordered quantity delivered by supplier A is a random variable with a known probability distribution. The secondary supplier (supplier B) always delivers the order in its entirety at a higher cost and can respond instantaneously. In order for supplier B to respond instantaneously, the manufacturer is required to reserve a certain quantity at an additional cost. Once the quantity received from the main supplier is observed, the manufacturer may place an order not exceeding the reserved quantity.


A mathematical model describing the production/inventory situation of the supply chain is formulated. The model allows the determination of the manufacturer's optimal ordering policy.


An expression for the expected total cost per unit time function is derived. The optimal solution is determined by solving a system of nonlinear equations obtained by minimizing the expected total cost function.

Practical implications

The proposed model can be used by supply chain managers aiming at identifying various ways of handling the uncertainty in the flow of supplies across the chain.


This proposed model addresses a gap in the production/inventory literature.



Yassine, N. (2023), "Inventory planning under supplier uncertainty in a two-level supply chain", The International Journal of Logistics Management, Vol. 34 No. 2, pp. 497-516.



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