Optimal Ordering Policies for Supply Networks with Disruptions

As the economy recovered with the winding down of the pandemic, businesses with complex supply chains could not bring their inventories back to optimal levels as their production was susceptible to disruption due to supply outages. Deriving optimal ordering policies as a way to mitigate the impact of production disruption represents a challenge in multi-stage decision problems given the complexity of the network and the uncertainty in the demand.

In the first part of the thesis, we formulate a stochastic inventory control problem for a general supply network model. Using the Bellman’s recursion and properties of the cost function at each stage, we characterize the optimal request decision as a threshold policy where the threshold computation is based on the marginal cost. Lastly, we validate that the policy developed minimizes the inventory cost and meets an exogenous random demand. However, the policy does not guarantee that the inventory level for each firm satisfies the constraints when a supply disruption occurs in the network.

In the second part of the thesis, we consider a serial network in which firms engage in production subject to disruption risk and they look to maximize their profit. We propose an algorithm to characterize a stationary optimal policy based on the closed-form solutions obtained from a discounted finite horizon problem for profit maximization. Finally, by computing the policy proposed as a function of the tier’s location and its disruption probability, we provide simulation results of the disruption effect in the supply network.