Online Demand Fulfillment in Highly Asymmetric Markets

Problem Definition: We study online demand fulfillment with limited flexibility in highly asymmetric markets, where some locations, represented by the set J _H have moderate to high market shares, while others have very low shares. Xu et al. (2020) is the first to establish that a positive generalized chaining gap (GCG) is a necessary and sufficient condition for bounded performance, which is defined as the expected lost sales as the total market size grows. While a high GCG signals a better performance, the presence of high market asymmetry results in a low GCG and a larger performance bound, making the bound less useful for assessing actual system performance. Therefore, understanding system performance in highly asymmetric markets remains an important question. Methodology/results: We introduce a network condition called J _H -connectivity, which ensures that after removing the markets with very low shares, the markets in J _H are still connected through the available suppliers. We prove that J _H -connectivity is both necessary and sufficient for maintaining bounded performance in highly asymmetric markets. This is achieved through a carefully designed online fulfillment policy that utilizes network partitioning and advanced analyses of mean-reverting processes using probability methods in an asymptotic context. Additionally, we offer strategies for network design to reduce the risk of J _H -disconnectivity. Managerial implications: Our findings indicate that even the well-known long chain structure may not ensure bounded performance in highly asymmetric markets, especially when low-demand markets are dispersed throughout the network. Instead, a “hub and spoke” network configuration with a shorter embedded long chain can help reduce the risk of J _H -disconnectivity and enhance system performance.