Optimal spatial pricing strategies with transportation costs
Carlier, Guillaume; Buttazzo, Giuseppe (2010), Optimal spatial pricing strategies with transportation costs, in Leizarowitz, Arie; Mordukhovich, Boris; Shafrir, Itai; Zalavski, Alexander, Nonlinear Analysis and Optimization II: Optimization, American Mathematical Society : Providence (R.I.), p. 105-122
TypeCommunication / Conférence
Conference titleInternational Conference on Nonlinear Analysis and Optimization in celebration of Alex Ioffe's 70th and Simeon Reich's 60th birthdays
Book titleNonlinear Analysis and Optimization II: Optimization
Book authorLeizarowitz, Arie; Mordukhovich, Boris; Shafrir, Itai; Zalavski, Alexander
Number of pages290
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Abstract (EN)We consider an optimization problem in a given region Q where an agent has to decide the price p(x) of a product for every x ∈ Q. The customers know the pricing pattern p and may shop at any place y, paying the cost p(y) and additionally a transportation cost c(x, y) for a given trans- portation cost function c. We will study two models: the ﬁrst one where the agent operates everywhere on Q and a second one where the agent op- erates only in a subregion. For both models we discuss the mathematical framework and we obtain an existence result for a pricing strategy which maximizes the total proﬁt of the agent. We also present some particular cases where more detailed computations can be made, as the case of con- cave costs, the case of quadratic cost, and the onedimensional case. Finally we discuss possible extensions and developments, as for instance the case of Nash equilibria when more agents operate on the same market.
Subjects / KeywordsOptimization; Pricing; Transportation costs
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