TY  - JOUR
A1  - Schlosser, Rainer
T1  - Joint stochastic dynamic pricing and advertising with time-dependent demand
JF  - Geophysical journal international
N2  - This paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time-dependent demand elasticities. We prove structural properties of the optimal expected profits with respect to time, inventory level, price impact, advertising impact and different model parameters, such as discount rate, marginal unit costs, and holding costs. We find that the value of an additional item (opportunity costs) is decreasing in the unit costs, the discount rate, the holding cost rate and the number of items left to sell. We also derive structural properties of optimal joint pricing and advertising strategies. This way, we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions. Among other properties, we show that a higher advertising impact leads to higher optimal prices and lower advertising rates, which in turn implies a lower speed of sale. The results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly. Our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly. Our analysis implies general results for pure pricing as well as pure advertising models with time-dependent demand elasticities. (C) 2016 Elsevier B.V. All rights reserved.
KW  - Dynamic pricing and advertising
KW  - Optimal stochastic control
KW  - Time-dependent demand elasticities
KW  - Structural properties
Y1  - 2016
U6  - https://doi.org/10.1016/j.jedc.2016.10.006
SN  - 0165-1889
SN  - 1879-1743
VL  - 73
SP  - 439
EP  - 452
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Schlosser, Rainer
T1  - Dynamic pricing and advertising of perishable products with inventory holding costs
JF  - Journal of economic dynamics & control
N2  - We examine a special class of dynamic pricing and advertising models for the sale of perishable goods, including marginal unit costs and inventory holding costs. The time horizon is assumed to be finite and we allow several model parameters to be dependent on time. For the stochastic version of the model, we derive closed-form expressions of the value function as well as of the optimal pricing and advertising policy in feedback form. Moreover, we show that for small unit shares, the model converges to a deterministic version of the problem, whose explicit solution is characterized by an overage and an underage case. We quantify the close relationship between the open-loop solution of the deterministic model and the expected evolution of optimally controlled stochastic sales processes. For both models, we derive sensitivity results. We find that in the case of positive holding costs, on average, optimal prices increase in time and advertising rates decrease. Furthermore, we analytically verify the excellent quality of optimal feedback policies of deterministic models applied in stochastic models. (C) 2015 Elsevier B.V. All rights reserved.
KW  - Dynamic pricing and advertising
KW  - Optimal stochastic and deterministic
KW  - control
KW  - Inventory holding costs
KW  - Finite horizon
KW  - Feedback heuristics
Y1  - 2015
U6  - https://doi.org/10.1016/j.jedc.2015.05.017
SN  - 0165-1889
SN  - 1879-1743
VL  - 57
SP  - 163
EP  - 181
PB  - Elsevier
CY  - Amsterdam
ER  -