Please, cite this article as: D. Hrabec, P. Popela, J. Novotn´ y, K. Haugen, A. Olstad, A note on the newsvendor problem with pricing. Proc. of 18th International Conference on Soft Computing MENDEL 2012, pp.410-415. ISBN 978-80-214-4540-6. A NOTE ON THE NEWSVENDOR PROBLEM WITH PRICING Duˇ san Hrabec 1 , Pavel Popela 1 , Jan Novotn´ y 1 , Kjetil Haugen 2 , and Asmund Olstad 2 1 Brno University of Technology Faculty of Mechanical Engineering Institute of Mathematics Technick´ a 2896/2, 616 69 Brno Czech Republic dusanhrabec@seznam.cz, popela@fme.vutbr.cz, ynovot35@stud.fme.vutbr.cz 2 Molde University College Britvegen 2, 6402 Molde Norway kjetil.haugen@himolde.no, asmund.olstad@himolde.no Abstract: The main purpose of the paper is to present a specific case of dynamic pricing for the newsvendor problem. Firstly, a short overview of the newsvendor problem is given together with references to selected literature and remarks to its applicability. Then, dynamic pricing principles are discussed together with references to a decision dependent randomness case in stochastic programming. The dynamic pricing problem deals with determination of selling prices over time for a product whose demand is random and whose supply is fixed. We approach this problem by formulating the newsvendor problem, which is introduced as a single period problem in our case. We focus on specific features of the demand function assuming a decision dependent uniform distribution. We assume that its support size linearly decreases with the increase of the price. Under such assumptions, the model has suitable computational features related to the expectation of the objective function. In addition, a possibility to increase the profit by change of the price may appear. The model formulation allows us to use the MAPLE software for symbolic computations and visualization of results. The test results for the selected data set are visualized at the end of the paper. Keywords: stochastic programming, newsvendor problem, dynamic pricing, MAPLE. 1 Introduction Newsvendor problem. By literature resources, the so called newsvendor (alternatively newsboy) problem has a long and interesting history that was initialized in 1888 by Edgeworth [3], who developed its idea dealing with a bank cash-flow problem. Porteus [22] can be utilized as a useful review for the basic static case and for its generalizations. The newsvendor problem is based on the idea to control the amount of the item, which should be ordered without knowing the future uncertain demand. We further specify it as a problem over a single- period with controlling of a single continuously divisible item. The objective of this stochastic single-period problem is to determine the ordered quantity for a fixed time period that will maximize the expected total profit.The demand is a random variable that is represented by a probability distribution. It is a simple example of a mathematical programming problem, however, it often serves well for introduction of general principles, see, e.g., [23] and [24]. Dynamic pricing. Recently, there is an increasing development of dynamic pricing strategies and their further applications in industry. There are three supporting factors: (1) the increase in availability of demand data, (2) the ease of changing prices due to new technologies, and (3) the availability of models for analyzing demand data and for dynamic pricing, see [4] for details. So, the dynamic pricing problem concerns on the determination of selling prices as a decision variable over time for a product under the demand and supply constraints. In optimization models, this idea leads to the generalization of traditional models when the price is not further considered constant as it becomes a new decision variable. The authors applied this approach to the lot-sizing problem, see [18], [5], and [6]. Further ideas and applications can be found in [4]. Recently, we have identified the link of dynamic pricing to so called decision dependent randomness in stochastic programming, see [17] for details and [7] for the original concept discussion. 18th International Conference on Soft Computing MENDEL 2012, Brno, Czech Republic, June 27-29, 2012.