Asymptotic behavior of optimal quantities in symmetric transshipment coalitions

This paper addresses the asymptotic behavior of optimal quantities in symmetric transshipment coalitions. First, we provide bounds for optimal quantities under general demand structure. Second, we show that if the variance of average demand diminishes as the number of newsvendor grows, the optimal quantities move toward the distribution mean after coalitions became sufficiently large. However, the limits depend on the type of newsvendors in the coalition and the magnitude of transshipment cost above a certain threshold. We also discuss the pooling anomaly in large coalitions in these settings and show that the optimal quantities always decrease (increase) to their limit if the single newsvendor's optimal quantity is above (below) mean.