The growth of e-retailing market is driving a rise in logistics cost and risk of late delivery. Collaborative logistics is a key solution to improve the situations. Logistics platform that connects multiple carriers, terminals, and warehouses helps to adjust transportation and storage capacity to meet demand. In recent years, wholesalers and trading companies have launched platform services, but these services are in a competitive environment with manufacturers’ direct sales services and 3PLs. For a successful platform business, pricing and lead times must be determined to increase the profitability of the entire supply chain. To contribute to strategic management of logistics platform, we develop a supply chain model consisting of one supplier, one 3PL provider, and one wholesaler who operates a logistics platform. Focusing on the customer’s choice of delivery service option, we incorporated the competition between a platform service and a 3PL service into the model. The wholesaler maximizes its profit by optimizing the platform service fee, while the supplier maximizes its profit by optimizing the unit sales profits. Through several numerical experiments, we evaluate the influence of several factors representing the supply chain on the optimal decision and profits of the supplier and the wholesaler. Since the proportion of the demand for shorter delivery time has a large effect on the profits, the wholesaler needs to set the appropriate platform service fee and the profit margin, and maintain stable management by balancing the profit from wholesale business and from platform operations.