Vehicle Sharing System Pricing Regulation: Deterministic Approach, Complexity results

Ariel Waserhole (1) , Vincent Jost (2) , Nadia Brauner (1)

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This paper gives complexity results on the deterministic versions of the Vehicle Sharing System Pricing problem. Solving these deterministic problems could give some Upper Bound on the general problem or help designing robust optimization algorithm. However we show that most of them are NP-hard. 1. We define the First Come First Serve (FCFS) flow, and the priced FCFS flow based on a scenario approach. 2. We define two deterministic problems based on the priced FCFS flow: Max FCFS Flow Trip Pricing and Max FCFS Flow Station Pricing. We show that they are both NP-Hard. 3. We define the Max FCFS Flow Station Capacities problem based on the FCFS flow and show its NP-hardness. 4. We talk about the Max Flow approximation on FCFS flow problems.

Domaines: Recherche opérationnelle [math.OC]

Ariel Waserhole, Vincent Jost, Nadia Brauner. Vehicle Sharing System Pricing Regulation: Deterministic Approach, Complexity results. 2012. ⟨hal-00727040v1⟩