Incorporating declared capacity uncertainty in optimizing airport slot allocation

Slot allocation is the mechanism used to allocate capacity at congested airports. A number of models have been introduced in the literature aiming to produce airport schedules that optimize the allocation of slot requests to the available airport capacity. A critical parameter affecting the outcome of the slot allocation process is the airport’s declared capacity. Existing airport slot allocation models treat declared capacity as an exogenously defined deterministic parameter. In this presentation we propose a new robust optimization formulation based on the concept of stability radius. The proposed formulation considers endogenously the airport’s declared capacity and expresses it as a function of its throughput. We present results from the application of the proposed approach to a congested airport and we discuss the trade-off between the declared capacity of the airport and the efficiency of the slot allocation process

Equilibrage robuste de lignes de production : modèles de programmation linéaire en variables mixtes et règles de pré-traitement

This work deals with a robust optimisation of production lines at the design stage. The design of such lines can be interpreted as an optimisation problem that consists in finding a configuration optimising individual objectives and respecting technological and economic constraints. We conside rtwo types of production lines: assembly and transfer lines. The first one can be represented as a set of linearly ordered stations where the tasks are executed sequentially. The second one is composed of transfer machines, including several multispindle heads. All tasks within a single head are executed simultaneously, while tools on a machine work in a sequential mode. We describe different approaches for modelling the uncertainty of data in line balancing problems. Our objective is to identify the approaches that best fit the context of the design. In particular, the attention concentrates on the robust approach. We propose a new optimisation criterion based on the stability radius of a feasible solution. Then, robust formulations are presented for the design of the assembly and transfer lines under variations of task processing times. We also develop heuristic methods whose results are used to improve mathematical models. Finally, a new hybrid resolution method is elaborated to solve different variants of the stability radius maximisation.Ce travail porte sur l’optimisation robuste des lignes de production au stade de la conception. La conception de telles lignes peut être interprétée comme un problème d’optimisation consistant à rechercher une configuration optimisant des objectifs individuels et à respecter les contraintes technologiques et économiques. Nous considérons deux types de lignes de production : l’assemblage et le transfert. Le premier peut être représenté comme un ensemble de stations ordonnées linéairement où les tâches sont exécutées de manière séquentielle. Le second type de ligne est constitué de machines de transfert comprenant plusieurs têtes multibroches. Toutes les tâches d’une même tête sont exécutées simultanément, tandis que les outils d’une machine fonctionnent en mode séquentiel. Nous décrivons différentes approches permettant de modéliser l’incertitude des données dans les problèmes d’équilibrage de ligne. Notre objectif est d’identifier les approches les mieux adaptées au contexte de la conception. En particulier, l’attention se concentre sur l’approche robuste. Nous proposons un nouveau critère d’optimisation basé sur le rayon de stabilité d’une solution réalisable. Ensuite, des formulations robustes sont présentées pour la conception des lignes d’assemblage et de transfert lorsque le temps de traitement des tâches est sujet à des incertitudes. Nous développons également des méthodes heuristiques dont les résultats sont utilisés pour renforcer les modèles mathématiques. Enfin, une nouvelle méthode de résolution hybride est élaborée pour résoudre différentes variantes des problèmes de maximisation du rayon de stabilité

Robust balancing of production lines : MILP models and pre-processing rules

Ce travail porte sur l’optimisation robuste des lignes de production au stade de la conception. La conception de telles lignes peut être interprétée comme un problème d’optimisation consistant à rechercher une configuration optimisant des objectifs individuels et à respecter les contraintes technologiques et économiques. Nous considérons deux types de lignes de production : l’assemblage et le transfert. Le premier peut être représenté comme un ensemble de stations ordonnées linéairement où les tâches sont exécutées de manière séquentielle. Le second type de ligne est constitué de machines de transfert comprenant plusieurs têtes multibroches. Toutes les tâches d’une même tête sont exécutées simultanément, tandis que les outils d’une machine fonctionnent en mode séquentiel. Nous décrivons différentes approches permettant de modéliser l’incertitude des données dans les problèmes d’équilibrage de ligne. Notre objectif est d’identifier les approches les mieux adaptées au contexte de la conception. En particulier, l’attention se concentre sur l’approche robuste. Nous proposons un nouveau critère d’optimisation basé sur le rayon de stabilité d’une solution réalisable. Ensuite, des formulations robustes sont présentées pour la conception des lignes d’assemblage et de transfert lorsque le temps de traitement des tâches est sujet à des incertitudes. Nous développons également des méthodes heuristiques dont les résultats sont utilisés pour renforcer les modèles mathématiques. Enfin, une nouvelle méthode de résolution hybride est élaborée pour résoudre différentes variantes des problèmes de maximisation du rayon de stabilité.This work deals with a robust optimisation of production lines at the design stage. The design of such lines can be interpreted as an optimisation problem that consists in finding a configuration optimising individual objectives and respecting technological and economic constraints. We conside rtwo types of production lines: assembly and transfer lines. The first one can be represented as a set of linearly ordered stations where the tasks are executed sequentially. The second one is composed of transfer machines, including several multispindle heads. All tasks within a single head are executed simultaneously, while tools on a machine work in a sequential mode. We describe different approaches for modelling the uncertainty of data in line balancing problems. Our objective is to identify the approaches that best fit the context of the design. In particular, the attention concentrates on the robust approach. We propose a new optimisation criterion based on the stability radius of a feasible solution. Then, robust formulations are presented for the design of the assembly and transfer lines under variations of task processing times. We also develop heuristic methods whose results are used to improve mathematical models. Finally, a new hybrid resolution method is elaborated to solve different variants of the stability radius maximisation

