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Static Dial-a-Ride Problem with Money as an Incentive : Study of the Cost Constraint

Abstract : In this paper, we study a taxi sharing problem. Given a set of clients with different transportation requests, the problem is to define a set of taxis that will be shared by the clients in order to reduce their bill by a given factor α < 1. To achieve this, each client shares the cost of the ride with other passengers. More precisely, the fragments of the ride in which the client is alone is fully paid by this client. On the contrary, for each fragment in which the client shares the taxi with other passengers, the cost is equally divided between the passengers. Firstly, we show that the problem consisting in searching for a unique taxi satisfying this cost constraint is NP-Complete, even if we do not impose this taxi to pick up every client. In addition, we show that, even if the factor α and the capacities of the taxis are fixed, the problem of satisfying all the requests is NP-Complete. Secondly, we propose a nonlinear MIP model. Nonlinearity is due to the computation of the shared price of the clients. We propose different linearizations. Then we establish some necessary conditions that are used to reduce the size of the problem. The end of the paper is dedicated to a numerical study of the model in order to evaluate its performances.
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Contributor : Alain Faye <>
Submitted on : Thursday, April 13, 2017 - 10:16:04 AM
Last modification on : Monday, August 24, 2020 - 4:16:07 PM


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  • HAL Id : hal-01507417, version 1


Alain Faye, Dimitri Watel. Static Dial-a-Ride Problem with Money as an Incentive : Study of the Cost Constraint. 2016. ⟨hal-01507417⟩



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