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

Abstract

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.

Keywords:

• Demand management
• retail supply chain
• dual channel operations
• dynamic pricing
• reference price

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Appendix proposes the optimality conditions for the general case, which is studied numerically in Sections 6.2.4 and 6.2.5.

2 In the equations system (5a(5a) $\begin{array}{rl}\frac{\mathrm{\partial }H}{\mathrm{\partial }{p}_s}& =0⟹D_s+p_s\frac{\mathrm{\partial }{D}_s}{\mathrm{\partial }{p}_s}\\ & +\text{β}\lambda =0,\end{array}$(5a) )–(5f(5f) $\begin{array}{rl}\frac{\mathrm{d}\lambda }{\mathrm{d}t}=r\lambda -\frac{\mathrm{\partial }H}{\mathrm{\partial }r},\lambda \left(T\right)& =0⟹\frac{\mathrm{d}\lambda }{\mathrm{d}t}=(r+\text{β})\lambda \\ & -p_s\frac{\mathrm{\partial }{D}_s}{\mathrm{\partial }r}-(p_o-c_o)\frac{\mathrm{\partial }{D}_o}{\mathrm{\partial }r},\\ & \times \lambda \left(T\right)=0.\end{array}$(5f) ), we are especially interested in understanding the role of the reference price and of the last-mile delivery cost in the retailer policies. This model can be generalised to integrate a distribution cost incurring on both channels and direct price interaction in both channels. In Appendix, we write the Hamiltonian function and provide the optimality conditions for this generalised model. Unfortunately, the complexity explodes and we are not able to derive formal guarantees for analytical results. Yet, in Sections 6.2.4 and 6.2.5, we provide numerical simulations of this generalised model to assess the robustness of our results.

Additional information

Notes on contributors

Régis Chenavaz

Régis Chenavaz is an Associate Professor of Managerial Economics and Operations Management at KEDGE Business School. His research focuses on managerial economics, operations management, and business analytics. Régis' primary research interest is pricing, considering dynamic contexts and psychological elements (dynamic pricing and behavioural pricing). Recently, he is interested in sustainable operations. Régis published in international journals like the European Journal of Operational Research, International Journal of Production Economics, and Dynamic Games and Applications.

Walid Klibi

Walid Klibi is a Professor of Supply Chain and Operations Management at Kedge Business School (France), Member of the Center of Excellence in Supply Chain (CESIT) of Kedge Business School. His research work focuses on Supply Chain Design, Supply Chain resilience, omnichannel retailing, and urban logistics, carried out in partnership with several international companies. He is also co-author of a book entitled ‘The Design of Value-Creating Supply Chain Networks’, and several articles in international academic and professional journals. He is an affiliated faculty of the Supply Chain & Logistics Institute, Georgia Tech (USA) and collaborating member of the Interuniversity Research Center on Business Networks, Logistics and Transport (CIRRELT) in Canada.

Rainer Schlosser

Rainer Schlosser received a Ph.D. degree in Operations Research from the Humboldt University of Berlin in 2014. Currently, he works as a senior researcher at the Hasso Plattner Institute for Digital Engineering in the Department of Enterprise Platform and Integration Concepts, University of Potsdam, Germany. He is the leader of the research group Data-driven Decision Support. His primary research interests include revenue management, optimal control, and dynamic systems.