Robust balancing of production lines:MILP models and pre-processing rules

This work deals with a robust optimisation of production lines at the design stage. The design of such lines can be interpreted as an optimisation problem that consists in finding a configuration optimising individual objectives and respecting technological and economic constraints. We conside rtwo types of production lines: assembly and transfer lines. The first one can be represented as a set of linearly ordered stations where the tasks are executed sequentially. The second one is composed of transfer machines, including several multispindle heads. All tasks within a single head are executed simultaneously, while tools on a machine work in a sequential mode. We describe different approaches for modelling the uncertainty of data in line balancing problems. Our objective is to identify the approaches that best fit the context of the design. In particular, the attention concentrates on the robust approach. We propose a new optimisation criterion based on the stability radius of a feasible solution. Then, robust formulations are presented for the design of the assembly and transfer lines under variations of task processing times. We also develop heuristic methods whose results are used to improve mathematical models. Finally, a new hybrid resolution method is elaborated to solve different variants of the stability radius maximisation

An evolutionary heuristic for solving the robust single airport slot allocation problem

We propose an evolutionary heuristic method for solving the robust single airport slot allocation problem. The proposed method aims to discover a new solution by applying one or several mutation procedures to the current best solution. The best solution is defined by a fitness value that covers constraints violation parameters and allocation properties. Constraints’ violation parameters control the feasibility of the solution. Such structural aspects allow us to move towards acceptable results after each evolutionary iteration. Allocation properties work in a similar manner but defining a solution quality via indicators measuring slot allocation objectives used in the literature, such as, total displacement, maximum displacement, number of rejections, and number of displaced requests. The method’s implementation has a flexible design providing the range of parameters that can be set to change the algorithm’s way of work. The benchmarking is done for different number of iterations, different weights of fitness function components, list of allowed mutations (for both equivalent and different mutation probabilities), and number of mutations per iteration. The efficiency of the method is analyzed from both computational complexity and direct performance comparison to the exact method. The results show that heuristic methods adjusted for the problem structure could be used as a general replacement for exact approaches which require an enormous amount of time to solve even some small size instances

AUTOMATION OF CALCULATIONS OF TECHNICAL CHARACTERISTICS OF MANOMETRIC TUBULAR SPRINGS

Tubular springs have received the name "Manometric" thanks to their initial use in manometric devices. For the wide use of tubular springs in various spheres of human activity, relevant methods of calculating their static and dynamic characteristics are needed. Many works have discussed the study of manometric tubular springs. The main method for calculating static characteristics of springs is the semi-membrane theory of shells, and to calculate the frequencies of natural oscillations, the spring was considered as a rod with a deformable cross-section. The article considers algorithms for calculation of static characteristics and frequencies of natural oscillations of manometric tubular springs with known geometric parameters of a spring and physical properties of a material. For calculations, in general, numerical methods were used, so for their implementation, it was required to develop programs for automatic design, in which the algorithms are implemented. The article describes the software systems for calculating the characteristics of springs: "Module" and "PCRMTP", which allow investigating the stress-strain state of the cross-section of tubular springs, determine their static characteristics with known geometric parameters, spring material, internal pressure and operating conditions. In addition, in the complex "PCRMTP" the possibility of calculating the frequencies of natural oscillations of tubular springs is realized. The automation of the design of tubular springs significantly reduces the labour input of selecting springs with the necessary characteristics and thereby eliminates the deterrent factor of introducing new designs

Maximization of production line robustness under task time uncertainties at the line design stage

International audienc

Invariant measures of genetic recombination process

We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory

Enhanced MILP approach for maximizing the robustness of paced transfer lines with uncertain parallel tasks and fixed number of machines

National audienc