PurposeThis paper aims to explore optimal pricing policies and characteristics of a two-level dual-channel supply chain under price- and delivery time-sensitive demand. Besides price of the product, the delivery lead time is also a crucial factor in customers’ purchase decisions. A longer delivery lead time would diminish customers’ acceptance and faithfulness on the online channel, while a shorter delivery lead time would lead to incorporation of a substantial amount of logistics costs. In formulation of mathematical model, the effects of delivery lead time on the manufacturer and the retailer’s pricing strategies and profits in cooperative and non-cooperative dual-channel supply chain are explained analytically.Design/methodology/approachThe analytical models are formed for both non-cooperative and cooperative scenarios under inconsistent and consistent pricing. The authors examine whether revenue sharing (RS) contract or delivery cost sharing contract can solely coordinate the dual-channel supply chain. If a single contract fails, then the combination of RS contract with delivery cost sharing to achieve channel coordination is discussed.FindingsIt is found that the RS or delivery cost sharing contract cannot coordinate the channel individually but revenue and delivery cost sharing contract jointly coordinate the channel. All analytical results are illustrated numerically, along with sensitivity analysis.Research limitations/implicationsThere are many correlated issues that need to be further investigated. First, one good extension to this research may include the consideration of the channel structure with competitive retailers. It will be interesting to analyze the performance of coordination mechanisms by considering the retailer as a Stackelberg leader in retailing.Originality/valueThe findings and subsequent methodological discussions aim to provide practical guidance to retailers who are allowing customers to choose how, when and where they interact and purchase by offering a combination of websites (fully functional and mobile-enabled), catalogs and stores with increasing convergence of channels.