Combining simulation with reliability analysis in supply chain project management under uncertainty: a case study in healthcare

Many projects involving supply networks can be logically represented by multiple processing paths from a project starting node to an ending one. Typically, each of these paths contains a series of stages, which refer to different actions that are required to complete the project. When the supply chain is working under deterministic conditions, computing the total time requested by each path - and, therefore, the project makespan - is a trivial task. However, this computation becomes troublesome when processing times in each stage are subject to uncertainty, which is a common situation in real-life applications. In this paper, we assume the existence of historical data that allow us to model the processing time associated with each stage as a random variable. Then, we propose a methodology combining Monte Carlo simulation with reliability analysis in order to: (i) estimate the survival function of the project (i.e., the function determining the probability that the project has not finished yet on or before an evolving target time); and (ii) the most likely 'bottleneck' path, i.e., the path showing a higher probability of being the slowest one in the entire project. Identifying these critical paths facilitates reducing the project makespan by investing the available budget in improving the performance of some stages along the path - e.g., by modifying the transportation mode at one particular stage in order to speed up the process. A numerical example, regarding a healthcare supply network, is employed to illustrate these concepts.