Dynamic Pricing and Advertising of Perishable Products with Inventory Holding Costs

33 Pages Posted: 20 Feb 2015 Last revised: 1 Jun 2015

See all articles by Rainer Schlosser

Rainer Schlosser

University of Potsdam - Hasso Plattner Institute (HPI)

Date Written: February 18, 2015

Abstract

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.

Keywords: dynamic pricing and advertising, optimal stochastic and deterministic control, inventory holding costs, finite horizon, feedback heuristics

Suggested Citation

Schlosser, Rainer, Dynamic Pricing and Advertising of Perishable Products with Inventory Holding Costs (February 18, 2015). Journal of Economic Dynamics and Control, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2566935 or http://dx.doi.org/10.2139/ssrn.2566935

Rainer Schlosser (Contact Author)

University of Potsdam - Hasso Plattner Institute (HPI) ( email )

Prof.-Dr.-Helmert-Str. 2-3,
Potsdam
Germany

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