Supply disruptions with time-dependent parameters

We consider a firm that faces random demand and receives shipments from a single supplier who faces random supply. The supplier's availability may be affected by events such as storms, strikes, machine breakdowns, and congestion due to orders from its other customers. In our model, we consider a dynamic environment: the probability of disruption, as well as the demand intensity, can be time dependent. We model this problem as a two-dimensional non-homogeneous continuous-time Markov chain (CTMC), which we solve numerically to obtain the total cost under various ordering policies. We propose several such policies, some of which are time dependent while others are not. The key question we address is: How much improvement in cost is gained by using time-varying ordering policies rather than stationary ones?We compare the proposed policies under various cost, demand, and disruption parameters in an extensive numerical study. In addition, motivated by the fact that disruptions are low-probability events whose non-stationary probabilities may be difficult to estimate, we investigate the robustness of the time-dependent policies to errors in the supply parameters. We also briefly investigate sensitivity to the repair–duration distribution. We find that non-stationary policies can provide an effective balance of optimality (low cost) and robustness (low sensitivity to errors).