On-demand logistics platform has been developed rapidly to respond increasingly customized demands. Many platform-based enterprises are facing difficulties in operating that resulting in inefficient resource allocation, high costs and top-down centralized decision-making process so that unsustainable on-demand delivery is an existing challenge. Such a platform service supply chain is highly influenced by fluctuating supply and demand. To solve this problem, this paper introduces an online double auction for on-demand pickup and delivery in the metropolitan cities, allowing both shippers and carriers dynamically enter and exit transactions. A multi-agent environment is created to automate the real-time auctioning through cyber-physical-system technologies. The proposed method aims at maximizing the social welfare and minimizing trade failures in the face of uncertainty of future agent types or the information of further bids and asks. The approach is extending the well-known McAfee's single-unit method, to allocate multi-unit on-demand logistics tasks using public, private, robot-enabled delivery capacities. It is observed that truthful bidding is a dominant strategy for each agent under this mechanism while realizing budget balance and individual rationality. The results show that the designed auction is more suitable to employ if supply-demand unbalance exists, compared with the fixed pricing mechanism. It suggests using more crowdsourcing resources rather than private carriers to improve transaction efficiency and transportation sustainability.