Supply chains facing stockout costs: mean-risk analysis and channel coordination

Stockouts pose persistent challenges to supply chain management, causing profit losses, damaging customer loyalty and reducing future orders. This paper studies risk-based decision models for a dyadic supply chain, incorporating opportunity costs due to stockouts. We first examine unconstrained mean-risk newsvendor models based on variance, standard deviation and semideviation, and establish unified critical-fractile-style optimality conditions analogous to the classical risk-neutral case. These conditions guarantee unique optimal solutions across diverse demand distributions. We analyse how risk aversion affects order quantities under normal, uniform and exponential demand, revealing its impact is strongest when stockout penalties are low but diminishes as they rise. Next, we examine channel coordination, and derive that stockout costs hinder global Pareto optimality (PO) under standard contracts such as buybacks. To overcome this, we propose a demand-dependent side-payment mechanism that restores flexibility. Within the wholesale price framework, we show that PO imposes stricter requirements than the supply chain's objective maximisation criterion. We derive implementation rules for local PO and demonstrate that, when the supplier faces no stockout cost, the wholesale price equals the supplier's unit cost. Finally, in the decentralised setting, we find that incentives for the retailer to misrepresent risk attitudes arise only when stockout penalties are significant.