A periodic-review inventory system with a capacitated backup supplier for mitigating supply disruptions

We consider a periodic-review inventory system with two suppliers: an unreliable regular supplier that may be disrupted for a random duration, and a reliable backup supplier that can be used during a disruption. The backup supplier charges higher unit purchasing cost and fixed order cost when compared to the regular supplier. Because the backup supplier is used at unplanned moments, its capacity to replenish inventory is considered limited. Analytical results partially characterize the structure of the optimal order policy: a state-dependent (X(i),Y(i)) band structure (with corresponding bounds of X(i) and Y(i) to be given), where i represents the status of the regular supplier. Numerical studies illustrate the structure of the optimal policy and investigate the impacts of major parameters on optimal order decisions and system costs.