Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from incomplete data is usually implemented with the Expectation-Maximisation algorithm (EM), which computes the relevant sufficient statistics (“soft EM”) using belief propagation. Similarly, the Structural Expectation-Maximisation algorithm (Structural EM) learns the network structure of the BN from those sufficient statistics using algorithms designed for complete data. However, practical implementations of parameter and structure learning often impute missing data (“hard EM”) to compute sufficient statistics instead of using belief propagation, for both ease of implementation and computational speed. In this paper, we investigate the question: what is the impact of using imputation instead of belief propagation on the quality of the resulting BNs? From a simulation study using synthetic data and reference BNs, we find that it is possible to recommend one approach over the other in several scenarios based on the characteristics of the data. We then use this information to build a simple decision tree to guide practitioners in choosing the EM algorithm best suited to their problem.

We study inventory control policies for pharmaceutical supply chains, addressing challenges such as perishability, yield uncertainty, and non-stationary demand, combined with batching constraints, lead times, and lost sales. Collaborating with Bristol-Myers Squibb (BMS), we develop a realistic case study incorporating these factors and benchmark three policies--order-up-to (OUT), projected inventory level (PIL), and deep reinforcement learning (DRL) using the proximal policy optimization (PPO) algorithm--against a BMS baseline based on human expertise. We derive and validate bounds-based procedures for optimizing OUT and PIL policy parameters and propose a methodology for estimating projected inventory levels, which are also integrated into the DRL policy with demand forecasts to improve decision-making under non-stationarity. Compared to a human-driven policy, which avoids lost sales through higher holding costs, all three implemented policies achieve lower average costs but exhibit greater cost variability. While PIL demonstrates robust and consistent performance, OUT struggles under high lost sales costs, and PPO excels in complex and variable scenarios but requires significant computational effort. The findings suggest that while DRL shows potential, it does not outperform classical policies in all numerical experiments, highlighting 1) the need to integrate diverse policies to manage pharmaceutical challenges effectively, based on the current state-of-the-art, and 2) that practical problems in this domain seem to lack a single policy class that yields universally acceptable performance.

In this study, we analyze and compare the performance of state-of-the-art deep reinforcement learning algorithms for solving the supply chain inventory management problem. This complex sequential decision-making problem consists of determining the optimal quantity of products to be produced and shipped across different warehouses over a given time horizon. In particular, we present a mathematical formulation of a two-echelon supply chain environment with stochastic and seasonal demand, which allows managing an arbitrary number of warehouses and product types. Through a rich set of numerical experiments, we compare the performance of different deep reinforcement learning algorithms under various supply chain structures, topologies, demands, capacities, and costs. The results of the experimental plan indicate that deep reinforcement learning algorithms outperform traditional inventory management strategies, such as the static (s, Q)-policy. Furthermore, this study provides detailed insight into the design and development of an open-source software library that provides a customizable environment for solving the supply chain inventory management problem using a wide range of data-driven approaches.