Dynamic pricing with reference price effects in integrated online and offline retailing

Omnichannel retailing is of growing importance. Yet, retailers lack knowledge about how to set prices overtime in their different channels, that is, in-store and online, which gives rise to a dual-channel pricing problem. The retailing issue is even more salient when consumers are prone to a psychological element, that is, when a reference price exerts influence. This article fills the gap by offering an analytical model of intertemporal price setting for dual channel pricing problem. We present an optimal control framework of dynamic pricing when (1) consumer behaviour is prone to a reference price and (2) the online channel is subject to the last-mile delivery cost. Analytical results, which hold for a general (nonlinear) reference-dependent demand formulation, inform about the relationships between the store and online prices over time and also about the market power of the retailer in each channel. Numerical results describe the features of three different phases of the planning horizon. The managerial recommendations show how a retailer sets differentiated dynamic pricing policies when offline and online channels are integrated. Such recommendations pave the way to more profitable omnichannel management.