Olivier Péton

The Dial-A-Ride Problem with Transfers

The Dial-A-Ride Problem with Transfers (DARPT) consists in defining a set of routes that satisfy transportation requests of users between a set of pickup points and a set of delivery points, in the presence of ride time constraints. Users may change vehicles during their trip. This change of vehicle, called a transfer, is made at specific locations called transfer points. Solving the DARPT involves modeling and algorithmic difficulties. In this paper we provide a solution method based on an Adaptive Large Neighborhood Search (ALNS) metaheuristic and explain how to check the feasibility of a request insertion. The method is evaluated on real-life and generated instances. Experiments show that savings due to transfers can be up to 8% on real-life instances.

Efficient feasibility testing for request insertion in the pickup and delivery problem with transfers

The Pickup and Delivery Problem with Transfers (PDPT) consists of defining a set of minimum cost routes in order to satisfy a set of transportation requests, allowing them to change vehicles at specific locations. In this problem, routes are strongly interdependent due to request transfers. Then it is critical to efficiently check if inserting a request into a partial solution is feasible or not. In this article, we present a method to perform this check in constant time.

Optimization of a city logistics transportation system with mixed passengers and goods

In this paper, we propose a mathematical model and an adaptive large neighborhood search to solve a two-tiered transportation problem. This problem arises in a prospective study that aims at designing an innovative distribution system for goods in congested city cores. In the first tier, goods are transported in city buses from a consolidation and distribution center to a set of bus stops. The main idea is to use the buses spare capacity to drive the goods to the city core. In the second tier, final customers are distributed by a fleet of near-zero emissions city freighters. This system requires transferring the goods from buses to city freighters at the bus stops. We model the corresponding optimization problem as a variant of the pickup and delivery problem with transfers and solve it with an adaptive large neighborhood search. To evaluate its results, lower bounds are calculated with a column generation approach. The algorithm is assessed on data sets derived from a field study in the medium-sized city of La Rochelle in France.

A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes

The main objective of this communication is to show how realistic-sized instances of the Pickup and Delivery Problem with Transfers (PDPT) can be solved to optimality with a branch-and-cut-and-price method, under realistic hypotheses. We introduce the Pickup and Delivery Problem with Shuttle routes (PDP-S) which is a special case of the PDPT relying on a structured network with two categories of routes. {\em Pickup routes} visit a set of pickup points independently of their delivery points and end at one delivery point. {\em Shuttle routes} are direct trips between two delivery points. We propose a path based formulation of the PDP-S and solve it with a branch-and-cut-and-price algorithm. We show that this approach is able to solve real-life instances with up to 87 transportation requests.

A multi-criteria large neighbourhood search for the transportation of disabled people

This paper addresses the problem of optimizing the transportation of disabled persons from home to specialized centres or schools. It is modelled as a Dial-a-ride problem (DARP), where several people share the same destination. Particular emphasis is placed on the objective function in order to consider several potentially conflicting interests. We propose a multi-criteria model from Multi-attribute Utility Theory based on the Choquet integral. The resulting multi-criteria DARP is then solved with a large neighbourhood search algorithm. This method includes classical destroy and repair heuristics as well as new operators exploiting the shared destination feature and criterion-specific operators. The algorithm is evaluated on a set of 14 real-world instances in the field of health care logistics, with up to 200 requests and 51 destination points.

Homogeneous analytic center cutting plane methods with approximate centers

In this paper we consider a homogeneous analytic center cutting plane method in a projective space. We describe a general scheme that uses a homogeneous oracle and computes an approximate analytic center at each iteration. This technique is applied to a convex feasibility problem, to variational inequalities, and to convex constrained minimization. We prove that these problems can be solved with the same order of complexity as in the case of exact analytic centers. For the feasibility and the minimization problems rough approximations suffice, but very high precision is required for the variational inequalities. We give an example of variational inequality where even the first analytic center needs to be computed with a precision matching the precision required for the solution.

A new consistent vehicle routing problem for the transportation of people with disabilities

In this article, we address a problem of the transportation of people with disabilities where customers are served on an almost daily basis and expect some consistency in the service. We introduce an original model for the time-consistency of the service, based on so-called time-classes. We then define a new multiday vehicle routing problem VRP that we call the Time-Consistent VRP. We address the solution of this new problem with a large neighborhood search heuristic. Each iteration of the heuristic requires solving a complex VRP with multiple time windows and no waiting time which we tackle with a heuristic branch-and-price method. Computational tests are conducted on benchmark sets and modified real-life instances. Results demonstrate the efficiency of the method and highlight the impact of time-consistency on travel costs.

A Large Neighborhood Search heuristic for Supply Chain Network Design

Many exact or approximate solution techniques have been used to solve facility location problems and more generally supply chain network design problems. Yet, the Large Neighborhood Search technique (LNS) has almost never been proposed for solving such problems, although it has proven its efficiency and flexibility in solving other complex combinatorial optimization problems. In this paper we propose an LNS framework for solving a four-layer single period multi-product supply chain network design problem involving multimodal transport. Location decisions for intermediate facilities (e.g. plants and distribution centers) are made using the LNS while transportation modes and product flow decisions are determined by a greedy heuristic. As a post-optimization step, we also use linear programming to determine the optimal product flows once the logistics network is fixed. Extensive experiments based on generated instances of different sizes and characteristics show the effectiveness of the method compared with a state-of-the-art solver.

Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

AbstractThis paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cut process in the standard ACCPM. The main issue is the calculation of a direction that restores feasibility after introducing p new cutting planes at the query point. We prove that the new analytic center can be recovered in O(p log ωp) damped Newton iterations, where ω is a parameter depending of the data. We also present two special cases where the complexity can be decreased to O (p log p). Finally, we show that the number of calls to the oracle is the same as in the single cut case, up to a factor