Prepositioning of emergency supplies and channel coordination: Considering a loss-averse supplier and government penalty

In humanitarian contexts, less attention has been paid to the bounded rationality of suppliers, which may lead to understocking of emergency supplies. Failing to recognize and correct understocking significantly impacts the reliability of humanitarian supply chains (HSCs). To bridge the gap, we redesign a humanitarian system composed of a local authority and a loss-averse supplier with a non-zero reference profit. Introducing an option contract and penalty mechanism into the public-private cooperation (PPC) in stocking emergency supplies. The conditions under which the supplier adopts either a stocking-to-order or understocking strategy are identified. The results show that the supplier's optimal reserve quantity of emergency supplies decreases with increasing loss aversion and optimism levels, with a greater sensitivity to changes in optimism than in loss aversion. Increasing the penalty coefficient slows the rate of decline in the supplier's reserve quantity if the loss aversion (optimism) level is low but has the opposite effect if the supplier's loss aversion (optimism) level is high. Humanitarian channel coordination is achieved under four conditions, two of which require that the supplier's loss aversion level must not exceed the loss aversion threshold and that the penalty coefficient must fall within a specific range. Additionally, a Nash bargaining model is developed to determine an optimal option price acceptable to the authority and the supplier, which enhances the willingness of the HSC members to jointly preposition emergency supplies. Finally, the case study shows that the PPC model leads to utility improvements for authorities and suppliers and provides direct validation of the PPC model's effectiveness. Our paper explains the motivations behind supplier understocking from a behavioral perspective and provides a penalty mechanism for regulating suppliers in line with government orders, which is of great significance for guaranteeing the reliable supply of emergency supplies.