Olivier Briant

The Optimal Diversity Management Problem

In some industries, a certain part can be needed in a very large number of different configurations. This is the case, e.g., for the electrical wirings in European car factories. A given configuration can be replaced by a more complete, therefore more expensive, one. The diversity management problem consists of choosing an optimal set of some given number k of configurations that will be produced, any nonproduced configuration being replaced by the cheapest produced one that is compatible with it. We model the problem as an integer linear program. Our aim is to solve those problems to optimality. The large-scale instances we are interested in lead to difficult LP relaxations, which seem to be intractable by the best direct methods currently available. Most of this paper deals with the use of Lagrangean relaxation to reduce the size of the problem in order to be able, subsequently, to solve it to optimality via classical integer optimization.

The aircraft ground routing problem: Analysis of industry punctuality indicators in a sustainable perspective

The ground routing problem consists in scheduling the movements of aircraft on the ground between runways and parking positions while respecting operational and safety requirements in the most efficient way. We present a Mixed Integer Programming (MIP) formulation for routing aircraft along a predetermined path. This formulation is generalized to allow several possible paths. Our model takes into account the classical performance indicators of the literature (the average taxi and completion times) but also the main punctuality indicators of the air traffic industry (the average delay and the on time performance). Then we investigate their relationship through experiments based on real data from Copenhagen Airport (CPH). We show that the industry punctuality indicators are in contradiction with the objective of reducing taxi times and therefore pollution emissions. We propose new indicators that are more sustainable, but also more relevant for stakeholders. We also show that alternate path cannot improve the performance indicators.

Exact and heuristic approaches to the airport stand allocation problem

The Stand Allocation Problem (SAP) consists in assigning aircraft activities (arrival, departure and intermediate parking) to aircraft stands (parking positions) with the objective of maximizing the number of passengers/aircraft at contact stands and minimizing the number of towing movements, while respecting a set of operational and commercial requirements. We first prove that the problem of assigning each operation to a compatible stand is NP-complete by a reduction from the circular arc graph coloring problem. As a corollary, this implies that the SAP is NP-hard. We then formulate the SAP as a Mixed Integer Program (MIP) and strengthen the formulation in several ways. Additionally, we introduce two heuristic algorithms based on a spatial and time decomposition leading to smaller MIPs. The methods are tested on realistic scenarios based on actual data from two major European airports. We compare the performance and the quality of the solutions with state-of-the-art algorithms. The results show that our MIP-based methods provide significant improvements to the solutions outlined in previously published approaches. Moreover, their low computation makes them very practical.

Large-scale standard pooling problems with constrained pools and fixed demands

We present a new variant of the standard pooling problem in which demands are fixed and there are specific constraints on the intermediate pool. We propose a new formulation composed of proportion-flow variables, and we design an exact branch and bound algorithm by combining existing algorithms. Difficult instances have been generated to demonstrate the efficiency of our method, and our results are compared with those of Couenne, a generic MINLP solver.

A cost estimation model to support automation decision in assembly systems design

Cost analysis is crucial in the design of assembly systems and the decision on their level of automation (LoA). This paper presents a cost estimation model of assembly system that is used to decide their LoA during the early phase of projects. Based on an extensive literature review, a complete cost model integrating multiple cost drivers is proposed. This model is then exploited to create the objective function of an integer linear programme model utilised to solve the LoA decision problem. The work provides a way to perform cost estimation of assembly systems alternatives and to decide the most appropriate LoA in assembly. The cost estimation model is built with a parametric approach allowing the definition of various optimisation objectives. The proposed integer programme, complement this approach by proposing the suitable constraints set, that describes the LoA decision problem.