Minimizing risk in Bayesian supply chain networks

We develop an approach for minimizing expected unmet demand in a supply chain modelled using a Bayesian network. We allow for nodes to be upgraded, subject to a budget constraint, to reduce the probability that the node becomes non-operational. We formulate the problem of selecting an optimal set of node upgrades as a linear binary integer program (BIP). Ours is the first formulation of expected loss minimization in Bayesian-modelled supply chains as a BIP. Unlike previous published formulations, our formulation allows for the conditional probability table of each node in the Bayesian network to be quite general, including allowing an upgraded node to have a nonzero probability of failure, and allowing multiple types of upgrades for a node. This reflects real world scenarios, including those in which node upgrades do not completely eliminate risk. We present computational results for small problems and illustrate how the solution set changes with the budget. Results for a larger food supply chain with 44 nodes and 63 arcs are also discussed. Finally, we present a preprocessing method for reducing the number of constraints needed for the BIP formulation, and evaluate the savings in run time achieved by applying our constraint reduction method.

Automated summary

In this article, we propose an approach to minimize expected unmet demand in a supply chain using a Bayesian network. We consider node upgrades to reduce the probability of node failure and formulate the problem as a linear binary integer program. Unlike previous formulations, our model allows for flexible conditional probability tables and multiple types of upgrades. We present computational results and discuss the application to a larger food supply chain. We also introduce a preprocessing method to reduce the number of constraints and evaluate the runtime savings achieved.