how to estimate the supplier fill rate when the supply order and the supply lead-time are uncertain?

Modern retail supply chains are more and more exposed to risks and uncertainties. supply risks such as the uncertainty of the supplier fill rate (sfr) directly affect the performance of a retail supply chain. the purpose of this paper is to investigate the supply uncertainty, where the order size and the supply lead-time are considered as decision variables. we aim at developing a more realistic approach to predicting the sfr. reviewing the relevant literature was the first step taken. we pointed out that while the scientific research on supply risk is growing, the literature lacks an accurate support tool that can predict the sfr. then, a case study was conducted in order to have a comprehensive view of the real context of sfr parameters. accordingly, we propose a new approach to predicting the sfr using the bivariate normal distribution. we illustrate the proposed approach using a real case study in tunisia.