Derivation of closed-form expression for optimal base stock level considering partial backorder, deterministic demand, and stochastic supply disruption

In the presence of stochastic supply disruption, the optimal variables of an inventory policy must be determined appropriately. Considering a two-echelon system comprised of a supplier and a retailer, the objective of this research is to help the retailer derives the optimal base stock level that achieves the minimum costs per unit of time regarding the stochastic unavailability of the supplier. The expression of the optimal base stock level is determined in closed-form in consideration of a continuous random variable of a disruption length together with a partial backorder of shortage inventory. A solution method which facilitates the retailer to derive the correct expression for the optimal base stock level is proposed. The applicability of the proposed solution method is illustrated through numerical experiments.