Mathematical Programming with Stochastic Equilibrium Constraints applied to Optimal Last-mile Delivery Services

Bayrem Tounsi 1 Yezekael Hayel 2 Dominique Quadri 3 Luce Brotcorne 1
1 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In e-commerce business, the delivery of products is a crucial part for the success of an e-shop. An efficient delivery system should offer various services and predict customers behaviour. The latter are influenced by the price of a delivery service, but also by its quality (perceived through congestion effect induced by customers’ choices). In this study, we introduce a bi-level model to optimize a delivery system. At the upper level, the provider control services’ tariffs. At the lower level, users react by choosing their delivery service according to a disutility function which icorporates the provider tariff and the congestion effects. We model the customers’ reaction using stochastic user equilibrium (SUE). We also present a sensitivity analysis for the SUE that gives explicit expression of the derivatives of customers distribution with respect to services’ tariffs. Based on a local search that exploits the derivatives information, a new heuristic algorithm for a delivery services pricing problem is developed and compared to others existing methods.
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Bayrem Tounsi, Yezekael Hayel, Dominique Quadri, Luce Brotcorne. Mathematical Programming with Stochastic Equilibrium Constraints applied to Optimal Last-mile Delivery Services. 7th International Network Optimization Conference, May 2015, Varsovie, Poland. pp.8. ⟨hal-01204647⟩

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