Sensitivity analysis of stochastic user equilibrium and its application to delivery services pricing

International audience; In e-commerce the delivery of products is a crucial part for the success of a e-shop. An efficient delivery system should offer various services and predict customersbehavior. The latter are influenced by the price of a delivery service, but also byits quality (congestion effect induced by customers’ choices) in a higly competitveenvironment. In this study, we introduce a bilevel model to optimize a deliverysystem. At the upper level, the provider control services’ tariffs. At the lower level,users react by choosing their delivery service according to a utility function whichincorporates the provider tariff and the congestion effect. We model the customers’reaction using Stochastic User Equilibrium (SUE). We also present a sensitivityanalysis for the SUE that gives explicit expression of the derivatives of customersdistribution with respect to services’ tariffs. Based on a local search that exploit thederivatives information, a new heuristic algorithm for the bilevel delivery servicespricing problem is developed and compared to others existing approachs.