A δ-shock model for reengineering of a repairable supply chain using quasi renewal process

In this study, a quasi-renewal process model with δ-shock is analyzed for a degenerative repairable supply chain with a single supplier source. The supplier of the supply chain system encounters shocks due to crisis events and, as a consequence, tends to fail if the interarrival time between two successive shocks is less than a random threshold. The non negligible repair time of the supplier and the random threshold time of shocks are modeled on a quasi renewal process while the shock arrivals are governed by a renewal process. The long-run average cost per unit time is derived by employing the reengineering strategy N, which is determined by the number of failures of the supplier. The optimal reengineering policy N∗ is obtained analytically by minimizing the long-run expected cost rate. Numerical illustrations and sensitivity analysis evidence the consideration of maintenance policy for a repairable supply chain to sustain its smooth running.