Managing unreliable suppliers under varying risk preferences: all-or-nothing versus fractional delivery guarantees

This paper revisits the classical newsvendor problem with unreliable suppliers, examining both risk-neutral and risk-averse formulations. We study multi-sourcing decisions under yield uncertainty, distinguishing between all-or-nothing (AON) suppliers, who either deliver fully or fail completely, and suppliers offering fractional delivery guarantees (FDGs) that ensure partial fulfillment under disruption. For the risk-neutral case, we show that the supplier ranking rule proposed previously, based on effective cost, is not optimal. Instead, we prove a cost-ordered dominance property: suppliers are considered in nondecreasing unit procurement cost (a higher-cost supplier cannot be active if a lower-cost supplier is inactive), while disruption risk affects the optimal quantities and the activation thresholds within this structure. Fractional guarantees generate nonlinear and potentially unimodal patterns in order quantities and service levels, leading to different activation behavior compared with AON models. In the risk-averse case, we extend the mean-variance formulation and demonstrate that an earlier study omitted part of the profit variability, resulting in an underestimation of risk. We derive the complete mean-variance expression and introduce a simplified weighted-variance formulation that captures risk more accurately while remaining computationally efficient. The results show that minimizing weighted variance activates all suppliers when stockout penalties are present, whereas minimizing full variance offers greater protection when reliability is low. Overall, our study offers clearer guidance for supplier selection and ordering decisions under uncertainty and risk aversion, providing new analytical and numerical insights into risk-averse supplier portfolio management.