A multi-location inventory system with occasional allocation under uncertain defective rates

In this study, a multi-location allocation problem is investigated under a temporary allocation system in light of the uncertain defective rate inherent to items. Based on the theoretical and modeling foundation of previous research, this study contributes in four main aspects. First, a robust optimization model is developed based on the budget uncertainty of the defective rate of items in a multi-location inventory system. Second, given that the determination of uncertainty relies on the subjective judgment of decision-makers with different risk preferences, a pivotal variable method is introduced to approximate the possible thresholds of the uncertain parameter within the expected interval. Third, a new evaluation criterion curve, illustrating the cumulative cost differences between the probabilistic and robust models, is employed through large-scale sampling to evaluate the performance of the two decision models. Finally, numerical experiments and sensitivity analysis are conducted to verify the performance of the decision effects under different defective rates and stockout costs, respectively. The results confirm the superior performance of the robust model, as shown through sensitivity analysis under thresholds of varying defective rates and stockout costs, and highlight the effectiveness of the proposed cumulative cost difference evaluation curve. The robust model offers significant cost-control advantages over the probabilistic model, particularly in high-uncertainty scenarios. This study provides a reference method for multi-location inventory allocation decisions with uncertain defective rates.